TheRPGSite

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Here I’m constructing a list and analysis of existing RPG’s innovations, unusual twists, and mechanical “bells and whistles”, some of them fairly obscure, partly to clarify my own thoughts but perhaps of interest to other would-be designers.
A given idea may actually be reused across a number of RPGs, so readers may find weird systems mentioned with regard to what's still actually a familiar idea. As this is intended to be understood by the most readers for design purposes rather than being a historical reference, I usually list the most common game using an idea (if I'm familiar with it) rather than the first. Where warranted fairly obscure games are discussed.
Anyone who wishes to discuss anything feel free to do so (honestly I expect little input, since tumbleweeds hate game design). I’m inputting data topic-by-topic for clarity. If you haven't visited for awhile, there's a good chance I've edited in additional notes since then.

Looking back on it, I do need to apologize for this thread not being the best organized; roughly speaking the first few pages deal with character generation, then core mechanics, then combat, then miscellaneous things, then powers/magic. If looking for notes on a specific topic or system I recommend using 'Search this thread' (near top of page, if logged in). Thanks to everyone who participated, anyone who does read this in future, by all means if you see an omission feel free to reply to the thread or PM me.

8 June 2014 - Added summary of contents here for ease of use (Only 3 years late...PS when designing your RPG don't forget you need an index...;) )

Summary of Contents with hyperlinks

Page 1 - Character Generation
Attributes - generation (http://www.therpgsite.com/showthread.php?p=496044#post496044)
Attribute Effects (http://www.therpgsite.com/showthread.php?p=496045#post496045)
Over the Limit  (http://www.therpgsite.com/showthread.php?p=501020#post501020)(attribute score range)(Page 7)
Races (http://www.therpgsite.com/showthread.php?p=496047#post496047)
Classes & Skills (http://www.therpgsite.com/showthread.php?p=496050#post496050)
More On Skills (http://www.therpgsite.com/showthread.php?p=496052#post496052) (#, ability modifiers, specializations)
Advantages/Disadvantages (http://www.therpgsite.com/showthread.php?p=496048#post496048) (see pg. 12 for more on point costs (http://www.therpgsite.com/showthread.php?p=515934#post515934))
Improvement (http://www.therpgsite.com/showthread.php?p=496053#post496053)
Character Design Interactions with Core Mechanics (http://www.therpgsite.com/showthread.php?p=496054#post496054)

Page 2 - Dice Mechanics
D100s (http://www.therpgsite.com/showthread.php?p=496055#post496055)
Additive Rolling (http://www.therpgsite.com/showthread.php?p=496057#post496057)
Multidie additive (http://www.therpgsite.com/showthread.php?p=496058#post496058)
Roll Under (http://www.therpgsite.com/showthread.php?p=496059#post496059)
Changing-Dice-Type (http://www.therpgsite.com/showthread.php?p=496060#post496060) (formerly 'step dice')
Universal Table (http://www.therpgsite.com/showthread.php?p=496061#post496061)
Dice Pools (http://www.therpgsite.com/showthread.php?p=496152#post496152)


Page 3 - more on Dice Mechanics
Dice Pools (take-highest) (http://www.therpgsite.com/showthread.php?p=496174#post496174)
Exotic dice mechanics (http://www.therpgsite.com/showthread.php?p=496195#post496195)
Non-dice randomization (http://www.therpgsite.com/showthread.php?p=496205#post496205)
Multiple resolution systems and the trend toward universalization (http://www.therpgsite.com/showthread.php?p=496230#post496230)
Effect (http://www.therpgsite.com/showthread.php?p=496263#post496263)
Cutting Down Excess Rolling (http://www.therpgsite.com/showthread.php?p=496338#post496338)
Extended Actions (http://www.therpgsite.com/showthread.php?p=496501#post496501)
(see page 12 for opposed rolls, open-ended and impossible rolls, bonus & penalty accumulation)
Safety Valves (i.e. luck points) (http://www.therpgsite.com/showthread.php?p=496547#post496547)

Page 4 - Combat
initiative /round structure (http://www.therpgsite.com/showthread.php?p=496912#post496912)
Actions per round (http://www.therpgsite.com/showthread.php?p=496919#post496919)
Hit Points (http://www.therpgsite.com/showthread.php?p=496987#post496987)
Damage (http://www.therpgsite.com/showthread.php?p=497236#post497236)
Critical Hits (http://www.therpgsite.com/showthread.php?p=567848#post567848) (page 14)
Armour (http://www.therpgsite.com/showthread.php?p=497457#post497457)
Movement (http://www.therpgsite.com/showthread.php?p=497479#post497479)
Movement & tactical combat (http://www.therpgsite.com/showthread.php?p=858973#post858973) further discussion (Skarg) (Page 23/ linked thread)

Page 5 - more Combat
Core mechanics & combat manuevers (http://www.therpgsite.com/showthread.php?p=497808#post497808)
Combat Moves (http://www.therpgsite.com/showthread.php?p=497810#post497810) (multiple posts)
      -Part I (http://www.therpgsite.com/showthread.php?p=497810#post497810) Basic Attacks, Attack + Movement Actions, Multiple Actions
      -Part II (http://www.therpgsite.com/showthread.php?p=497811#post497811) - Movement, Defense, Cooperative Actions
      -Part III (http://www.therpgsite.com/showthread.php?p=497813#post497813) - Initiative Actions, Damage Modifying Moves, Special Attacks, Recovery Actions, Miscellaneous
Terrain & Environment (http://www.therpgsite.com/showthread.php?p=498457&highlight=rolling#post498457)


Page 6 - general adventuring
Vehicles
Adventuring Situations (http://www.therpgsite.com/showthread.php?p=499134#post499134) e.g. saves, encumberance, luck rolls, starvation/thirst
Perception (http://www.therpgsite.com/showthread.php?p=499647#post499647)
Craft & Repair (http://www.therpgsite.com/showthread.php?p=499692#post499692)    


Page 7 - general campaign & Misc.
Social Checks (http://www.therpgsite.com/showthread.php?p=500236#post500236)  
Equipment & Currency
Morality  (http://www.therpgsite.com/showthread.php?p=501506#post501506)        
Weapon Proficiencies & Strength Requirements (http://www.therpgsite.com/showthread.php?p=502060#post502060) (and weapons design)
Super Powers  (http://www.therpgsite.com/showthread.php?p=502173#post502173)  

Page 8 - Powers, Magic        
Powers List (http://www.therpgsite.com/showthread.php?p=502739#post502739)
Power Advantages & Limitations (http://www.therpgsite.com/showthread.php?p=503267#post503267)
Psionics (http://www.therpgsite.com/showthread.php?p=503270#post503270)
Chi
Magic - underlying concepts (http://www.therpgsite.com/showthread.php?p=506030#post506030)
Magic - who can use it (http://www.therpgsite.com/showthread.php?p=506031#post506031)

Page 9 - More Magic
Magic- spell failure (http://www.therpgsite.com/showthread.php?p=506430#post506430)
Spells per day
Magical skills,
Varieties of Magic (http://www.therpgsite.com/showthread.php?p=507383#post507383)

Page 10 - Still More Magic, Misc.
Miscellaneous Magic (http://www.therpgsite.com/showthread.php?p=507599#post507599) notes
Monsters (http://www.therpgsite.com/showthread.php?p=508959#post508959)
NPCs (http://www.therpgsite.com/showthread.php?p=510085#post510085)

Page 12 - back to resolution systems mostly
More HP/damage/injury systems (http://www.therpgsite.com/showthread.php?p=512932#post512932) (RobMuadib)
Open-ended & impossible rolls (http://www.therpgsite.com/showthread.php?p=513155#post513155)
Contested Actions (http://www.therpgsite.com/showthread.php?p=513728#post513728)
Constrained Design Spaces (http://www.therpgsite.com/showthread.php?p=513841#post513841)
Controlling Bonus & Penalty Accumulation (http://www.therpgsite.com/showthread.php?p=515042#post515042)
Point systems & costs (http://www.therpgsite.com/showthread.php?p=515934&highlight=variable#post515934)

Page 13
Unknowns in design (http://www.therpgsite.com/showthread.php?p=522902&highlight=rolling#post522902)              
Sample Online Probability Calculators (http://www.therpgsite.com/showthread.php?p=522909#post522909)

Page 14
Conceptual Scope (http://www.therpgsite.com/showthread.php?p=523732#post523732)

Page 15
Complexity (http://www.therpgsite.com/showthread.php?p=617130#post617130) (moved from pg. 17)
Thought Processes In Designing / Hybridization How-To / Conversion between systems (http://www.therpgsite.com/showthread.php?p=627226#post627226)

Page 16
Divine Ascension (http://www.therpgsite.com/showthread.php?p=645535#post645535)

Page 17
Alternate Realities and the DRF (http://www.therpgsite.com/showthread.php?p=729072#post729072) (J Arcane)

Page 18
Types of derived attribute  (http://www.therpgsite.com/showthread.php?p=729408#post729408)(?)

Page 19
Resource Management (http://www.therpgsite.com/showthread.php?p=729936&highligh#post729936)
Exploding dice probabilities (http://www.therpgsite.com/showthread.php?p=730883#post730883) (ggroy)

Page 20
Abstraction level (http://www.therpgsite.com/showthread.php?p=753326#post753326)
Edges & centres (http://www.therpgsite.com/showthread.php?p=753404#post753404) (link) (Clash)

Where a note refers to hypothetical speculative mechanisms or my own designing, rather than an existing game, the note is being rendered in italics.
An (*) under edit notes refers to a note not incorporated into the thread's document version.

Attributes:
 
An attribute (aka ability score, stat) represents a character's inherent ability at a range of related tasks. Attributes are normally possessed by all characters - at least all player characters - and often all monsters as well. A few games may have "customizable" attributes (i.e. FUDGE had sets flexible from campaign to campaign; Fuzion also suggests adding extra attributes for some campaigns if desired and then giving out more stat points to buy them). More rarely an attribute set may vary from character to character - e.g. where a roll has a default and various attributes are potentially definable for characters (Over The Edge, Cortex +) (thanks to RobMaudib for noting these). A system may let a character use a default rating if they have no applicable rating; this works particularly well with attributes rated positive/negative around an average of 0.
Certain attributes may also be used for some inanimate objects e.g. a bridge might have a passive STR for how much weight it can support, or a door for how hard it is to break down; most objects have some form of durability and vehicles will have some sort of Speed rating. Mechanical sources of damage (spear traps and the like) may need 'Str' scores for modifying damage, or this may be assumed to be built in to base damage.
See the posts on 'NPCs' and 'Monsters' for discussion of games where those lack scores.
 
Number of attributes used in a system varies dramatically i.e..
0- Wilderness of Mirrors, FATE, The Agency (see last section of post), ZeFRS (see 'untrained skill use' for notes).
'Searchers of the Unknown' for AD&D ditches all attributes to just use a monster stat block (AC, MV, HD, hp, #attacks, damage), though it does roll hit points...effectively a single stat of 1-8 [all HD reroll on level-up), Mutant Bikers (see last section).
1- TWERPS (Strength, apparently used for everything - stat checks, combat, HP).
'Over the Edge' lets players choose freeform traits, but arguably also has one 'attribute' (despite different characters skinning it differently) inasmuch as one trait must incorporate fighting ability, and is used to set hit points.
2 - Prince Valiant; 3:16 (in both cases the two are essentially 'Fighting Ability' and 'Non-Fighting Ability'). Supergame 3E has 'Fitness' and 'Insight' (physical and mental).
3 - TriStat (Mind, Body, Soul), The Fantasy Trip (GURPS predecessor)(STR, DEX, INT)(just two, STR and DEX in original MELEE book); Fighting Fantasy (Skill, Stamina, Luck); Lejendary Adventures (Health [including body and mind], Precision, Speed)
4- GURPS (Strength, Intelligence, Health, Dexterity); Amber (Strength, Warfare, Endurance, Psyche)
5- Savage Worlds (Strength, Vigour, Agility, Smarts, Spirit)
6- D&D (Str, Dex, Con, Int, Wis, Cha)
Games with 6 attributes will sometimes determine randomly a stat affected (e.g. by a curse) with 1d6.
7- TORG (Str, Dex, Toughness, Mind, Spirit, Charisma, Perception)
8- Palladium (Strength, Prowess, Phy. Endurance, Intelligence, Mental Endurance, Men. Affinity, Beauty, Spd)
9- Storyteller (Str, Dex, Sta, Int, Wits, Per, Cha, Manipulation, App. ), DC Heroes (Str, Dex, Body, Int, Mind, Will, Influence, Aura, Spirit)
10- Fuzion (Int, Will, Presence, Technique, Reflexes, Dexterity, Con, Str, Body, Movement); Rolemaster
11- Harnmaster (Str, Sta, Dex, Agility, Eyesight, Hearing, Smell, Voice, Int, Aura, Will  (13 if you want to count Frame and Morality).
14 - Space Opera (Physique, Str, Con, Agi, Dex, Int, Intuition, Leadership, Bravery, Empathy, Psionics, Technical Aptitude, Mech. Aptitude, Electronic Aptitude
 
Balance between attributes can be a delicate affair where number of stats are low, though these aren't (IMHO) inherently broken. While having 4 stats that are all used for 1/4 of skills/game functions should work...there are are however examples of systems with low numbers of stats that are quite min/maxable - GURPS for example being originally designed for fantasy, STR is important there for hand-to-hand damage etc, but becomes much less valuable in settings as soon as firearms (or blasters) make an appearance, while DEX remains invaluable. GURPS 4E reduces cost of STR and Health compared to Int/Dex, and uses STR to determine hit points (though perhaps this makes Health the new dump stat..)..Tri-stat reputedly is fairly easily broken as well. Random roll systems are less susceptible to breakage, though more stats makes a series of lucky rolls less likely. Many games end up having a "god stat" which dominates, while class-based games (D&D) often have class functions based off a 'prime requisite' that make it critical to members of that class. Passively operating stats (Constitution) are sometimes disliked as being dull.
 
Higher numbers of attributes mean each individual stat is less likely to give overwhelming advantage. However, more stats does usually mean more points, so that it becomes easy to max out one or two attributes with relatively little opportunity cost (by spreading out the effects of dumping across several stats).
 
Games with low numbers of stats tend to have stats which are 'fuzzy' in terms of interpretation, while more stats means each becomes more specific in what it measures. D&Ds 6 attributes for instance are all quite vague (Dexterity combines hand/eye coordination and agility, Strength includes size and muscle, Wisdom includes willpower and judgment, Charisma can include looks and personality), which has the advantage that a player can choose to interpret a number in a variety of ways to support different character concepts, while Size or Luck or Willpower are harder to interpret creatively, but are clear and measurable.
A lot of very specific attributes can lead to checks having to be modified by more than one attribute (e.g. HarnMaster).
 
 
A fairly comprehensive listing of attribute sets for a number of RPGs is available at:
https://web.archive.org/web/20130730183539/http://www.fudgery.net/omnium-gatherum/lag.html (https://web.archive.org/web/20130730183539/http://www.fudgery.net/omnium-gatherum/lag.html)
 
Some of my favourite obscure attributes are Size (most commonly seen in the Runequest/BRP family of systems, very useful for modelling a number of things like lifting objects and hit points), Speed (frequently handled messily) and Power (as seen in RQ, SenZar and Stormbringer, this stat is handy if games are going to have a lot of soul damage/soul eating going on, given a working system for attribute damage). In games not treating Size as an attribute, it often modifies attributes such as Str; in other systems height/weight may be figured backwards from the Strength score, or Str may be explained to be a relative value (to other creatures of the same size) with Size and Strength separately modifying physical tasks. SpaceMaster has a Psionics attribute which is a potentially interesting idea. Tunnels and Trolls has a 'Luck' attribute; one interesting idea from MSPE based on that is designing background to factor in how (un)lucky a character is, giving low Luck characters more bad events (another idea I'd toyed with was for a games with random background and rerolls based on Luck, having a character be able to spend those in random background generation). Another common-ish idea is splitting up "Dexterity" into an actual Dexterity (hand/eye coordination) and Agility (as these may be very different).
 
Other innovations, good or bad include:
-subabilities: some systems divide each stat into multiple substats which are related. 2E D&D in the “skills and powers” era divided each stat into 2 subabilities (an idea originally from Star Frontiers); one could be raised by lowering the other, or one would start equal to the other, with a random variation of +/-d4. This tended to be broken since often one subability mainly affected one classes' abilities (such as spellcasting) and could be dumped by other classes to raise the other which was often generally useful, and since the AD&D stat tables were built around non-linear progression - S&P fighters with Str 17 could have 'Muscle' 19, going from +1 on damage to +7.
Nexus the infinite city had three attributes (cost 10 pts/level) with 4 subattributes each (3-5 pts/level); it also lets characters 'pair' subattributes (e.g. Bravado = Charisma & Will, Physique = Strength & Toughness, Quickness is Speed & Move) which gives a cost discount for raising both at once (5 for both).  Feng Shui kept this setup for stats although the stats are set by archetype and might as well be 12 entirely separate stats. GURPS also has this via advantages (e.g. “split” STR for taking damage vs. everything else). TriStat dX has a "Less Capable" defect for creating e.g. characters that are undextrous despite high BODY; this is fairly handy since it has only three stats.
Subabilities can also exist in a sort of ad hoc fashion e.g. AD&D also had separate Con values for resurrection (original score only) and everything else, or Rifts Atlantis has a giant squid with outrageous lifting capacity (like 60,000 tons) but relatively low tentacle damage.
SenZar has a number of special powers many of which have 'mods' (+1 to +5) adding directly to a stat for some specific purpose, such as 'Eagle Eyed' and Perception, or Seduction to Presence; it has the issue that mods often cost the same as full attribute points, for a stat of 11 or less.
Skills can also provide a similar function in some games.
Subabilities main purpose is to allow characters or monsters that are good at [subability] even though their general attribute is low. If the subabilities line up mostly with skills this can be accomplished with less complexity by having attribute give a higher base skill (e.g. D6 Star Wars: a low score can still be bought up to a high value) or a skill purchase discount (Savage Worlds) rather than a separate modifier (a la d20 system), although the former two options do make cross-matching attributes and skills much more awkward. See also post #8 ("attributes and skills"). Whether a 'use skill rating in place of attribute' works to replace a subability however would depend somewhat on how the various system numbers are scaled. Arguably it may generally be better to just have more attributes to start with rather than fiddling around with 'subabilities'.
 
- groupings of attributes: a number of systems including DC Heroes, Fuzion and the the Storyteller system, have broad categories within the attributes (such as “social attributes” or “active attributes"). This may help in determining which attribute should apply to a given task, but also IMHO tends to give large sets of attributes and/or strange edge cases or extra attributes (like DC Heroes using INT/WILL for Perception checks; Storyteller having Willpower as a rating distinct from the normal attributes). Storyteller uses its grouping largely to generate attributes (split 7/5/3 between the categories initially) while DC Heroes uses the groupings to determine which attributes apply to tasks on its action table, with all the categories needed to generate consistently-scaled resistance and effect values. Amazing Engine paired stats in character generation; multiple characters generated from the same "player core" had the same base number of dice to distribute but could change which stat of the pair they prioritized, the idea being that players would play similar-but-not-identical characters when/if the game moved to another AE setting. Task-resolution where a roll is directly against [attack score - resistance score] can also generate a need for some extra stats to exist so they can follow a different range e.g. Dallas RPG (see contested actions (http://www.therpgsite.com/showthread.php?p=513728#post513728)).
-attributes could also be split into 'primary' (important) and 'secondary' (less important) groups e.g. in Leading Edge Games' Aliens game there are several 'secondary' attributes which are always rolled (3d6), though primaries can be point-buy (or are 3d6 twice take highest); other systems use this less overtly e.g. DragonQuest has point buy for primary stats but rolls Appearance (same scale but no point exchange is allowed due to App's lower value), as does 1E D&D with Unearthed Arcana comeliness. MERP has an Appearance (d100+Presence primary stat bonus), which can be switched with a primary stat with GM approval, but usually only if APP is raised & primary is lowered.
 
Slightly related to 'grouping' of attributes, an rpgnet thread awhile back discussed the ordering of the ability scores in D&D. OD&D wrote scores in order Strength, Intelligence, Wisdom, Constitution, Dexterity, Charisma (the 3 prime requisites for main classes + secondary attributes); 1E added thief and so went Strength, Intelligence, Wisdom, Dexterity, Constitution, Charisma (4 primes + secondary), 3rd ed went Str/Dex/Con/Int/Wis/Cha (physicals then mentals), 4th edition had order Str/Con/Dex/Int/Wis/Cha (similar, but also ordered in pairs for determining defenses i.e. Str and Con both determine Fortitude defense).

-attribute customization - an attribute's definition and hence what its modifiers affect may vary. In simpler RPGs a high/low stat may generate fiction which adjusts if a modifier will be used, circumstantially (i.e. in 0D&D if a character with a low CHA is ugly they might ignore some of the penalty by wearing a bag over their head, which wouldn't have helped if their lack of Charisma was actually due to an annoying personality; David "Zeb" Cook in the 2E AD&D PHB suggests a Dex 3 character might be 'naturally clumsy or as blind as a bat', but here is (he remarks elsewhere) reminiscing about an 0D&D character he knew - the idea doesn't quite work in 2E without much DM handwaving, mostly ad hoc penalties - the Dex adjusts range penalties and surprise, but 'perception' checks in 2E more often default to Wis and/or Int. Systems with more complex rules may allow for formal adjustment to what a stat modifies i.e. in 3E D&D a character with low DEX might still be a crack shot due to Zen Archery, letting them apply their Wisdom modifier to ranged attacks instead. The oWoD Storyteller system allowed characters with very high stats (4+ on a 1-5 scale) to choose 'specialties' which let them reroll 10s on specific related tasks i.e. a character with Appearance 4 might have 'busty' or 'exotic', while a character with Intelligence 4 might have 'visual memory' or 'analytical'. Hero System lets a character apply some power modifiers to stats e.g. to increase knockback for Str.
Another interesting example is in Dungeon Crawl Classics, where every character has a LUCK score but where what rolls this modifies is largely determined by a 'birth augur' table - a character who 'survived plague' adds their Luck modifier to magical healing, while a character who 'survived a spider bite' adds it to saves vs. poison (the stat also has some universal uses e.g. vs. critical hits and for spending in play). The augur roll description is slightly at odds with low score effects (e.g. a character with a low Luck who is 'born on a battlefield' would have a damage penalty, rather than bonus). Its perhaps odd realistically, if balanced, that a character can't have 0 or 2+ augurs (if you're born on the battlefield you can't also survive plague). Probably a roll should only be required if the character has positive Luck.
-attribute effects may be 'customized' by race, like AD&D dwarves having a poison/magic save bonus of +1 per 3 1/2 Con other characters don't get.
-another idea here (http://forum.rpg.net/showthread.php?545826-Customizing-Stats-with-Class) customizes attributes by 'class'; every character might have a Body attribute with the Str-fighter adding this to more physical rolls and the swashbuckler to dodging.
-(another form of 'customization' that might be useful would be to have a generic 'power' attribute that reskins to different classes in different ways - magical power for a mage, psionic power for a psion, etc. - with effects like determining power points or modifying class-related skills. Having this separate would let this be balanced better than the usual setup where different classes get their bonuses from a normal attribute instead, blowing out its importance and e.g. making all wizard characters have 18 Int). Depending on how you look at it, you could think of the core archetype power ratings for the oWoD storyteller games [Generation, Arete, Rank] as being sort of like this across their various games, although they're not considered 'attributes' exactly by their home systems)

You might expect games that are attribute-based and using class to use more either extra attributes for certain classes or attribute customization to differentiate classes, but I can't think of many examples here, perhaps because its an unusual pattern. An early 'Sorcerors Apprentice' magazine added a 'Piety' spellcasting stat for use with an optional Priest class for Tunnels and Trolls, while WHFR has non-zero magic ratings for wizards only. Class features or skills that require a raw attribute check to function might be said to give some 'redefinition' to an attribute.
Primarily attribute-based games with classes can encourage certain classes to get bonuses to their key stats. Warhammer 1E/2E, while not exactly a class system, has 'advancement schemes' that give warrior types more 'weapon skill' attribute increases in their profiles.

-extra attributes for certain characters. For instance, original Fighting Fantasy had the option of playing magic-users in an expansion book; these rolled up a 'Magic' score giving spells per day in addition to the normal Skill, Stamina and Luck (which suffered penalties). 1E Shadowrun had 'Magic' scores for magic-users, although this was nearly always (barring rare effects) the same as Essence which everyone had (default 6 rather than rolling). The Golden version of d20 (see notes under advantages) had feats allowing characters to roll up extra stats.

Games can also have powers or skills that operate on the same scale as attributes, letting these function as extra 'attributes' if needed despite not being defined as such (Marvel Super Heroes, DC Heroes, Savage Worlds).
(From a purely technical standpoint you could say that an 'attribute' is really something all characters have, and in that sense maybe a supernumery attribute isn't really an attribute. However, within the context of their game systems these function just like the ubiquitous stats, so I find the term reasonably useful still).

Thanks RobMaudib for some additional discussion

Unusual Attribute Arrays
Systems often have a few oddities in their attribute structure, as a consequence of their evolution or of attribute 'grouping'.
-Icons has similarly named but very different stats  "Determination" and "Willpower" - Determination giving points for roll bonuses while Willpower is for resisting mental attacks. It inherits one from parent system MSH; the other developed for dealing with FATE aspects.
-Storyteller has a Willpower (for point spending) separate from its 9 basic attributes that are forcibly fitted into a 3x3 conceptual grid leaving no 'room' for it. (it is initially calculated as a derived attribute in some forms e.g. nWoD Resolve + Composure, but can subsequently increase; in other versions e.g. original Mage it has a set base, varying largely due to 'freebie point' spend).
-D&D uses Wisdom for perception checks in 3E, something not consistently handled by any stat previously. Keeping the traditional 6 scores shoehorns this in along with its use for determining willpower and judgment.
-Cadillacs and Dinosaurs (T2000) Agility does not include manual dexterity; Archery and Firearms are STR-based skills.
-Maelstrom uses raw attribute checks for tasks, and has 'attack skill' and 'defense skill' as two of its nine attributes (there are also separate Speed, Agility + Knowledge, Will, Persuasion, Endurance, Perception. Point budgets mean that a higher Attack character will, in general, have slightly lower Speed/Agility. Actually, HERO is somewhat the same in that offensive and defensive combat values (OCV and DCV) are separate, although those are IIRC not defined as 'attributes' exactly. Interlock and Fuzion have separate combat and non-combat dexterity (Technical or Technique vs. Reflexes); Marvel FASERIP has separate 'fighting' and 'agility'. In most cases this is to prevent Dex being overpowered (a 'god stat').

Minimizing Numbers of Attributes
This can be handled by bundling several functions together into one stat, handling divergence between characters as a Skill (e.g. FATE Physique) or Advantage (GURPS "Strong Will"). Some injury systems (specific injuries/wound boxes) reduce need for a 'CON' or similar type stat. Stats can also be replaced with fixed numbers e.g. Movement Rate or Size based on species, or a fixed # of 'bennies' instead of having a variable Luck stat.
You could imagine a system which made high attributes a skill special ability, for instance a damage bonus from a high 'Fighting' type skill might be described as due to beefiness (and add to might-related physical rolls too) or as due to finesse and instead help on more Dex-like checks.
Another interesting approach doing away with attributes is for free rpg 'The Agency' (supernatural 60s spy game). Characters here just have skills; most skills default to a level of 'normal' (2 dice), but a character gets 1-2 skills that are 'poor' (=1 dice), representing a weak area e.g. athletics for an intellectual character, survival for an aristocrat, or science for the man-of-action type.
Mutant Bikers of the Atomic Wastelands (FUDGE) likewise has no stats. Some skills (Take It Like A Man, Interact with Others, Notice Things Happening, Move Real Fast, Figure Things Out) describe the same areas as attributes, but with no indirect modifications e.g. Figure Things Out won't improve 'Fix Broken Stuff' as well. Some Gifts may also be attribute-like.

Preference for stat-minimization climaxes in the Death To Ability Scores! movement (DTAS). A argument by some gamers (particularly 4E D&D players) is that ability scores (attributes) are a bad idea for various reasons. For instance (from here (http://forum.rpg.net/showthread.php?691496-Next-New-Playtest-Packet-Up/page15)):

QuoteDo you really like using ability scores? Or are you just used to them? Because it seems as though you only want ability scores to be worth a +1 or +2 bonus at most and reduce them to vestigial bits. Put bluntly, it's not worth keeping the mechanical and meta-fictional baggage of ability scores if they're going to provide only a token bonus.
It's not worth the system mastery trap of needing to pick the sneaky class, the sneaky score, and the sneaky skill to have a sneaky guy worth a damn. It's not worth the twin bugbears of being mechanically punished for having a socially skilled fighter or true Vancian wizard (ie, a well-rounded adventurer like wizards actually are in Jack Vance's Dying Earth books); or being called a munchkin power-gamer because your fighter has to have an 18 STR to not suck but you roleplay your 8 CHA dude as a generally pleasant person. It's not worth watching the light go out of a new player's eyes because they wanted to play a guy based on their favorite fictional character but the realities of ability scores make it impossible.

All of the specific concerns here are fixeable by various means - if they are a problem - but this may be useful to keep in mind. In related design, storygame 'A Wilderness of Mirrors' avoids ability scores partly for that reason (saying super-spies should have all 18s).
See also: post #67 Over the Limit (http://www.therpgsite.com/showthread.php?p=501020#post501020) deals with difficulties of representing large ability scores

recent edits: Mutant Bikers note (*).; TORG gave stat list

Generating an attribute score usually falls into two categories: Random determination (die roll) or Point Buy. Some attributes may instead have a fixed base (e.g. Essence in 1E Shadowrun =6 base minus cyberware, or movement rate may be treated as an attribute but derived from race). Archetype systems (Feng Shui, TORG, Shadowrun) also sidestep either with prebuilt characters.
 
Point-buy is sometimes only for attributes, while in other systems the same pool may be used to purchase powers, skills, advantages/disadvantages, etc. Random roll is faster, but less “fair” and potentially abusable by cheating etc. The more attributes a game has, the less likely statistically that random-roll will generate a super character and the more involved a point buy system becomes. Where a system is fully random, there is less pressure for attributes to be equal in game importance and houseruling in additional attributes is easier (often seen e.g. with Tunnels and Trolls). (Palladium is also an interesting case: being 3d6 in order Strength being weaker in modern games where guns are suddenly available, is less of a problem).
A random system also allows rolling of minor non-attribute-related stuff, for instance, a random chance of a character having 'noble birth', being ambidextrous, or being psionic, is more acceptable in a random system than if everything was balanced apart from that roll, since a characters total value is much harder to quantify. Random systems also give an idea to GMs of how common high or low scores should be for NPCs which may not be as clear for point-buy games (particularly if the GM is allowed to build NPCs with any number of points). Random games usually limit the amount of bonus from attributes somewhat (e.g. 0D&D). There are sometimes rules for re-rolling 'hopeless' characters, or this can be left to GM fiat, or discouraged.
In games where a lot of player skill is involved (old school games), surviving with low attributes can be seen as 'hard mode' and something of a badge of honor (e.g. cf. Man Rider story here (http://gibletblizzard.blogspot.com.au/2013/03/man-rider-love-story.html)).  

Point buy systems quite often add slightly less logical attribute effects to attributes, to balance their relative importance, often particularly noticeable in systems which have evolved from random to point-buy across multiple editions. Some point buy systems (e.g. DC Heroes, HERO) charge different numbers of purchase points/stat point, depending on the attribute, thus avoiding both balance and realism issues but adding further accounting to chargen. While a good point buy system makes character generation theoretically fairer, a bad point-buy system may not be terribly fair, with some character concepts at a disadvantage if stats are same cost but different importance (e.g. to a given class) or if breakpoints are easily exploited. Even bad point-buy does let players get the characters they want though, within budget, which purely random rolling doesn't.
 
Given that both point-buy and random-roll have pros and cons, it is naturally harder to create a system that allows both as options, as this sacrifices some of the advantages of both systems. A 'mixed' system will need to be designed to meet point-buy needs not necessary for random-roll (such as all attributes being equal value), and would have to compromise on # attributes, and the need to have wide bands of similar ability vs. eliminating abuseable breakpoints. Random rolls for things outside the attribute system might need to be converted to point-buy as well, and some sorts of roll modifiers (like races giving re-rolls, e.g. a la T&T Anniversary Edition below) may be harder to duplicate or balance in point buy.

A mix of random and point-bought characters in the same party is almost as unequal balance-wise as if everyone were generating stats randomly (the odds of a huge discrepancy falls as number of randomizing players falls), although it still gives a player more opportunity to create the character they want. Point-buy and random-roll are usually geared to give out similar point totals, perhaps favouring random slightly unless a player is expected to roll multiple times. (one, 2nd Ed. Advanced Fighting Fantasy, assumes point buy with random averaging much lower totals)
 
More on Point Buy
Point buy may be at a linear cost, 1:1 up to a given threshold and 2:1 or more past that (e.g. Dying Earth, and 6E Hero lets the GM set a soft cap of their choice as a campaign houserule), require points equal to current rating, or require use of a table to calculate the scores. A fairly common design flaw of many point-based systems is to shift between using a linear cost in chargen, to a non-linear cost in character advancement, or vice versa, creating trap options. For instance Storyteller goes from linear cost to ‘triangular’ [current stat x 5], while 3.5E D&D goes from requiring [points equal to current modifier, minimum 1] to raise to a fixed +1 per 4 levels. A fighter with Str 17, Charisma 8 who advances to 4th level can add +1 to the Strength (worth 3 points) or +1 to their Cha (worth 1 point). In the opposite case, a storyteller character who wants to raise their attributes with experience should leave some of their stats at one dot to make the process cheaper; most pronounced in oWoD Vampire, whereas Mage  and I expect later games often uses [new stat]*x rather than [old stat]*x.
A possibly interesting rpg.net thread on this here: http://forum.rpg.net/showthread.php?713092-Rant-Linear-chargen-points-quadratic-experience-points-Whyyyy/page1 (http://forum.rpg.net/showthread.php?713092-Rant-Linear-chargen-points-quadratic-experience-points-Whyyyy/page1)  discusses why its off used (complex costs are too annoying when building every number on a character at once) and has a proposed solution (pregenerated arrays), implemented for nWoD here (http://forum.rpg.net/showthread.php?713136-NWoD-Stat-Skill-Arrays). The system also moves to linear costing in 'The God Machine Chronicles'.
This same problem can of course apply to buying skills or other abilities as well. Of the White Wolf games Aberrant is perhaps the worst for multiple resource pools with 'nova points', 'freebie points', 'stat points' and then XP all having different costs. Prebuilt 'archetypes' make it easier to fit out starting characters despite complex costing, but actually make linear-then-nonlinear costing worse by hard-coding trap options as standard careers and so reducing player choice.
FantasyCraft makes deliberate use of non-linear costing by having abilities which are '+1 to whichever is lower of two listed stats, choice if equal' - meaning that a higher value boost can be gotten if a character spends more points in a secondary attribute as well.
Linear-cost stat purchasing is simpler but doesn't help players' tendency for players to max out the main attributes for their class/race much. It is most viable if there are few points to distribute (Savage Worlds), if a grid is used (Storyteller), or if 'dimishing returns' is fundamentally built into the core resolution mechanic i.e. HERO characteristic rolls, and GURPS 4E use 3d6-roll-under meaning that the same number of points generates less and less return in terms of increase in chance of success. Linear systems often also have an un-even scale, where an 'average' score is less than half the maximum, meaning that lowering one score to minimum isn't enough to raise another to max. Both Storyteller (1-5, but with 2 rather than 3 being considered 'average') and Savage Worlds (the same 1-5 scale but described as dice types so d6 average, with 1 step below for d4 and 3 steps above for d8/d10/d12) do this.
Non-linear cost point buy gets increasingly annoying for larger scales of attribute numbers.

Point buy elaborations:
*Amber Diceless uses an Auction in which characters compete to purchase values in the games’ attributes. The number of points spent on an attribute in the auction is permanently recorded, but the number itself functions as an ordinal rather than cardinal/fixed quantity; it has few if any rules-specified modifiers or effects, only being used for comparison against other players (highest score wins). Players who do not bid may reduce their base scores below 'amber rank' to 'Chaos Rank' or 'Human Rank', which do have some defined debilitative effects. The auction may complicate bringing in new players/replacing dead PCs.
*vaguely similarly, "Cop Show" has a chargen system where players go around in a circle, and what each player specifies they're good at makes the next player bad at it. http://www.criticalmiss.com/issue11/BlockBuster.html (http://www.criticalmiss.com/issue11/BlockBuster.html)

*3.x D&D suggests just giving out a standard "array" of scores (thanks Beejazz) i.e. 15,14,13,12,10, 8 for PCs (the "elite" array) as something simpler than points. Its interesting to note that if you're doing this for 5E, the number of 'odds' in the array should be chosen carefully as characters have different numbers of +1s to raise stats (a normal human gets six +1s, a feat human two, and most nonhumans one - therefore you need three odd scores before a standard human is worthwhile compared to a "feat human". Where the odds are might also give an interesting choice between boosting highest or reinforcing a weakness (e.g. I quite like 18,17,16,15,14,13 for a high-power game).

*A few point systems give players bonus points for stuff such as detailing the character's back history or volunteering to write a campaign journal (DC Heroes, Risus, Amber).

*Shadowrun 1E is effectively point-based but points in various categories are determined from a Priority Grid.
The (slightly descended from it) Storyteller game uses basic attribute groupings (Mental/Physical/Social) to generate scores - starting at 1 dot in each and adding additional 7, 5 or 3 dots depending on priority (max. 5), in order to constrain min/maxing.
*3.x D&D uses point-buy with a "standard array" of pre-bought scores often used to speed up character building e.g. PCs/elite NPCs may use [15,14,13,12,10,8], equivalent to 25 point buy. Apocalypse World gives each class a choice of several arrays.

*some point-buy systems cost different attributes differently based on their importance (HERO).

*a couple of games let one attribute start with a higher maximum than the others. Mutant:Year Zero does this based off role (class?) 'key attribute' - this can go to 5, while other stats go to max. 4, when splitting points; Pathfinder and 4E D&D do this indirectly, give humans a racial bonus to a stat of their choice after points are allocated, so that one stat goes to 20 rather than 18. Apocalypse World has a stat advance related to class as one possible option initially. All these keeps maxed attributes slightly rarer (by limiting them to a specific class, and one per character, so perhaps characters are more diverse).

*The old Conan RPG from TSR (cloned as ZeFRS) has a system where characters don't truly have attributes, but where a character buys skills and their ranks/10 determine a 'default' for other skills in that group (an interesting idea, but with its table-based system the tiny increases in default were hardly worth tracking).

*Fuzion rates stats 1-10, with a 2 being an 'everyday' person score. Cost is linear. Normal humans are limited to a 7-8 but 'superhumans' can have more than 10, and with GM approval a character can put whatever number of points into scores (as written this could be 50+ though probably not intentionally).

*5E D&D lets character either random-roll or point-buy characters, but point buy can't purchase a base score over 15 on a 3-18 scale.

*Two-Fisted Tales uses a 1:1 linear cost for attributes, but one attribute "Weird" determines attribute max. (for other scores) and so needs to be increased to buy up other stats to especially high levels.

*Freerpg hi/lo heroes has a set of stats which can be either 'high' or 'low'. A player chooses Build (Quick or Powerful), Mentality (Logical or Intuitive) and Temperament (Bold or Cautious) which sets all their stat values e.g. a Powerful character will be high for Damage but low for Move.

*The Pathfinder 2E playtest instead of giving out points gives raises (each worth +2 if a score is up to 18, or +1 if a score is higher). Each character gets a number of increases that can be applied to any stat, plus raises limiting to one or two particular stats for race, class, and 'background'. If random rolling instead this replaces most of the raises (not some racial increases). Overall effect is somewhat similar to FantasyCraft or perhaps 13th Age but sort of more 'granular' with the raises rather than exact points.

More On Random Rolls
Random rolls are generally a bell curve roll such as 3d6 (by tradition and to duplicate IRL bell curves i.e. keep extraordinary scores rare). World of Synnibarr, Chivalry & Sorcery and "The Arduin Adventure" use d20 rolls for stat generation; "The Compleat Arduin" uses smaller linear rolls, such as d10+6, with exact dice/bonus depending on stat and race). Fantasy Imperium uses d100 (rolled under directly for checks); Rolemaster uses d100, but with the derived bonus modifiers following a bell curve. Toon uses a d6 roll for attributes (but characters can't die, probably have as much fun failing, and sometimes need to fail checks to get results).
It is theoretically possible to have a 1-100 system that follows a bell curve; dark legends exist of an RPG which uses the "Danish Lottery Dice" (d34) to generate a bell curve from 1-100 [3d34-2]. See http://forum.rpg.net/archive/index.php/t-60023.html (the thread there suggests the game in question might be Metascape, but this is definitely incorrect). (It is also possible to do a 1-100 steeper bell curve with 4d20+d24-4).
The boardgame (more or less) Flash Gordon & The Warriors of Mongo - see review here (http://www.advanceddungeonsandparenting.com/2010/02/rpg-ahead-of-its-time-flash-gordon.html) (thanks to Philip for mentioning this game elsewhere), apparently used 3 "averaging dice" to generate stats; these were common in wargames and are six-sided dice labelled (2,3,3,4,4,5).
A very few systems with random stat generation have 'rolling up' occurring as part of the random roll. These include Tunnels and Trolls (triples add and roll over in later editions; derivative Mercenaries, Spies and Private Eyes adds +2d6 on triples, once only), Palladium, or in a sense AD&D with its 18/percentile Strength. Palladium rolls up for a 16-18 on 3d6 or in the original Palladium Fantasy game 17-18, with 12 on 2d6 also granting +d6. Aliens Unlimited lets aliens with 4d6 roll up if they get a 16-18, but not if their roll is already higher. 12 on 2d6 is OK (letting disadvantaged races sometimes get the equivalent of a normal stat roll) but this is otherwise questionable...and would be equivalent mostly to just having a bonus table that scales up faster. Arguably since races rolling 4d6 or 5d6 at least don't roll up, it lets the system, rarely, create humans say with Troll-equivalent strength, I suppose. Mutant Epoch and TSR's Marvel Super Heroes have roll-on-a-table-determined stats which likewise vary tremendously, but with the attribute check system (table lookups) mitigating most game effects of high numbers (aside from raw damage in the case of Str in MSH).

Random generation is only rarely used by systems with small attribute ranges (like Storyteller's 1-5 scale), since generating the scores would possibly involve less dice (and so be very variable) and also since shifts in the number are more significant. Exceptions do exist like the GDW House System (1-10 range, rolled on 2d6-2, reroll if 0) or Anima; Beyond Fantasy (1-10 range, rolled on 1d10). A low-scale system could still have randomly-allocated points without being too imbalanced (i.e. with six attributes, roll d6 for an attribute point to see where it goes; roll again for each stat point in the spend pool - one heartbreaker 'Pits and Perils' does this, with a roll on a table to see which stat a character is 'Mighty' in). Another, 'dungeonrobber', has a separate d6 roll for each stat, with a 6 giving a 'High' rating. In general however, it seems that low scales such as 1-5 tend to have PCs often-to-always have some stats around the maximum level, making these sorts of scales more suited to the assumption the PCs are heroic/exceptional.
Point allocation is also less math-intensive with smaller attribute scores - in part games with low stat scales (i.e. 1-5) sometimes seem to have more attributes, perhaps partly due to this and partly due to the need to balance attribute effects by sub-dividing powerful stats.
Random rolling can be used in games with very few stats but its not a good idea. The worst system I've ever seen for this was the 2-page freerpg Dementia - roll 2d8 points and divide them across 8 attributes, and checks are under stat on d8.
A similar idea of point-buy with a random number of points can be seen in (I think badly misnamed) Dragon magazine #132 article "A Little Less Super" for DC Heroes 1E, which has a random 'origin' roll that adds from 0 to 10,000+ character generation points to the base of 250 ('no extraordinary origin' 0; mutation (minor) 250, scientific origin (major) 1,100; other-world origin 10,000; multi-origin roll d10 times). It rationalizes powerful characters as multi-origin e.g. explains that Superman has an 'other world' origin (Krypton), a 'chosen one' origin (destiny) and a scientific origin 'due to Krypton's advanced civilization'; while Cyborg has 'personal injury' and 'scientific'.

 Random variation in a single variable only also occurs in Over The Edge (hit points only) and in some 3.x D&D games with point-buy where the only random roll left is also for hit points; optional rules may however make that nonrandom as well. Ringworld (BRP based) has the usual RQ attributes but with a devastatingly important random roll for age that gives a huge variation in number of discretionary skill points.

Other random-roll elaborations:
*a few random-roll systems generate PC stats by making a random roll for each stat, then looking up result on a table e.g. Mutant Epoch, Star Frontiers, Marvel Super Heroes (all of these these use d%). This can be used to reduce odds of unworkably low scores, or likelihood of higher scores, or otherwise adjust the range as desired.
Games which normally use dice sometimes use a table in special circumstances: D&D 3E in the DMG (and 2E in 'High Level Campaigns' monsters with ability score rules) have tables for monster scores, so say a monster race with a 4 Int normally might vary from Int 2 to Int 6 based on the 3d6 roll and a table lookup.
*Unearthed Arcana (1E AD&D) has a class-specific random-roll system for humans giving different # of dice by stat e.g. a barbarian would get 9d6 for Str (take 3 highest) but only 3 for Charisma. (This also gives humans good stats). An oddity would be that since class is thus set when dice are rolled, it could create characters who would be better off dual-classing.
*2E AD&D (skills and powers IIRC) had a system whereby 24 dice are split between stats, with a minimum of 3d6 and maximum of 9d6. This gives results somewhat similar to UA's (instead of choosing from the arrays, you engineer your own) however with the differences being that class choice isn't set finally if the rolls don't go according to plan. However, more dice do add steadily diminishing increase in the average such that [all 4d6] is the optimum for total point production, 4d6-arrange-to-taste being probably slightly better.
*T&T 30th anniversary (Alternative Rules) the player rolls 18 d6s, then allocates 3 per ability. Some races may "take two worst rolls" for an ability, or reroll e.g. 5s and 6s (similar ideas could be applied to the Unearthed Arcana/2E rolling system, above). (Racial modifiers like this are more difficult to calculate the effect of though, and its particularly tricky to cross-apply the random effects onto a 'point buy' system and have characters from either system be equivalent).
 
*Grodzichi's "Low Fantasy Gaming" RPG gives out one 15 automatically, then rolls 4d6-drop-lowest for the other 6 stats. It also allows players to copy other players' rolls with a slight (1-3, GM discretion) point penalty.

*'Beyond the Wall' is random but using a 'lifepath' system to generate stats (along with some skills, etc), instead of rolling directly. Events can create links to (and bonuses for) other players' characters.

*Tunnels & Trolls normally does stats as 3d6 in order (sometimes with triples add and roll over), but house rules I've seen on the internet have also included tests of player skill such as shooting basketball hoops (get it in and get an 18; otherwise you get a 3), or beer-chugging. T&T gives high-level characters a sort of access to 'point buy' with the 19th level Omniflex spell, which lets the caster rearrange a target's attribute points between stats, as long as the total is unchanged (in 7th Ed. T&T, Omniflex can also be used to generate an infinite stat-gain loop together with the spell Unlucky Bees, which deals damage equal to the target's Luck score and then adds a point to permanent Luck if survived- shift the Luck points gained to other stats with Omniflex and repeat).

'The Gang Hack' (scooby doo) has a system of 3d6, where a roll of 15 means the next score is rolled on 2d6+2 to balance it.

*systems sometimes give bonuses to characters from previous characters e.g. Synnibarr and Dragonlance (both random roll) add bonuses for "dying heroically". Bushido (point buy?) was notable for adding part of a dead characters 'Honour' score to the new characters stat (encouraging heroic death). TSR's Amazing Engine let a character earning XP add it to either itself or to the "player core" it was generated from, for use in other settings. (Related to this AD&D Dark Sun had 'character trees' where a character advancing also improved other backup characters in the tree, but this actually didn't affect attribute scores directly - is more a rough analogue of 3E's bringing in replacement characters at the same level).
 
*Games can have rules for randomly generating characters based off parent's scores rather than wholly at random.
(this could be based off one set of known scores for a known PC score, or assume scores for both parents are known).
A 1-10 or dice pool game could do this pretty easily (for each stat, roll both parents' stats as a dice pool at a TN generating half as many successes on average; add results for both parents together), or a game might have a table including [as parent A/as parent B/slight modifier/roll randomly] type results [Talislanta essence extractors].

*2nd edition D&D generates attributes randomly, but with a variety of methods. Not all are balanced but assuming multiple methods are available, there are trade-offs between them. Method IV (4d6 drop lowest twelve times, take the six highest and arrange to taste) generates characters who are generally superior but rarely have 18s, while VI (base 8 for each stat, add 7d6 where desired) generates a couple of poor attributes and some very high scores) but not as severely as IX (divide 75 points as the player sees fit). IV characters tend to be better at raw attribute rolls (e.g. proficiency checks) with their higher scores whereas VI characters have better modifiers (hit, damage, HP, etc.), by having a couple of really high scores, high enough to get a bonus on its odd nonlinear stat charts. See here (http://www.purpleworm.org/forums/viewtopic.php?f=7&t=1001) for discussion.
Early 2E with no optional rules is geared more toward the lower methods (I,II,III), while more optional rules and later books include some inflation, e.g. if you're using the Complete Fighter, it recommends using method VI (quasi-point buy with base 8 then add on 7 d6 rolls), since 'kits' add a further set of prerequisites on top of the default class and race minimums.
2E also includes prerolled 'arrays' by class in a number of optional class books (Complete Ranger, Paladin, etc.). Arrays are not necessarily balanced so some rolls (usually on a d12) are better or worse. Powerful classes' stat minimums fail to enforce rarity using this, instead boosting the overall numbers for their arrays. While the books also have 'kits' with stat minimums, the arrays don't go as far as to tailoring particular kits e.g. at worst a ranger using the Ranger array only has a 2-in-12 chance of making Giant Killer despite its requirements being fairly modest (Str 15+/Dex 15+). Class-specific arrays are useful for generating NPCs, however.
Methods where you roll a set a numbers, then arrange as desired (IV,V in AD&D 2) are a sort of 'poor man's point buy'). Generally point buy gives more choice and balance. There is some extra individual variation in that different arrays give slight differences in min/max options - e.g. in D&D a 13 for one stat might give a +1, for another no bonus. Or otherwise different breakpoints, etc.
*Basic D&D (e.g. BECMI, Moldvay B/X) rolled 3d6 in order, though after choosing class a character can raise the class 'prime requisite' by 1 by lowering another prime requisite [Str,Wis, Dex, Int; not Dex or Cha] by 2, representing neglecting exercise, studying etc. to focus on their classes' main area.
The Rules Cyclopaedia interestingly has conversion guidelines to AD&D to cover it most often using 4d6 drop lowest: for Basic to Advanced it recommends +2 to a classes' main "prime requisite", +1 all others, while vice versa is -1 prime requisite, -2 all others.

*Mutant Epoch has a straight series of random rolls as the base method, but more interestingly with GM approval a player can choose  to either allocate rolls randomly, or reroll their lowest score. It uses special rolls for some characters (bestial humans [equivalent to Gamma Worlds' Mutant Animals] might use different dice to determine Appearance) in which case these rolls can't be switched, just because its not procedurally possible.

*user Omega on another thread (18/10/14) mentioned a system where 3d6 is rolled for stats, and each is assigned as they're rolled, adding some uncertainty (do you put a highish stat in your most-important stat, or hope you can roll something better?).

*Rolemaster gives characters a current attribute and a "potential attribute" which is the highest it can be raised to with level advancement. Potential attribute is rolled, with a range that decreases as a score approaches a perfect rating.
A slightly similar effect occurs in Powers & Perils, which has a rolled 'base stat' that is multiplied by a purchased multiplier of x1.5 to x4 (bought from a budget of 2d6+14 multiplier points).
 
*one freerpg listed on jhkim's darkshire list (I forget which one) limits one attribute on the basis of another - ST cannot be greater than 4 more than CON (I think) due to the character's frame not being able to support the extra muscle.

*Ars Magica, which has a system where attributes center on an average of 0, IIRC has a system where players pair up to roll and receive opposite numbers (if one gets a +3, the other gets a -3). This is generally a particularly bad idea for game balance, although Ars Magica's 'troupe play' approach does mean that its not strictly one character per player.  

*Spawn of Fashion has random stats, as well as rolls for other things ('body table'), one of which 'hearty' lets a character roll twice for each attribute.

*DCC [Dungeon Crawl Classics] has a 'funnel' system where four randomly generated 0-level PCs are run through a meatgrinder 0-level adventure, with the best survivor promoted to 1st level. Its relative Mutant Crawl Classics also does this, although a significant part of the randomization of a character - the mutation roll - unfortunately (in a weird but balanced way) only appears at 1st level, with 0-level characters not having mutations yet.
\:) :) :) :)/
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*Dark Fantasy [Tim Barrett's]- has most stats rolled on [4d4]x5. It has partly-random, partly-calculated attributes. The large stats/even number of dice lets calculated attributes be set on the same scale e.g. Mind Power and App are rolled normally while Leadership is 2d4x5 + 1/4 MP + 1/4 MP.

Balanced Random Results:
GURPS free supplement 'Caverns and Creatures' gives characters a random roll on a table, which lists pre-built attribute arrays. Hence stats are randomly determined but in theory no roll is worse than any other roll.
Icons random-rolls stats and # powers, partially balancing this by reducing Determination score if results are high.
An optional idea proposed for D&D is to roll three times (e.g. with 3d6 or 4d6-lowest - potentially the player could choose) with the roll being one number and [25-roll] another number i.e. a character with an 18 will also have a 7. Note this balances in terms of total points but assumes linear costing. For 3.x the total (e.g. 25) should be an odd number as this splits into an even and an odd attribute number, whereas an even number could split even/even or odd/odd (with a lower total modifier).
Another approach to arrays is to roll several dice and group specific numbers as pluses - for instance 10d6 might give 1,2,3,3,4,5,5,6,6,6 = three scores of +1 (single rolls of 1,2 and 4), two of +2 (double-3,double5) and one +3 (triple-6).
A card-based approach that gives balanced approach listed on rpg.net here (http://forum.rpg.net/showthread.php?769192-3-x-Alternate-Ability-Score-Generation-Methods/page2):
Each player gets a set of twelve cards, from four through nine twice.  
___   ___   ___   ___   ___  ___    
[u]|4|[/u]   [u]|5|[/u]   [u]|6|[/u]   [u]|7|[/u]   [u]|8|[/u]  [u]|9|[/u]      

___   ___   ___   ___   ___  ___    
[u]|4|[/u]   [u]|5|[/u]   [u]|6|[/u]   [u]|7|[/u]   [u]|8|[/u]  [u]|9|[/u]
For each stat, the player draws two cards and adds the numbers together (not replacing them after). Each player will thus end up with six stats in the range from 8-18 and the same number of stat points. (Note that used with 3E-5E, characters can still end up with a different number of odd scores and so differing total modifiers).

Combining Random-roll and Point Buy (on the same character)
A couple of games combine point-buy with random roll. Middle Earth Role Playing (MERP) by ICE rolls character stats randomly (on d100), but gives classes the option to replace one of their rolls, the score allocated to their classes' prime requisite, with a 90. This lets a player drop their lowest dice roll, unless they min/max by placing a roll that's already 91+ in their key score. Gamma World 7th edition (the D&D 4E compatible version) gives the player an 18 and a 16 in the two prime requisites of the characters (or an 20 if both are the same), and randomly rolls the remaining less important scores.
Palladium's Rifts lets characters with terrible physical ability score rolls upgrade them by choosing classes with attribute minimums - Borg especially replaces scores with fixed values, while Crazy and Juicer also have reasonably high minimums. Super powers (Heroes Unlimited, via Conversion Book I) can also replace values. Like the above these act as failsafe systems for ensuring minimum rolls, though they have an in-world justification.

Other combination systems - a houserule from RPGnet for generating D&D stats rolls 2d6 for each, then gives bonus 'rolls' of 6,5,4,3,2,1 between them (one per stat), giving the same overall average as flat 3d6 but some control.
In a sense, random games where a player distributes dice between stats, then rolls them, are also a combination of random and point buy (controlled). Some (Method VI 2nd Edition, 8s for all stats plus 7d6, or the T&T alternative rules method above) roll and then allocate, while others (Amazing Engine) allocate and then roll. The Amazing Engine variant gives a very wide spread of possible scores since both # dice and the final rolls vary and it is more difficult to implement a cap to scores (you can't say "you can't add more dice if it takes you over X" - they just roll, and may get over X), giving its attributes a very nebulous scale.
Another approach for games with separate stats/modifiers is to buy the modifier, use that to calculate the base stat, then roll the remainder, preventing characters from buying stats to optimal breakpoints only (this was suggested in the recent Rolemaster playtest as a houserule - it has 1-100 stats with a breakpoint every 5).

*Blue Planet (Synergy system) has a combined point buy/random roll system designed for an attribute range where 0 is average. The player gets a base # of points depending on the campaign, then opts to spend points to advantage an attribute, or earn points by disadvantaging an attribute; the player rolls 3 d10s with the number of points used as the target number and successes being stat points gained (if advantaged) or lost (if disadvantaged).

*Dragonquest (http://www.fantasist.net/dragonquest.shtml) uses point-buy after rolling on a table which determines both # points and maximum attribute buyable (these two things generally oppose each other on the table). While interesting, this has a net effect of generating characters who are across-the-board very competent, or characters who can “max out” an attribute, but who have fewer points to spend to buy these higher attributes. I wouldn't really recommend this since its extremely random - moreso than rolling 3d6 in order for stats - and manages to be uninteresting (providing no input into final character) at the same time.
See page 16 for more discussion of Dragonquest. A similar table shows up in AD&D 2E's Skills & Powers.

Character Modelling & Other Options
A possible third alternative to rolling or using points, Marvel Super Heroes has the option of using "character modelling" to design a character. Here the player assigns numbers to the character (that they think the GM will allow!) and the GM vetoes anything too excessive. This is normally, but not always, done based on a given fictional character; its almost an ad hoc point buy system which works by being balanced against random character that's normally random (if there was a real point buy system, players would probably have to use that). This idea, while abuseable, seems like it could have advantages over many actual point-buy systems; as a D&D-type example, it would allow a GM to do things like weigh up relative importance of attribute values to particular characters (i.e. if the fighter PC wants a high Cha this probably isn't game-breaking since unlike the sorceror it doesn't drive a bunch of spell DCs or damages, so why not let them have it rather than making them dump it for more Strength?). Though in context, MSH doesn't have classes and attributes are generally about the same value from character to character.
This approach is very similar to how GMs in most games will effectively produce an NPC, assuming they aren't diligent enough to stat out every NPC in their city in advance. Apart from MSH it is not often seen for PCs, though.

A few games just gave out pregenerated characters and hence have no system for generating attributes e.g. the archetype systems in Feng Shui (although characters can sometimes adjust stats slightly), Talislanta, or Shadowrun. More extremely, the original Indiana Jones game by TSR, or the recent Marvel Heroic Roleplaying (MHR) Cortex+ game provide not just archetypes but exact characters. On the other hand, the old Demonspawn game books were written for a specific hero, mighty barbarian Fire*Wolf, but did still make you roll stats randomly, possibly giving you a gimpy barbarian.

Timelords (original version) assumes the player will play themselves as a PC, and uses a series of tests/notes to determine the player’s attributes.
(Though you could think of this as a sort of random roll...).

Improving Attributes
After character generation, attributes can sometimes be improved with experience (sometimes not). They may be capped in the same way as initial attributes, or be freely improvable.
Point-based systems like GURPS can let them be bought up with points (sometimes at extra cost compared to purchase with initial points - 3E GURPS doubles the cost after chargen, while in DC Heroes its at x5); systems where xp is spent rather than tracked are also basically this. Level-based games can have automatic bonuses from level (e.g. +1 every 4 levels in 3E), or this can be an option e.g. Savage Worlds (where a character can pick up a stat increase once/rank, also balanced vs. skill raises or new Edges). In either case the bonus is keyed to level advancement, whereas point/xp spending makes a character choose between a stat increase and an increase to something else. Talislanta let characters spend xp to buy either a level or a stat point (25 xp for either), while SenZar has 'fate point' awards for stat increases separate to XP awards. Another interesting system here is Tunnels and Trolls which has very excessive stat raises; stats start at 3d6 but depending on the attribute an increase at level-up can be from + 1/2 level (IQ,CHR, DEX) to +1x (ST, CON) to +2x level (Luck).
Games can also have random checks for improvement (Rolemaster allows checks with increase up to the limit of a roll for potential stat, which is checked upon levelling up and can actually result in losses on a poor roll; old gamebook series 'Where the Shadows Stalk' had a random table which could either improve or worsen stats, rolled at the end of each adventure; Stormbringer has checks as (IIRC) a result of occasional game events; Spawn of Fashan reportedly has a table of attribute increase chances by class, with cumulative chance increasing if the check fails, then resetting to base chance when the check succeeds), or a skill can be learned that increases stats (Palladium). Sometimes stats can also be improved via training (Runequest).
Magic that alters stats can sometimes also be found - this may have separate limits e.g. 3E D&D limits inherent bonuses to +5 maximum (over initial value), while AD&D lets wishes raise scores at 1-point-per-wish to 16, then 10/point from 16-20 (or 11 to go from 18 to 19, with 10% added to exceptional Str each time), and 20 per point beyond (to a hard limit of 25) - but does not record 'initial' scores (making the initial randomization fairer in high-magic campaigns). (The 10 wishes/point is sufficiently tight that a house rule I'd seen was to make that the rate for Limited Wishes'). 2E also has an Enhance spell in Legends & Lore (wizard 8th level) which adds d4 to another's stat (max 22), but drains the wizard [that amount +1] Con points so was rarely used - though if the wizard's Con is <17, they could raise a target's score to 22 and replace those Con points for 1 wish each, exploiting the difference in exchange rate.
Avalon Hill RuneQuest allowed to DEX to be trained to 1.5x its initial value, while for ST/CON the lower of the two could be trained up to match the other score, or both up to SZ if that was higher.
Gamma World has mutations which can increase stats - usually as part of chargen, though characters exposed to radiation could also mutate. GW 4E (1992) used attribute modifiers in an interesting way to calculate amount of increase, with Heightened [Attribute] adding 6+modifier points, i.e. a score of 10 (+0 mod) would gain 6 points to 16, while a score of 18 (+3 mod) would gain only 3 (to 21).
Another mutation "Allurement" has a Mutation Power rating, with the modifier adding to Cha; this is interesting since MP can often be raised, unlike Cha, so the mutation is sort of changing an attribute into a more easily modified 'derived attribute'.
Attribute maximum can sometimes be modified by an Advantage (e.g. Shadowrun 4E has an 'Exceptional Attribute' quality letting a character raise a score +1 above the normal racial limit for 20 build points; stat itself sold separately).

Where stats are rolled randomly and level raises are point-buy you could consider these games to also be a hybrid of random/point buy attribute generation, at least for high-level characters.
A game might have an 'improvement roll' for an attribute e.g. you need to fail the attribute check to gain points in the attribute (Sharp Swords and Sinister Spells) - that randomizes in a way that's counter to the initial randomization of attributes i.e. moves toward balancing it despite it being random.

Losing attributes
On a less positive note, characters can sometimes have attribute loss. Commonly this is due to a result of critical hits or serious damage (e.g. Palladium has this as a side-effect of negative HP (roll on table), Werewolf has 'battlescars' (roll on table), Apocalypse World lets a character 'break' one of their stats (-1) to not die. Ageing or magical mishaps can also lower attributes.
Attribute loss tends to be a feature of old-school or random-roll chargen systems; stat loss in point buy may be a 'fate worse than death'  as a character can be replaced with a freshly built one to avoid the point loss.

Order of Operations
When generating a character, attribute score generation is often (but not always) the initial step.
In games such as AD&D where a random roll limits access to class/race, it has to come first, while in Alternity race is selected first (and establishes minimum scores for point-buy); likewise for Palladium Fantasy where race sets number of dice to roll for stats, race is first. Point-buy systems may put class selection before ability purchase so players know what stats should be prioritized. A system which buys everything (stats, skills, advantages) from a single "pool" might also not have an order of operations, with everything purchased simultaneously.

NOTE: games with random-roll attributes will fairly often roll other things e.g. handedness, class, psionics, educational level, strange medical traits, whatever - this can reduce a need for a complex advantage or feat system since stats already generate imbalance between characters that makes it OK for these extra factors to vary. Point-buy systems may need to give costs for other things besides stats as well.


(thanks to Phillip for additional notes on Dragonquest and Conan; info on systems w/o chargen from J. Arcane, in other threads). 22/1/16 - improvement as a 'mixed' system for high level.

Edit notes: made 'order of operations a heading (*); revised notes on Palladium rolling up (*), MSPE (*), Cop Show (*), "A Little Less Super" (*)

Stat Range
The statistic range (i.e. 3-18, 1-100, etc) normally depends on what dice rolling mechanism is used. Higher scales are generally useful to handle “ability damage” (or random stat determination) but usually also mean that not every point will give a character a benefit. d100 systems can get that fine grained, though recalculating lots of skills may still be painful/discouraged - e.g. HarnMaster, where each skill is the average of three values.
The range of ability scores may just consider player characters or may be designed to consider monsters or other things as well (see Scale, as well as monster design).

Attribute Damage
Depending on the system, attribute damage may be used to handle things like physical damage, fatigue, or spell points (e.g. Tunnels and Trolls uses attribute damage for all three of these), or poison (3.x D&D), though derived scores or non-numerical wounds or conditions can be used instead.
Attribute damage is normally given out using a linear cost; HERO system expresses “Drain” (a power) amounts in terms of purchase points - as the system is point based and its stats vary in purchase price per stat point. Marvel Super Heroes has a mix of damage that is based off stat points (Health off normal attacks, a linear amount), or that causes a Rank reduction (Endurance loss from killing damage) such that losses are scaled up for characters with bigger stats. Dice pool systems are a bit granular for stat loss to work well, but can have proportional losses via rolling [stat] and having successes become the new current stat (e.g. seen in an event card for Arkham Horror). (one example of a dice pool game that does work for stat loss is the Spartacus boardgame - damage can come off multiple stats - see also "take-highest dice pools" post).
Attribute damage is sometimes problematical due to either messy modifier recalculation, or characters being relatively squishy against it in games with heavy HP inflation but relatively fixed stats (e.g. 3.x D&D). AD&D/older D&D tended to not have central rules for ability damage, so individual instances had specific rules e.g. for duration of the effect.
Attribute damage sometimes does not have the full effect e.g. The Fantasy Trip subtracts damage from STR, but always uses the full STR for what weapons a character can wield.
(I think logically a system can have any three of the following four - large enough numbers for ability damage to work, no derived modifiers required, die rolls remaining relevant/bonuses under control, and roll-over).

Other twists: 5E has an unusual case where something similar to attribute 'damage' is used as a check. As a second stage after a primary Int check is failed (d20 + mods as usual), an Intellect Devourer rolls 3d6 and if this roll is greater than Int, the targets Int is reduced to 0.

Modifiers
Attribute scores may be used directly in game mechanics or may have secondary “modifiers” which are used by the game mechanics – compare e.g. GURPS (roll under stat on 3d6) or White Wolf (roll dice equal to the stat) and D&D 3E (Strength score of 13 = +1 modifier on Strength rolls on d20) or perhaps even Savage Worlds' named derived attributes [Toughness = 1/2 Vigour die type +2]. As noted above having a separate rating and modifier may be useful if the raw score is used to absorb damage directly.
The problems with modifiers however are that they a) add another layer of calculations and b) generate breakpoints where extra attribute points don't increase the modifier. This is noticeable for instance in 3E-5E D&D, where odd numbers don't benefit the character. Or DC Heroes has tables where e.g. 5-6, 7-8, 9-10 use the same column (despite 1 AP representing a doubling in score) although optional rules give a slight bonus to an attacker if both are using the same 'column'.
3E D&D attempts to balanced odd numbers by making these into prerequisites for some feats (e.g. 12-13 are +1 and 14-15 are +2, but a character needs a 13+ to learn Dodge or a 15+ to take Two-Weapon Fighting). 4E D&D adds a +1 modifier to all stats at new 'tiers' of 11th and 21st level, so that initial point-buy decisions are flipped at level 11 to 20--all the odd numbers become even and vice-versa).

Some games use both the modifier and the raw score in different cases e.g. 2E AD&D (d20 roll under stat checks vs. combat modifiers) or reputedly 13th Age triggers monster attacks based off natural die rolls - if their natural attack roll on d20 is > target's score a special effect can be triggered.
Sometimes the modifier will adjust rolls for the attacker, while the defender uses the full score as a target number (IIRC Alternity). That could be thought of as a way to cut down the number of calculations modifiers generate - not directly since one is still required for each roll, but by a 'back door approach' since calculations we'd normally forget about, that generate target numbers, are being reduced. Unless modifier is calculated at 1:1 however (e.g. 14 = +d4 on d20) this does generate 'asymmetry' (see post on opposed contests). Also, not every roll is opposed so the modifier is still a bit more work than if a roll was just '+stat'.
At a psychological level people possibly like modifiers since they provide a big attribute score, while having a bonus that's small and so easier to add up.


There are a few models from which modifiers can derive:
 - 1) they can be proportional to the raw attribute; or
 - 2) they may be a plus/minus based on the difference from an 'average' attribute, which gets +0. Building modifiers based around '0 for average' minimizes additional math to some extent, and means multiple modifiers can be applied to a single roll more easily, or that checks with no modifier are more or less balanced. Proportion-based '0 is nonexistent' results means that rules like 'does not add Dex modifier to AC when surprised' are consistently bad for all characters without more explanatory rules. Multipliers to the bonus in a plus/minus system affect weighting of the bonus, while in a proportionality system a reduction is always a penalty. A plus/minus system could make attribute specific costs less awkward (if buying STR costs more than buying APP, say, then 'average' still has cost 0 in both cases).
Certain game functions (weight lifted, damage absorbed) more logically derive from an objective scale where 0 represent nonexistence, while appearance modifiers for instance perhaps suit '0 is average' (i.e. poor looks is a hindrance, high looks is a bonus). If based around +0 for average, the set of numbers giving no modifier is sometimes larger than other bonuses (i.e. 9-12 no modifier, then +1 at 13-15, +2 at 16-18 so that the average range is 4 numbers wide, rather than 3 numbers for each higher bonus level) which might be considered a mathematical flaw. This doesn't always happen e.g. in 3E each 2 points is consistently a 1-pt change in the modifier, and it can be deliberate - e.g. Moldvay Basic uses a modifier scale of -3 for a 3, -2 for a 4 or 5, -1 for a 6-8, 0 for a 9-12, +1 for 13-15, +2 for 16-17, and +3 for 18, which is close to +/-1 = 1 standard deviation, based on the distribution of 3d6.
 - 3) they increase in slowly-widening ranges, so that spending points on a stat gives less and less real return. (Marvel Super Heroes' ranks - these are used on a table rather than being an additive modifier).
A couple of games add in penalties for high attributes e.g. Superbabes gives a HP penalty for high Looks. Nuelow's freerpg "Fairies!" had a personality bonus for high Int but then a penalty for very high, saying that 'mid level geniuses each have their own brand of charm' but assuming high-Int characters would be overly arrogant.
Games sometimes have bonuses for high attributes but no penalties for low attributes - the prime example being Palladium (aside from Rifts Ultimate Edition). The argument for this IIRC being that it encourages role-playing low stats, although it isn't particularly good modelling.

Whether an attribute modifier is applicable to a roll may depend on class, race, or advantages. For example in original D&D (Greyhawk expansion) only fighters could get a to-hit/damage bonus from a high Strength score; in AD&D, only fighters could get a Con bonus to hit points of more than +2 per die; AD&D 2E voadkyn (wood giants, Complete Book of Humanoids) as a racial penalty gained no Str bonus on to-hit rolls (the same could be gained as an artifact curse of 'great strength but great clumsiness'); modern games often have cross-matching e.g. 4E D&D having powers based off various stats, or some 3E feats changing what stat can modify a skill or save (much more possible in 3E as compared to 2E because of the universal stat modifier table).

In some games modifiers are used only during character generation (i.e. Dragon Warriors) and so do not take up character sheet real estate, though break points may still exist. Dragon Warriors is also interesting in having basically two varieties of modifiers; though not named explicitly stats can give a larger 'primary' modifier, or a smaller 'secondary' modifier, depending on how strongly they influence a derived attribute. Most derived attributes in it are affected by one primary and one secondary modifier.
Basic Role Playing/RQ uses a system of category modifiers for groups of skills where a stat might add +1% per point above 10 (primary), or +1% per 2 points (secondary); multiple attributes can affect skills since the modifiers are quite small. HarnMaster determines "skill bases" as an average of 3 attributes, then multiplies these by a *2, *3 or more depending on how easy the skill is to use.

Defining multiple modifiers for a single stat can also be used to reduce the number of breakpoints which have no mechanical effect; it would be conceivable to have a 3E-5E D&D-esque modifier system where every stat point is useful due to having two modifiers, one that increases at 'evens' and the other increasing at 'odds' (on different tasks). (An idea I was toying with for a Savage Worlds hack -  i.e. 2 dice take highest - was  to have attributes give pluses alternating between primary roll and 'wild die' i.e. a +1 score could add +1 only to the skill die, while a +2 would add +1 to either skill die or wild die, then +2/+1, +2/+2, +3/+2. Eventually dropped as too complex.).[/I]
Another idea for avoiding 'dead points' would be to give bonuses to only some skills e.g. with 5 skills, a 10 score might be a +0 to all skills and each point adds +1 to a different skill (so all are +1 at score 15). This works with the concept that an attribute as being really a loose collection of different abilities, e.g. 'Dex' including reaction time, hand/eye coordination and agility; likewise a Cha point might represent 'attractiveness' only if the bonus was assigned to Seduction.
At least one game has two levels of derivation – in effect modifiers from modifiers - and so three columns on the character sheet. In Earthdawn a character attribute generates a “step number” and that “step number” generates a number or type of dice to roll e.g. Str 15 = Step 6 = d10 (the intermediate “step number” can be modified by various factors such as skill levels). It has been suggested the main reason for the multiple layers is to give D&D-like attribute scaling for familiarity to D&D players.
(this sort of effect could be used to scale back the modifier of an attribute e.g. having CON affect Physical skill which then affects Toughness threshold).
 
Attributes vary in their significance/ weighting on tasks - either alone or in combination with other factors. An attribute may absolutely determine success/failure e.g. +12 score may absolutely fail a contest vs. a +13 (Amber, though circumstancial modifiers are common), have a massive effect on success (Tunnels and Trolls stats often range from 10 to 50+, with a random roll of only about +2d6), be rolled as a dice pool, be rolled under directly on d20 as in AD&D (i.e. +5% per stat point), or apply only a minor modifier or bonus percentiles i.e. +1 per 2 points on d20 (D&D), +1 per 5 points on 3d6 (HERO), etc.
Tasks are also affected by skill (or level) to a varying extent, giving rise to variable weightings for both. The weighting may be heavily toward attribute (Warhammer, skill-less systems), 50/50 i.e. 1/2 stat + 1/2 skill (Storyteller, Cyberpunk), or heavily toward skill (i.e. 3.x, BRP). In other cases, stat may have no direct effect on some rolls but may give a cap on skill rating (e.g. Savage Worlds) or additional points to spend; this is discussed in some more detail under Skills.
(thanks to RobMaudib for additional notes).
Note that 'weighting' is affected not just by the theoretical range but also by the distribution within that range. A storyteller character rolls dice equal to Stat+Skill, for example, but stat defaults to 2 whereas skill varies from 0-5, giving more 'spread' in possible numbers and so probably a slightly higher real influence. (Admittedly this is arguable since skill scores of >3 require freebie points or xp).


In some systems attribute and skills do different things making the relative weight hard to determine. Skills may also vary upward more than attribute, e.g. with level, so that impact of attributes gradually decreases.
The 'weighting' can be directly modified in some games, from task to task. The GDW House System (e.g Cadillacs & Dinosaurs) suggests rolling under the 'average' of all applicable skills/attributes; many older systems manage weighting varying from task to task by having multiple sub-systems that work quite differently e.g. a character in 2nd Ed. D&D rolls under Str on d20 for some checks, and applies a smaller modifier for to-hit rolls, rather than having the same bonus for each. A stat/stat modifier will be more valuable to a player obviously if it affects a more critical character function (some as combat), and also varies depending on how easy it is to get modifiers in other ways, or where used by a different subsystem that gets or uses stat bonuses differently (e.g. see damage, post #34). These sort of effects may factor into design decisions about relative cost of attributes, or even how many attributes if an attribute is split because it has become too valuable.
Relative weighting of skill/stat perhaps indirectly affects what can be defined as a stat or skill. For instance, if stat has a relative high weight, a system could have a Size as a stat and then Strength as a skill, whereas a high weighting of skill, or big increases with level, would make it too easy to make characters all heroically muscled or lead to too much level-inflation in Str, suggesting Str as the stat (and hence Size probably an advantage).
Its probably desirable for stats to have a greater impact on raw stat rolls vs. skill rolls (arm-wrestling vs. climbing), though with most mechanics that will generate 'dead space' for the skills- a d100 might allow for +2% per point for one and +1% for the other, but for d20 it probably requires every 2nd point to be unused. Its perhaps surprise D&D didn't decide to do something with this, e.g. to have a 13 Str give a +3 on raw Strength checks.


Modifiers or tables build in a buffer between the score itself and the modifier in the dice roll, giving more leeway in possible stat range (useful for instance to limit bonuses for randomly rolling stats, but a possible problem for point buy since players are incentivized to buy up to specific breakpoints only). For example, HERO uses a 3d6-roll-under system for most attribute checks but characters have a very wide range of possible scores since a check is made by rolling under [8+(Stat/5)]; D&D went from 3-18 using roll under to an open scale in 3.x, with adoption of a d20+modifiers system (which made odd numbers like 13,15 give no extra bonuses; to compensate odd numbers are used as feat prerequisites).
Modifiers most often increase linearly (e.g. +2 to a stat = +1 to the modifier) though certain systems (Rolemaster, FATAL) provide bonuses that start to increase faster toward the far ends of the normal range (Palladium gets a similar effect by increasing the stat at the upper end of the range; a roll of 16-18 initially gets +d6 extra attribute points). AD&D has complex & irregular modifier charts, though it also tends to have bonuses increasily faster at the end of the range (in a random-roll system giving a small chance of a huge modifier).
Some systems while linear cap maximum modifiers i.e. Rifts notes that many bonuses 'max out' at 30 (in the case of PP, strike bonuses stop increases but the characters starts to receive an initiative bonus instead); GURPS caps 'skill defaults' at 20 regardless of the character's actual stat. The capping effect may mean that past this point flat negative modifiers can be ignored (e.g. imagine a rule for Palladium where a character took a -6 Physical Prowess when using their offhand; with a 30 cap for strike bonuses, characters with a 36+ PP would be effectively ambidextrous).
A couple of games include the modifier for a stat of infinity ('Beyond' in Marvel Super Heroes, or '*' in SenZar).

Where a game has fairly limited bonuses on rolls from attribute (and/or used a die with a large linear range), it may require additional bonuses from ad hoc factors to generate logical results. 3.x D&D for example also applies 'size modifiers' to Str rolls to ensure that giants etc. have a reasonable chance of breaking down doors; DMG II for the game has a prodigy NPC template that gives a +2 to one stat, and also adds a +4 on d20 rolls. 3E-derived OGL game FantasyCraft has archetypes like 'Strong' which provide only a +2 to Strength [+1 modifier], but also give a 'double boost' perk (character can spend 2 action dice on Str rolls).
Marvel Heroic gives especially strong characters a Strength dice, but the contribution from Strength itself is low enough that the idea of using it for a 'strength check' is meaningless and questions such as 'can I throw a car at him?' are determined by GM arbitration rather than mechanics; this sort of thing is generally a feature of conflict-based resolution which determines if characters succeed or fail independently of how they attempt to solve the problem. Marvel Heroic characters can however have 'SFX' traits which add to ability-related pools, so that The Hulk can be generally stronger than other characters with the same Strength of 'Godlike /d12'.
Games can also add modifiers on attribute checks routinely for other reasons e.g.:
-4E D&D adds +1/2 level (the 30th level wizard with Strength 10 might have +0 from Strength, +15 from level) for consistency between mechanics.
(similarly, I'd seen an 0D&D houserule where you get to add +level to your (3-18) stat before rolling under with e.g. 3d6, or 4d/5d for a hard check).
-Savage Worlds gives a 'wild die' d6 in addition to the stat die, taking the highest - meaning a wild card with d4 Smarts, theoretically fairly dim, has a better chance of passing a Smarts check than a non-wild-card NPC with average (d6) Smarts; the extra die adds more of a 'curve' to results (reducing odds of critical failure).
-Castles and Crusades has 'primes' which decrease target numbers, largely replacing skills.
These sort of add-ons are potentially undesirable in being a 'kludge' on a system, or at least extra complexity. (Also, arguably players often like big numbers for stats, or at least a feeling their characters stats are superior, so having a low stat + a static bonus for a 'prime' or 'wild die' or 'level' may be less satisfying than a big number despite the same mathematical success chance. Such a system can obscure ridiculous results; a 30th level 4E halfling may be more acceptable with Str 8, extra +15 to Strength checks, than with Str 38). Also note that these improve success modifiers without affecting other functions of the attribute e.g. the Str 8 level 30 halfling has a better chance of breaking down the door than a 1st level 20 Str barbarian, but still has a lower lifting capacity.
Something else reminiscent of this would be 'deadlands' (see 'varying dice type' post): this is particularly weird in that attribute scores are have both a dice type and a number of dice, but only the dice type transfers to skill checks; the number of dice is used only for raw checks so a character might be good at stat checks but bad at skills, or vice versa. In a sense the 'number of dice' is effectively an add-on to the score that kludges the attribute checks but has no impact on skill.

Conversely, 40K future RPGs (Dark Heresy, Deathwatch) has a system for supernatural stats which increases modifiers to normal tasks without giving auto-successes on checks: creatures can have supernatural attributes letting them double their combat modifier, but which doesn't increase the stat for normal d100 under stat 'skill checks'. The bonus increase does exaggerate breakpoints for PCs with unnatural stats, potentially up to +2 on d10 for a 1% difference in stat. See e.g. description here (https://wh-40k.obsidianportal.com/wiki_pages/unnatural-characteristic) for details of how this sort of thing works.

Games where huge stats provide huge modifiers can also have systems to scale back relative modifiers e.g. JAGS, GURPS. See post 68 (Over the Limit).

Modifiers from attributes are sometimes considered to be independent from the skill/derived attribute they modify, or sometimes no distinction is made between points gained off attribute and other points. 3.x D&D (which opts for the first approach) often uses "skill ranks" (not including modifier) or "base attack bonus" as prerequisites for other abilities. Another instance would be GURPS where skill is bought based off [difference to attribute] rather than final score. Examples of the other approach would be Feng Shui or WEG (d6)Star Wars; in Star Wars a character might have a Strength of 4D, a Swimming skill of 5D, and improvement costs for the ability would be based off the total skill (i.e. 5 character points to raise it to 5D+1), regardless of base attribute.

Modifiers also vary in how pervasive they are through a game system. In some games modifiers may be rarely used and only on a handful of checks (Palladium), in others every task may have one or more modifiers (3E D&D). Modifiers can also sometimes be used negatively (e.g. Size and hiding).

Super Attributes
Superhero/mutant games may also allow for "super attributes". These might just just increase a stat, or be a rule letting characters buy up stats to ridiculous levels [e.g. DC Heroes]; however, some games have separate power rating which applies to "super strength" or the like - this makes power cancelling or powerless alter egos easier to adjudicate. In Aberrant in particular, rolls are [stat]+[mega-stat] which therefore doesn't require lookup of a modifiers table or the like, made reductions for dormancy, or being depowered, or on the other hand bonuses from use of abilities like shapeshifting, very easy to apply. Because 'mega attribute' dice potentially are more valuable than regular stats and make them irrelevant (2 successes per success, or 3 on a 10, plus extra abilities from enhancements) mega-stats can't be purchased to a level higher than the base stat e.g. a Str **** character could also buy mega-str up to **** (but not *****).  This same sort of principle sometimes is used in costing of 'feats' or the like; some Savage Worlds Edges like Charismatic that boost social rolls also have a Spirit minimum, the controlling attribute for these skills, to prevent a low stat from potentially being bypassed with other bonuses
 
Immortal - the Invisible War lets characters buy attribute points (in the game called "motes of immaculum") free-floating, so they can be reassigned between stats ("halo colours") at will. These are more expensive than regular points, although balanced a little bit by Immortal's difficulty system which normally requires additional stat rolls to accomplish actions - i.e. shooting someone through fog with an injury might require a red check (resolve) for the wound, a blue check (awareness) for the fog, and a yellow check (expertise [Dex]) for the attack itself. Without multiple stats being simultaneously applicable on a task, a free floating +1 might as well be +1 to all stats.
 
(relating to the idea of free-floating attributes, rather than super attributes per se, Fireborn has a rule on "stances" where a character can move dice from one stat to another, up to a maximum equal to skill. This handles e.g. a tradeoff between defense and offense, but was useable on most checks. Shifting dice this way on non-combat tasks is also common, the side effects then being largely irrelevant. Shifts from stance are very significant and with 1:1 exchange rate and so make actual attribute allocation in character design maybe not super important, although a characters split in physicals/mentals does also give their initial # of bonus physical skill points/mental skill points, which don't reallocate as easily)

Special Abilities from attributes
Games may also detail special abilities gained from super attributes, e.g. Aberrant added a list of Enhancements with purchase of a "mega-attribute" allowing selection of one enhancement e.g. Lifter (Mega-Strength), Taint Resistance (mega-intelligence), Regeneration (Mega-Stamina), etc.
A few other games with 'super attribute' powers often likewise add specific abilities as well as just a stat boost: Mutant Epoch lets characters with mutations raising stats to roll 'hazard checks' twice; Palladium super attribute powers in Heroes Unlimited often give a grab-bag of miscellaneous abilities as well as a raw stat increase e.g. greater lift capacity, extra skill bonuses, an extra attack for heightened Physical Prowess (Dex), or extra SDC (basically hit points) for heightened Physical Endurance. FantasyCraft has human 'talents' which add a bonus to a stat and related thematic effects - a character with the talent actually doesn't necessarily have a high stat, though it would be common (as point spending is most efficient that way), T&T Deluxe lets characters who roll triples generating stats (on 3d6), add and roll over, and specialists are also permitted to double their die rolls on certain saving throws relating to attributes (for instance, a 'ranger' DEX specialist can double their 2d6 when attacking with a specialty ranged weapon, or add +lvl to other ranged weapons' instead).

Other games have added extraordinary abilities directly based on very high attribute scores. AD&D included spell resistances and Regeneration for scores of 20 and above; the revision of the Immortals rules for Basic D&D included some special abilities for scores up to 100 such as "reload crossbow by hand at double rate" or "can cock trebuchet by himself or herself". Rolemaster also included the option of special abilities for very high scores (a number of lists being provided in Rolemaster Companion III which included the equivalents of talents, spell-like abilities, additional mechanical bonuses like increased healing rates or reduction of specific penalties; Companion IV expanded the list of strength effects to allow use of larger weapons one-handed etc.). While the abilities were often interesting, these often were things other systems would handle in a less ad hoc fashion though rules based off modifiers - Strength requirements for large weapons or a built-in adjustment to healing rate from Con, for example.
In 3.x D&D "Feats" were used to define exceptional abilities, with very high statistics being required for some feats (i.e. 19+ Dex for "Quicker than the Eye", 13+ Str for bastard sword proficiency, or 17+ Dex for Improved Two Weapon Fighting).
 
Conversely, games may also add specific disabilities for very low attribute scores. In Low Fantasy Gaming (d20) characters get bonus languages equal to Int modifier, and are illiterate if their Int mod is negative.
2E D&D notes that characters with an Int of 3 "cannot speak a language, although they may communicate via grunts and gestures", while Amazing Engine characters with a Fitness of less than 10 or so (on a scale up to 100) cannot run.
Games sometimes add these disabilities for situations where a stat is temporarily rather than permanently impaired i.e. Tunnels and Trolls 5th ed., where spellcasting burns Strength points, has a STR reduction to 2 indicatating possible unconscious and collapse (3 is considered fine since character stats are rolled on 3d6 - "while a character with a Str of 3 may have muscles which resemble water, they are obviously a viable character").

Fringe benefits for low scores: games may also attempt to compensate low-rolling players. objectionable game FATAL gives low Int characters a roll for "retard Strength". Some AD&D GMs may give characters ad hoc special abilities to compensate for low stat rolls - see thread here (http://www.therpgsite.com/showthread.php?t=26763). "Red Box Hack" allows only one PC per party of a given class; if two players want they same class, the lowest total attribute points wins first pick.
Modifiers can also be applied negatively in some cases, and/or it may be beneficial to fail some rolls (whether this is good design being debatable - its often particularly a bad idea with point buy, given that a low score is there a result of high scores elsewhere).

Attribute range: An attributes' range in the context of the system might represent a fairly routine range of ability, or it may be possible to roll or build a character that is severely impaired in an attribute, a setup possibly creating trap options for players. This could happen as a result of overly simplistic design (i.e. the designer sets up a random roll with wonky results, or uses the same modifier for both d20-based skill checks and HP rolls using d6, or decides that 1-10 is an intuitive-seeming numerical range regardless of the probabilities this would generate), or because PCs and NPCs have identical mechanics and a PC gets a more NPC-appropriate result (such as rolling up a 1st-level D&D fighter with 1 HP). Systems can allow maxing out of some attribute, but with the point cost reducing a character to broken elsewhere (Cthulhutech).

Fractional Attribute Values
Attributes may sometimes use fractional values (i.e. if a single whole point is meant to represent a major shift, like a doubling in lifting capacity [suggested by Stormbringer - the poster here, not the RPG]. A couple of games also use fractions in special cases such as D&Ds 18-percentile Strength (where the main score has a score from 01 to 00, generated with percentile dice), or HackMaster (which has percentile values for every stat e.g. 13/47 Dexterity, with characters getting minor increases to each percentage as they level). AD&D percentile Strength is interesting in that bonuses to Strength can be treated in any of three different ways entirely arbitrarily: a single point may skip all the d% business (18 to 19) as with racial bonuses, may give a 10% increase (the Wish, Strength spells) or may improve Strength one 'bracket'/row on the table e.g. from 01-50 to 51-75, or 91-99 to 00.
Pyramid 3-34 suggests a variant rule for GURPS to give fractional ST points to small characters (e.g. Str 2.5) to better differentiate between them, as most otherwise have identical Str (about 2). Allowing Str down to 0.5 also lets the system model birds, bats or 3" little people (there are of course other approaches to do this; see the post on Scale).
FUDGE allows 'half ranks' where each 2nd use of the rating gets a +1 bonus.

Derived Attributes

Many games have “derived attributes” (aka figured attributes, secondary attributes) which are calculated from the basic attributes in some fashion.
These can include
*ratings which are derived from a single attribute in a complex fashion, and perhaps subject to additional modifiers. [e.g. Savage Worlds as noted above generates a number of 'derived attributes' just to convert its dice rolls into averages - so Vigour of d6 becomes Toughness 5 [i.e. 2+half the die], then adds bonuses for armour].
*averages of two attributes (e.g. Runequest/BRP Hit Points = average of CON and Sz; movement rate is derived from STR/DEX in some systems e.g. Mutazoids);
*scores which have a base value derived from an attribute, plus additional points gained from level advancement or class bonuses, and perhaps random rolls (D&D Hit Points; spell points or psionics points in many systems ).

Alpha Omega reportedly has multiple levels of derivation, with normal derived stats (secondary attributes) being used to calculate further derived stats (tertiary attributes).
Dominion commonly uses a number of calculated averages for skills, so as well as skills based on the attributes these averages are listed as "composites" including a Combat Composite (Vigour, Agility), Priestcraft Composite (Stamina, Intuition  - strain on body and soul) and Witchcraft Composite (Intellect, Luck). Whether a characters rounds up or down ("Favourable Rounding") varies - a character can get it if they roll it as an ability, or if initial attribute rolls are low. Across many systems Combat or Magic are frequent situations where multiple attributes get involved also for game balance reasons: a character that's good at fighting or magic tends to dominate the game, other skills less so, though realism can also be a concern (RQ, HarnMaster).

Ouroboros Engine has a sort of 'reverse derived attribute' in Health: Health = ([Prowess+Charisma]/2)
What is interesting about this is that this is justified as being that healthier characters are more charismatic (attractive) rather than the reverse i.e. "the figuring runs in an unintuitive direction".

A derived attribute may be designed to be used in checks of some sort, or to function as a resource (e.g. hit points, spell points) (or both).

Derived attributes can have a result similar to “sub attributes” –discretionary points or special modifiers can give a character a derived attribute quite different to the normal base stat for some purpose, such as characters with low CON but lots of hit points. However, a derived attribute is typically calculated to perform a specific purpose – it will have a scale appropriate to that which is probably different to the base stat, and not interchangeable with it for other purposes, whereas a system using subabilities would probably let a character use their subability for a variety of skills and checks.

Some skill-less systems use derived attributes extensively in place of skill checks. A few examples of this (apart from older versions of D&D) are:
-Dragon Warriors; no skills (only classes in the form of “Professions”): the normal attributes are similar to D&Ds; derived attributes are strongly modified by class/level and include Attack, Defence, Evasion, Magical Attack, Magical Defense, Health Points, Stealth and Perception.
The main writers of DW also wrote a "Blood Sword" game book series: this is relatively complex and has a system like derived attributes (Fighting Prowess, Damage, Psychic Ability, Awareness, Endurance) based off choice of class and level (rank), but without their being any rolled attributes that modify them - e.g. any 3rd rank Warrior has Fighting Prowess 8, damage 1d6+2).
-Gamma World 4E (by which I mean the 1992 Nesmith edition, not the latest version); a limited system ofskills for classes is included, but most tasks rely on derived values including attack (“THAC”), mental attack (“MHAC”), Mental Defense (MD), AC, Health, Perception, Stealth, Remain Unseen, Speed (Base +Dex modifier), and Robot Recognition, and Hit Points. Different classes receive improvements at different rates and most characters get discretionary points every 2nd level as well (a flaw in the system being that 'one point' is added directly whether added to a base-0 value like THAC or suboptimally to a 35-60+ hit point total); the 1-point-improvement gives very conservative increases. GW's system also shows how the derived attribute approach can be slightly clunky, in that lots of numbers are generated, many for defaults that would be 'just an attribute check' in another system. As well as generating confusion or redundancy between derived attribute checks and ability checks e.g. Dex or ranged-THAC to lasso something, Health or Con to avoid food poisoning. Derivation also gives a tighter hold over how numbers are gained, but which may be not particularly worthwhile unless the numbers are very finely tuned to produce results.

-Castles & Crusades uses ability checks for many routine tasks, with skills are replaced by 'primes' - a character choose 2-3 primary stats for which their target numbers are greatly lowered.
Palladium might also be classified as a “derived attribute” system, though a very strange one; it has an extensive skill system but no attribute-check system and (for combat at least, and in a sense attribute checks) largely runs off derived attributes which are based off the skills, instead of using skill checks directly. Characters can get extra SDC (a form of hit points), bonus attacks per round, saving throw bonuses and attack bonuses, as well as attribute increases, by selecting the right skills. Monsters usually have detailed listings of attributes like Str, Dex, Int etc. equivalents, but with this information having usually limited use (there being no defined rules for making attribute checks).
 
Fuzion uses a lot of averages and other figured stats, although its mostly skill-driven.
Characters in derived attribute games are more complex (have more numbers) than in pure attribute games, though not so complex as with skill-driven games. Derived attributes often exist to interface with a particular sub-system, and there can be confusion as to whether the derived stat or the raw stat should apply e.g. Gamma World 4E lists lassoing as a use for a Dexterity check, rather than ranged THACO, or there can be uncertainty about whether to use Health vs. Constitution. AD&D likewise can have circumstances that could call for either a Dexterity roll or a saving throw - each of which would have very different mechanics chances of success chance, depending on character level.
Derived-attribute games may list monsters with just the derived stats, though usually raw attributes are often required as well: 0D&D had monsters with only brief statistics (hit dice, move, etc) and no ability scores, while increasing numbers of optional rules through 2nd edition often meant the GM had to determine monster statistics (Strength for grabs, Dex for trip attacks, mental stats for psionics rolls, etc), and increasingly high PC attributes often left monsters behind, until the High Level Campaigns sourcebook by Skip Williams (and then 3E) included monster stat generation rules. Holmes basic used Dex rolls for initiative, but neglected to include monster DEX scores.
Conversely, Palladium often gives monster ability scores despite these usually having no mechanical effect beyond what would already be included in the combat bonuses.
(See also here (http://www.therpgsite.com/showthread.php?p=729408#post729408) in this thread for a description of different types of modifiers).

Usually 'derived attributes' vary more than attributes do, but there are exceptions e.g. 4E D&D, HarnMaster Endurance (see next). Derived attributes bonuses can be kept under control by various methods e.g. using the best of two scores (4E D&D defenses), forcing low scores to be bought up if a modifier is negative (skills and powers skill scores), increasing base value and using a greater divisor to work out a modifier, changing to a different resolution method for relevant checks, etc. [see 'controlling bonus and penalty accumulation'], or making something an average of multiple attributes. A more controlled derived attribute can be deliberately used instead of an attribute to reduce its game influence e.g. Harnmaster originally had a single Endurance score for injury/death checks, but to prevent this being the 'god stat' in later editions made END the average of Str, Will and Stamina. A game might also give characters work-arounds for low values, e.g. advantages /class features letting them substitute another value or otherwise avoid a problem (e.g. the AD&D illusionist has a 'phantom armour' spell which absorbs damage, to go with its awful hit points).
Derived attributes are usually recalculated if the modifying attribute changes, although exceptions exist. D&D "hit points" having a minimum of 1-per-level means a later increase can be better than starting without a penalty. AD&D "Comeliness" is partly rolled, plus a small Cha mod initially, but later increases 1-for-1 if Charisma increases; Comeliness is higher for artificially-enhanced Charisma, though stat increases are so rare in AD&D this may be reasonable. Arduin gives double Con bonus to HPs for rolls over 16 initially, but not if Con is raised later.

A game could theoretically be categorized into one of three groups this way:
*Derived Attribute driven games (derived attributes are used for most checks); as discussed above.
 
*Skill driven games (i.e. most tasks use skill checks); these tend to have lengthy skill lists - basic tasks like Spotting and Listening may require skills (an exception to this being Barbarians of Lemuria, which has only a few abstract 'careers' but which depends almost wholly on GM interpretation). The major problem designing these though, may be balance between skills and the tendency of players to crank up combat skills in particular. Having rules for untrained use of skills is particularly important. (a 'skill driven' game could include both games with level-scaling skills a la 4E/5E D&D, but more commonly skills are improved individually). NPCs in these systems tend to be complex, with lots of skill numbers - it becomes more difficult to fairly generate one 'on the fly'.
 
*Attribute driven games (i.e. most tasks use raw attribute checks)- Tunnels and Trolls, Warhammer Fantasy 1E/2E, Marvel Super Heroes; HERO system, Amazing Engine; Summerland, Apocalypse World. SenZar also used attribute checks for most tasks i.e. skills and saves vs poison and magic etc, although attack and defense are level-based, as are hit points/magic points/attacks per round. Trinity [White Wolf] normally uses Stat+Skill like Storyteller, but has simple 'quick start' rules which has no skills and purely uses attribute checks (Physical, Mental, Social, Willpower [Psi] i.e. seducing someone rolls just Social, hacking a computer rolls just Mental).

(http://i1239.photobucket.com/albums/ff507/BSJ17/tntega_064_zpsgpsnzgqp.png)
Above: the level-up screen from the Crusaders of Khazan video game, showing fairly faithfully the extent of 5E Tunnels and Trolls' level-up options. CON increase is equivalent to getting more HPs, while ST, LK or DEX increase combat ability and IQ or DEX affect magic use.

Attribute-driven systems are usually fairly simple, at least as far as players/gameplay is concerned. This simplicity means that some differences between characters are flattened out -e.g. there's no distinction between a racial bonus to a stat and increase to stats reflecting skill/experience.
Monster statistics blocks usually need to include a full set of statistics (the exception here is Tunnels and Trolls, which often only defines only a single 'Monster Rating' for creatures); this is potentially simpler than other approaches which may require listing stats + a large set of skills or derived attributes, although some derived attribute games don't list attributes at all (older versions of D&D). Attribute-driven games usually have to build in attribute increases to give character improvement - a 'high level' character will have very high STR, CON, etc. and perhaps be somewhat superheroic.
Most of these (apart from early T&T, or the Trinity quick start) have skill lists;, a character either has/doesn't have a skill. To improve a skill a character must raise the related attribute (e.g. a WHFR pickpocket has better pickpocketing than other characters because their career provides DEX raises)- this gives some results similar to e.g. GURPS complex skill defaults but often has other side effects.

This distinction between the categories is related to the split between class/level and skill-driven systems but not quite the same. Most derived attribute games seem to be class/level games but level-based games can also be skill-driven with skill scores set by character level (Rolemaster; 3.x D&D for the most part), or even attribute driven (Tunnels and Trolls prior to 7th edition uses levels, but level advancement just lets the character increase their raw attributes - STR, DEX, CON, etc.). In practice most games are an admixture of the three types, but will trend toward one setup primarily. Where a dual setup is evident, a split seems to most often occur between the combat and noncombat (skill) systems e.g. 2nd Edition D&D has a bolted on skill system (Non Weapon Proficiencies) that are (almost) pure attribute checks, while class features and attacks/saves are derived attributes (notably, it lacks any form of attribute improvement aside from magic so unlike in most attribute-based systems the skills are permanently frozen).
Over time games often seem to evolve toward more complexity, which often means attribute-based or derived-attribute move toward being skill-based. Often an attribute-based game can add in skills giving minor bonuses without roll difficulties having to change much.

Proponents of non-skill based systems may prefer less complexity in character generation as one reason for this.
A game's premise will set some parameters about how much actual differentiation needs to be represented between characters - if everyone is an adventurer, perhaps that's not much. OTOH if a game is really specific, skills can at least differentiate two fairly identical characters based on background. Another question is if gameplay is likely to want or need skills to do extraordinary things or whether they're largely about fire-building or the like - as some said of 2E: "Most nonweapon proficiencies are redundant statements of skills that all characters should obviously have, but are part of the game because the players do not trust the DM to assume the PCs have obvious abilities without some quantitative rule to defend themselves". - M. Keaton on 2E NWPs, Forum, Dragon #257.

(thanks to Rob for BRP notes)

Related Posts: see also skills post for attribute+skill
Edit note 12 July: note I have revised my opinion of 5E, moving it from 'attribute driven' to 'skill based', despite skill bonuses being minor/binary.

Edits: mega-stat/edge purchase notes(*), weighting and distribution (*), low fantasy gaming note

Most fantasy or SF games have a ‘race’ selection step in character generation. In class based systems this gives extra differentiation between members of a class. Individual races may be part of a game for ‘system first’ reasons (the race has abilities that are interesting in the context of the game mechanics), or ‘setting first’ reasons (e.g. a desire to include something different to regular race options of other games). How much of the total 'pie' of character abilities is race-derived and how much is class-derived varies: D&D is maybe 75% class, while in say Tunnels and Trolls race is most important (giving up to x3 or more stat modifiers).

Systems with detailed advantage/disadvantage or power systems may be able to avoid defining a “race” option in chargen completely (e.g. HERO) – to belong to a given race only requires the player choose appropriate powers or Edges/Hindrances. Other point-based systems (e.g. GURPS) allow races as packages of point-costed abilities, sometimes with slight cost modifications compared to purchasing abilities individually. deadEarth is somewhat Gamma World-ish, but instead of mutant animal being a race a character might roll up a single 'cross-mutation' with whatever other animal species, on the standard mutations table; a player can't choose their 'race' and also, your 'race' could change if you're exposed to radiation and gain a cross-mutation, or get a roll that makes you lose a mutation.
 
Systems which evolved without detailed advantage systems usually provide the option of choosing a race, which then gives various advantages/or hindrances. Some of these games (e.g. Pathfinder in accessory rules), have race-creation systems. Savage Worlds Deluxe has a core system that almost could do away with race and just let characters choose advantages, but doesn't quite work since number of permitted advantages/disadvantages per character is fairly small - the optional race creation system adds a couple of new abilities but mainly increases the budget of merits and flaws.
2nd ed. D&D has a system for race creation based off converting monster manual creatures mainly, assigning them stat modifiers and the like but keeping listed abilities and largely not balancing them particularly. A couple of games that are human-only have races corresponding to different human geographical types/cultures (Conan D20, Zenobia). Spycraft attempts to have diversity in characters without it being racial, with the choices being Class and Specialty.

Some races being more powerful than others has been balanced in various ways in RPGs including:
Racial limitations and balancing factors (e.g. being unresurrectable, being unable to choose more powerful classes), point costs, level adjustments (3E D&D), having the race count as an Advantage or feat (e.g. FantasyCraft), having the race count as a class (e.g. Basic), having only a low % chance of being able to play a given race (race determined by a separate roll e.g. Dragonquest, Mutant Epoch), ability score requirements (sometimes of less powerful attributes), needing GM permission to play a member of a race, reduced maximum levels (D&D), slowed advancement or levelling (e.g. 2E AD&D xp penalties, Fantasy Trip overmen stat-buy costs [Space Gamer magazine #28]).

Race & Class
Systems may be designed so that particular races strongly favour particular (hopefully, stereotypical) classes, or can be designed so that combinations are relatively open. Some race/class pairups can be disallowed either specifically, or indirectly as a result of racial ability score, alignment, background or other class prerequisites being unachievable.

Basic D&D allows selection of races as classes (primarily for simplicity). This balances racial options at a (deliberate) cost of flexibility; with this setup it is not necessary to worry about how a given race's stat bonuses or abilities will synergize with class features as the PC can't select another class, and racial abilities can probably be more powerful. Basic races can modify attributes to a variable extent the same way classes do, by lowering Str, Wis, or Int in exchange for raising the "prime requisite" of the race, at a 2:1 exchange rate (2 points lost = 1 prime requisite point gained, in whatever the classes' main stat is). Basic in places found this confining: the Shadow Elves supplement for BECMI included a number of general skills for shadow elves that duplicate thief abilities, so that thief-type characters can exist despite everyone in shadow-elf society being basically fighter-mages (there are also rules to create shamans as a special add-on, costing XP).

Tunnels and Trolls usually allows any race/class though 5E notes that leprechauns 'have to be wizards' since they have innate magic, and also giving them limits in weapons useable (2 dice or less) 'not because of lack of weapons training, but because a leprechaun couldn't use anything bigger than a knife'. Hence, the rules use the class limitation to ad hoc represent a (logical) racial ability. (OTOH, Fairies are even smaller and can theoretically be warriors...they can use very few weapons anyway due to low Str, which would be even more of a handicap to a wizard in 5E T&T due to Str-based spellcasting).
Weapons having a 'dice limit' also produced strange results for an optional Arduin 'thief' class (Sorceror's Apprentice magazine); thieves could use weapons up to 4 dice e.g. normal swords, troll PCs picking up the class were likewise limited to 4 dice although a troll's 'sword' would be about a 12d weapon.

3.x D&D treats unusually powerful races as classes, allowing multi-classing between monster “Hit Dice” and regular class levels; this generally works badly for most multi-class combinations, however (this costs caster levels, means 'first level' (x4) skill points are gained for a monster Hit Die instead of e.g. rogue or ranger, and "level adjustment" may cost an inviable number of hit points).
Dungeon Crawl Classics (DCC) treats races as classes - interestingly, in spite of characters starting at 0-level without class abilities. To qualify as demihuman at level 1, a character must roll the race as part of a 'profession' initially e.g. 'dwarven mushroom farmer'.
Palladium treats some races (the more powerful ones) as 'Racial Character Classes', but most are available with any class. Some 'Rifts' classes are a product of augmentation e.g. juicers or crazies, with some class/race combinations not totally prohibited but with augmentation giving a random chance of death or lobotomization.
D&D variants sometimes attempt to limit particular 'unstereotypical' race/class combinations: they may be banned completely (AD&D), made a higher cost (Aces & Eights, reportedly), or given other penalties i.e. 3E D&D has "favoured classes" to avoid suffering xp penalties, or FantasyCraft (1st printing) had iconic classes/specialties which caused penalties to action dice unless modified via a feat. Conversely (and more difficult) some races may be rewarded for particular class combinations - 13th Age half-elves have an ability to subtract 1 from 'natural' die rolls 1/combat, to synergize with bard/fighter/ranger/sorcerer abilities which are triggered by odd natural die rolls/even natural die rolls.
Classes can also be customized for particular races e.g. if a class gets selections of other abilities, some of these may be race-specific. 3.5 D&D has 'racial substitution levels' which let characters trade in abilities for more racially themed abilities.
As well as thematically-adjusted versions of classes, powerful races might be given 'powered down' versions of classes - e.g. Palladium would have a few alternate versions of some classes for specific races, or 2E D&D has 'demi-paladin' kits giving some paladin abilities to non-human fighter/clerics.
Races may also have 'multi-classing' as a specific ability e.g. the AD&D half-elf (or 3E human, due to having any class as a favoured class). For elves or dwarves, multi-classing may be intended to represent the effects of long lifespans - starting characters being 50 or 100 years old and so get to be trained in two or three classes. A friend's skill-based game had a similar effect by having Willpower modify skill cap (a proportion of total points), with elves having lower Willpower and hence being forced to spread their points around.

Raw stat bonuses can lead to some pairups of race/class being useless; in 4E D&D for instance, slight accuracy bonuses are critical due to monsters of the same level having set defenses (the 'tyranny of accuracy') so that not having a racial +2 is generally considered quite poor. This led to later versions of races being given more choices on where to put their +2. 4e neo-clone '13th Age' tries to fix this by giving out some stat points [+2] for Race and some [another +2] for Class, with it however not being possible to apply both bonuses to the same stat. (Having this work seems like it would depend on how multiple-ability-dependent classes are, and I don't know the system well enough to comment on if it succeeds).  
Another unusual variant is, reportedly, Barbarians of the Aftermath (a post-apocalyptic expansion for Barbarians of Lemuria). Characters here can have racial options like 'mutant bear', but these cost 'career' skill points from the characters normal 4 career skills.

Race Progressions: races sometimes have scaling abilities, either because race is a class and has 'levels', or a race might just have the option to pick extra abilities later, or a race might get abilities scaled automatically based on a skill or something else - quite often an ability might unlock in an ad hoc way at level X (e.g. raptoran flight powers in D&D 3.5), or a weirder example is Newflesh characters for d20 Gamma World which roll a bonus biotech every time their base Fortitude save increases.
Classes can sometimes have race-specific variations that particular races can take, e.g. 3E 'racial substitution features', or some Dungeon World options; this might apply to initial characters, or could be seen as a form of race 'progression' where racially appropriate abilities are delayed to higher levels.
The Pathfinder 2E playtest also has a lot of racial abilities that are feat-based or gained with level progression; this has tended to generate complaints it doesn't make a lot of sense or that 'at 10th level your PF2 elf feels like they're as elfy as a 1st-level PF1 elf'. (A prioritization of game balance over reality). A way to compromise might be to have racial abilities that occur at level-1, but to have actually leveraging them fully require abilities that are gained at higher level, say if an ability requires a difficult skill check to use, or be partly limited like how reach needs 'Combat Reflexes' to use fully in 3E, or be a scaling rather than flat bonus.


Race & Attributes
Race can interact with attributes by providing a bonus to a stat (D&D variants), changing # of dice rolled for stats (Palladium), changing the maximum rating allowed for purchase in a stat without any change in cost (SenZar “GenMax”), applying a separate bonus on attribute checks without changing the score (e.g. Rolemaster adds a numeric bonus, FantasyCraft gives special abilities like 'double boost' to some races, Whitehack and Low Fantasy Gaming have  characters roll 2d20 pick best or pick worst /D&D Next advantage/disadvantage if a stat is racially modified), altering point cost for a given score (LegendQuest), or applying a multiplier to the base attribute (Tunnels and Trolls - normally rounding down, though Deluxe 'trends toward the natural mean', rounding down for multipliers and up for divisors - multiplication as an idea works badly with 'point buy', with 7E's point buy option ignoring race. Multiplying after chargen due to race change can also give crazy stats since bonuses from levelling or magic are then doubled or tripled as well). Adding flat bonuses to a score with point buy and an increasing cost per point basically provides a discount in cost e.g. in 3.5 D&D point buy an elf and a human can both have 16 Dex, but it costs an elf 6 points and a human 10, if the racial mod applies after stat purchase. (The opposite effect apparently occurred in Shadowrun-4E, where it was more optimal cost wise to buy a metatype for cheap Str or Body and then spend the points elsewhere, resulting in mixes like 'troll magician' being most point efficient, presumably due to mod applying before stat purchase).
 
Bonuses can be variable e.g. +d4; even a 'flat' +1 in AD&D can give a very variable effect (none to a lot) due to the strange way the bonus table is constructed, with a boost at around 10 often having little effect while 18 to 19 Strength for example gives a huge boost. Bonuses could be conditional rather than automatic - e.g. "slum dwarves have a 40% chance of gaining a +1 to Str" [hypothetical example], or Mutant characters in the Big Bang Comics RPG roll 3d6 for stats like other characters, but doubles/triples add and roll over. Characters can of course have attribute penalties - often a fixed minus though Palladium for instance uses fewer dice for low stats (e.g. elves roll 2d6 for PE with 12 rolling an extra d6, vs. humans 3d6 with an extra die on 17-18 [differs from later Palladium's 16-18]). Mutant Epoch has pluses for racial advantages but usually gives 'penalties' by defining an alternative rolling method, like d6 Appearance for a mantis-man or 3d6 for a mouse-man's Str,  perhaps since base attribute scores can be enormously variable (10-100) so that it would be easy for a penalty to cripple low-rolling characters without affecting exceptionally high-rolling characters much. Its also possible for a race to set a score at a fixed value e.g. Gamma World 7th Ed. (4E D&D compatible) which had race-as-class, set one racial 'prime requisite' at 16 instead of rolling, or 18 if both races rolled have the same 'prime requisite'.
 
A race might also apply a separate bonus on attribute checks without changing the score (Rolemaster, Castles & Crusades' extra "prime" for humans, 3.5 size bonuses, FantasyCraft 'action boost' powers increasing action die benefits), or an attribute can be modified non-numerically but by noting that for a certain race it operates in a specific context e.g. 'Appearance' stats may be assumed to be specific to the character's race in some systems, or Strength may be relative to other creatures of similar size/scale (as seen for some BECMI Basic D&D races e.g. in the flying gnome supplement "Top Ballista", FUDGE, or "Supernatural Strength" in Palladium). Race can also lead to 'ad hoc' adjustments of task difficulty: 0D&D notes that 'smaller and lighter' characters (e.g. halflings) may be limited to opening open stuck doors on a 1-in-6 chance, rather than the usual 2-in-6; the vagueness gives the GM some leeway to consider the characters Strength on that as well - '...c'mon DM, Bilbulk has a Strength of 16, he should still be 2-in-6...'. AD&D by comparison gave halflings a -1 to Strength but no other open doors penalty, overall a much better chance).
 
Races in some systems can also have "attribute minimums"  either enforcing rarity and/or to give 'plausible' results while keeping stat bonus not too high (e.g. AD&D 2E where no race including giants can have a Str mod. of more than +4). Some character generation methods can also be off limits to certain races e.g. AD&D Unearthed Arcana Method V (noted above under random-roll elaborations) generates very high attribute scores (up to best 3 out of 9d6 for some stats) but is limited to human-only (an early Dragon Magazine expands this to nonhumans).
 
Races can indirectly modify statistics, e.g. by having a point cost to purchase leaving fewer points to buy attributes (GURPS); or similarly 1E Shadowrun required a nonhuman character to reduce points in skills, cyberwear etc. by choosing "Metahuman" as 1st pick on the Priority Grid. Conversely, some 3E D&D races (such as undead or constructs) have "nonabilities" which are inapplicable (-) instead of having a score, which can act as dump stats raising scores overall (the elf with a 6 Con gets a Con of - when it becomes a vampire, avoiding the penalties but keeping high scores elsewhere bought with point buy).
 
To a lesser extent stats can also be modified through different access to classes which add stat bonuses (2nd Ed. Palladium Fantasy). Some systems can encourage PCs with high scores in certain attributes by adding incentives for the player to buy a higher scores (the dwarf gets an extra bonus to saves based on their CON, AD&D, or the Basic dwarf or elf earns bonus XP for a high 'prime requisite'), or removing penalties (the 3.5 half-orc with a 3 Intelligence has PC-minimum Int and so ignores the -2 racial penalty). Racial class limitations in AD&D also slightly discourage demihumans with high scores as many classes with high ability requirements (paladin, 2E specialist wizard, 1E ranger, monk) are human-only.
 
(In general I feel that "racial modifiers" to scores are perhaps largely unnecessary in point-buy systems - they often just lead to complications in the math involved if costs are non-linear (as in 3E). If you randomly roll your stats a +2 Con for being a dwarf makes sense, but if you're going to buy them anyway, you could just buy a higher CON to represent your dwarf being sturdy. The same can apply to classes, too - Maelstrom for instance has point-buy attributes, then adds optional occupation-specific bonuses and penalties that are redundant, largely cancelling out).
(A really extreme case of this that's especially awesome is the deity Ka, in the old Basic D&D Immortal's rules. Immortals normally have ridiculous AC and Hit Points, and can buy fairly silly Str and Con depending on their level; Ka is just described as being as intelligent allosaurus and is like 30-ft-long, which is entirely flavour text in the Immortals' rules; the only power needed to do it is "Size Increase" which actually lets you vary your size, IIRC. He also purchased I think about a 60 Strength, but any high-level Immortal could do the same. Though building younger Ka as a junior immortal would be problematic. The simple Immortals' handbook 'choose a couple of powers' option replaced fairly complicated and messy BECMI rules letting Immortals build avatar bodies from scratch.).
 
Talislanta gives a character exact attributes based on a racial template, with only 1-2 extra points of customization permitted (though multiple templates may exist for one race, which are different classes). In point systems a race may also have a point cost, indirectly reducing attributes (GURPS) or race choice may exist outside the point system (SenZar).

Race Availabilty
Availability of unusual races may be limited by minimum stats, a separate die roll (DragonQuest, World of Synnibarr, DCC where race is built into occupation roll e.g. 'dwarven herder', The Mutant Epoch; this last is interesting in having different tables by level of player experience), or GM fiat (e.g. only one nonhuman per party).
 
Race and skills:
Races may affect skills (in skill-based system, this gives some effects parallel to how race affects class).
Race-specific special abilities that interact with the skill system in an interesting way: reroll X checks (particular stat?), cross-match Y checks, autosuccess for Z checks, particular 'subeffect' gained more easily, action point cost for skill W reduced.

Races often modify skills (both with direct bonuses or indirectly via attribute modifiers, allowed classes). Races can also adjust skill costs (e.g. Dragonquest elves can buy Courtesan ranks for half xp), or cap skills (e.g. AD&D was notorious for giving 'level limits' to demihuman characters). Race can also just give bonus skills (5E D&D) - this makes e.g. all elves 'perceptive', but generally keeps bonuses under control since its redundant with perception from class or background, instead of stacking to make elves better than other characters.
Changeling gives certain 'kith' immunity to botching for about two thematic skills (you can still fail, just not epically); SenZar lets the arboreal Azaar raceclimb trees without a skill check (which 3E D&D also does via Climb speed allowing an automatic take-10), given that without this such characters would logically die.
Star Wars SAGA often gave races particular 'rerolls' on skills, an effect somewhat analogous to how 5E D&D gives some races 'advantage' on particular checks.
(This sort of 'reroll' power is something that is sometimes found as a selectable power e.g. a 'feat' or 'mutation' [like Mutant Epoch's super attribute mutations giving stat rerolls), showing how a race can be built largely of packages of generally-applicable advantages. That being something Whitson Kirk touches on in his 'design patterns' book too, with the darkvision trait).
How race affects skills can flow into how 'class' works, or not, since classes can be design to be skill-driven, or be a different set of rules. An example of this may be Gamma World 5E (the d20-system based Gamma World) synthetic characters, who are specifically bad at multi-classing because they are meant to be designed with particular core programming, paying 'cross-class' cost (2x) for skills gained from multiclassing, despite an increased skill cap.

Races may have specific weapon options either due to size, or via specific racial abilities (free weapon proficiencies, bonuses to damage with particular weapons), or through attribute modifiers (STR/DEX/etc). Note free weapon proficiencies given out for a race synergises negatively with some classes' having the same proficiency (e.g. barring extra rules, elves getting longsword for free is pointless to a warrior who already gets longsword). While size would be expected to modify weapons use, some systems tend to overlook this (e.g. 2E AD&D Dark Sun half-giants have no specified ability to use larger weapons).
Bonus skills for races can be useful in matching them to setting expectations around background e.g. if elves usually come from the forest, bonus Survival (forest) makes sense, or bonus Elven language makes sure all Elves can speak Elf. However, lots of built in skills can also cause problems when a character has an unusual background, say if they were raised by dwarves for whatever reason.

Other racial abilities:
Races can modify advantage purchase costs (e.g. AD&D 2E Skills & Powers trait system elves can purchase Allure more cheaply, while halflings receive a discount on Glibness).(cf. varying point costs (http://www.therpgsite.com/showthread.php?p=515934#post515934)). Games with 'feats' may include some race-specific feats. Racial abilities are sometimes defined as advantages - generally, meaning other characters can pick them up as well (though it could also be just to tie them better into some advantage-based subsystem, such as a power with a target number based on # advantages; 3.5 psionics has a a couple of abilities like this, e.g. a HP bonus based off # psionics feats known). This might also be specifically avoided so as to keep races more unique (e.g. 4E D&D specifically gives each race one 'power' unique to it while having a fairly consistent format - elves can reroll attacks ('elven accuracy') while halflings get 'second chance' forcing opponents to miss more often, humans get a bonus class power for their class, half-elves one class power from a different class, dwarves 'resilience' letting them use 'second wind' as a minor action).

Racial disadvantages might be allowed to be "bought off" with advancement if other disadvantages are, e.g. this is allowed for Alternity vampires (Dragon #264) who start with Pallor, and Vulnerabilities (Sunlight, Fire) "at the standard rate of 2x the cost of the flaw".
As well as raw attributes, race can also modify "derived attributes", most frequently hit points (due to size, for example)(see section below); interesting things here include Amazing Engine's Slathorp (which are amorphous and lack 'body points, having more wound points instead), or the way nonhuman anatomies (wings, extra legs) interact with detailed critical hit tables. Systems may also have racially derived saving throws (Battlelords of the 23rd Century). Race frequently also adjusts movement rate, whether that's a stat, derived score or something else.


Race and 'hit points'
Race often affects 'hit points', generally larger characters being tougher (an exception to this is 3E D&D/d20 system, where for creatures built as PCs, stat modifiers or reach would usually give a 'level adjustment' which would reduce total HPs). HPs are sometimes directly set by race, sometimes determined by 'size' (e.g. FantasyCraft). If hit points are just a stat (as in Tunnels and Trolls), race will have to give a stat modifier, which may cause weird effects e.g. a Tunnels and Trolls Troll gets x3 CON score for size, and hence is also much more likely to be able to pass a save to hold its breath underwater (for example). Using 'race as class', race may give class variations e.g. in Hit Dice. Races may get an ad hoc modifier, e.g. half-giants in AD&D Dark Sun doubled their Hit Dice (e.g. a fighter would get 2d10 per level). Extra toughness can also be generated by special abilities, such as a 4E dwarf having 'second wind' as a free action.

Final Notes
As with advantages, the more complex and detailed the games' other systems, the more specific a character's racial abilities have to be e.g. compare GURPS where exact Strength, movement, advantages and disadvantages would need to be defined, vs. say FATE where a character could have an aspect of 'Worlds's Greatest Donkey Mathematician' and apply the aspect bonus as required to running (physique rolls), not being allowed in bars (a compel), etc, albeit with GM adjudication frequently necessary.
Racial modifications are generally similar regardless of attribute systems, although this might be expressed as an attribute modifier in one game and miscellaneously in another. For instance, Rolemaster notes that different races have strengths in different areas of stat bonus modification (elves), background options (humans), Resistance Roll modifications, or Body Development ranks; comparatively a different game might just have various races getting bonuses to different attributes and yet cover almost the same ground due to the scope of what attribute scores cover.

Balancing racial special abilities: special abilities are sometimes 'overly limited' in game terms of what they can do e.g. 4E D&D thri-kreen have 4 arms - which just gives them the ability to draw objects as a free action (=equivalent to the quick draw feat) - and an encounter power with multiple claw attacks.
Special abilities might sometimes need extra skill points invested to work (e.g. making mind flayers take 'martial arts' skill ranks to get brain extraction special ability to work).

Racial subvariants
Fantasy games can have multiple slightly-different versions of races.
3E D&D for instance has 'jungle dwarves', 'desert elves', etc. as options in its 'Unearthed Arcana'; the variant choice is available for free and lets a player substitute a couple of racial abilities for e.g. terrain-based abilities. Some of these alter ability modifiers, etc.
AD&D 2E in contrast sometimes treats a racial variant as a 'kit' e.g. jungle dwarves have a  'barbarian, jungle dwarf' kit in Demihumans of the Realms. Making it a kit limits class choices in this case; unlike other race options it also takes up the kit 'slot' (i.e prevents a character being a Champion or Verminslayer or whatever).
In other games, FantasyCraft often has 'splinter races' which require a Feat to select. Talislanta has individual archetypes for racial variants, incorporating specific skills / base attributes /special abilities (there is one archetype, gao sea rogue [pirate], which is complicated by allowing various races). Some races are explicitly barred from picking up magic as a secondary skill where this would be imbalanced - the warrior race of Thralls are racially unable to understand magic, while the dual-brained 'Sindarin' normally have huge Int scores, but have one brain go crazy and die should they try to learn spells.

Race customization: some games may allow characters to slightly vary or tweak racial abilities. One of the more extreme cases was 2nd Ed. Skills and Powers, which gave a race a budget of character points which let them buy either the normal abilities (plus very slightly more), or adjusted abilities including abilities from other variant races and slightly specific or unusual abilities - extra weapon bonuses for instance. It was slightly weird in that you could, for example, have some elves who didn't have infravision or other really standard abilities. This sort of thing let players duplicate some extra abilities that might often be 'feats' or 'advantages' like 'racial weapon familiarity' within the expanded race-creation system, or could also be used as a race-creation tool for variant races by the GM if restricted from player use. This sort of thing might be duplicated by DIY race-creation in other games like Pathfinder, with GM approval, if you didn't have enough options already. Advantages/disadvantages can also modify - for instance it might be useful to have a disadvantage that takes away a racial ability for characters with unusual upbringing (e.g. elves who were raised by humans and can't speak elven) or ancestry; disadvantages are probably uncommon enough that's more reasonable than say Skills & Powers.

Interspecies Hybrids
The  2014 playtest revision of Synnibarr uses points to buy races, and lets characters buy multiple racial packages to be a 'hybrid' which I thought was interesting - the hole here being that humans cost 0 and get some minor abilities. Starcluster 3E has a system where a hybrid rolls for inheritance of individual traits/body parts; other games may have defined races for each racial type (like D&D half-elves and tieflings). 3E D&D has 'templates' which add sets of bonuses for being e.g. half-dragon, half-fiend, etc. Systems where race is represented by buying individual features avoid a need for cross-breeding rules - a character can buy a few appropriate abilities and claim to be a cross-breed. If a game has a race creation system (Pathfinder) this might also be used to build half-breeds.
A d20 game in progress here (https://forum.rpg.net/showthread.php?792323-I-am-designing-my-own-d20-Fantasy-game!) has Races which "consist of two Features each; a Primary and a Secondary feature. You can create a hybrid of two races by taking the Secondary Features of two different races."
Class systems sometimes include classes that progressively mutate a character into a different race, e.g. Dragon Disciple in 3.5 D&D (or Stoneblessed, or Gamma World D20's 'hybrid' advanced class [i.e. prestige class]). This approach mostly suggests a 'target' race duplicated has to be more powerful than the base races available, since otherwise a player would just choose to be the target race to begin with.
TrollZine #3 has an inheritance table for Tunnels and Trolls which lists 'Half Breed' as an option - "Pick an attribute multiplier of another race for one attribute and substitute for yours. You resemble that race" - the option here having to be an attribute modifier as T&T races only give attribute modifications. Unfortunately not selectable except at random.
Whitehack as noted in attributes, treats a race as a tag which counts as one of a characters' 'group' choices, and gives 5E-style advantage on two attributes (roll twice and take the best), chosen by the player rather than expressly defined AFAIK, as well as disadvantage whenever the GM deems that appropriate. Half-breeds pick only one attribute, a bit suboptimal although the GM may also choose to ad hoc penalize them less.

A common issue with half-breed races, for some reason, is that they may get abilities belonging to neither parent race.

Systems without races
A couple of class-based games that don't have a race selection option, instead add another 'step' to maintain a satisfactory number of choices. Mostly this means human-only worlds:
*the d20 Conan RPG has different races that are human ethnicities, but in a D&Desque format including attribute modifiers, skill bonuses, weapon proficiencies etc.
*Spycraft has every character select a 'talent' and a 'specialty' (FantasyCraft inherits this, with humans only getting talents but specialties for all, for an unusually complex chargen system). Talent is more race-like (attribute modifiers and special abilities) while specialty resembles a background (in the 5E D&D sense) or sub-class/kit add on to class.
*Beyond the Supernatural (Palladium) has a two-step class selection setup, where a character chooses a "Psychic Character Class" (P.C.C.) that includes attribute modifiers and special powers, then an "Occupation" which determines their skills.

Race and Game System
In games where there are several different games that are highly compatible, a character's "type" (which you could think of as either race or class, maybe) is actually determined by which game system you're using.
For example, its possible to have a Storyteller game where one character is a Vampire, one a Mage and one a Wraith, though those are technically different, compatible, 'systems' rather than being a 'pick race' option that's explicitly outlined in chargen. Something similar might be said to exist for Palladium (e.g. Rifts), or in other games where crossovers are allowed e.g. a D&D/Gamma World hybrid game might have what's basically an informal  'pick world of origin' chargen step for the player, before the normal race and class selections.

Race and edition changes
A race can have a 'niche' in one version of a game and have it eroded in other versions. One example of this is the AD&D gnome, which seems to exist to let dwarves be magic-users; another example is the Pure Strain Human in some gamma world versions - having a niche in that with more Int they have more technology, vs. this becoming e.g. a 'class' function (Examiner) in 4E (1992 edition) when classes were added.

(http://i1239.photobucket.com/albums/ff507/BSJ17/1181273823271_zpsgdh1xpsu.jpg)


These are defined traits which (unlike attributes) not every character has.
They might be binary (you have it or you don't), or come in multiple levels (less commonly).
Usually cost is related to how useful an advantage is, although apparently GURPS 1E (thanks Estar) sometimes under/over costed advantages to enforce rarity instead -http://forums.sjgames.com/showpost.php?p=1566965&postcount=3  (http://forums.sjgames.com/showpost.php?p=1566965&postcount=3)
Some advantages are fairly specific (you get a +x in a particular circumstance). Others are not just bought but then must be 'defined' further e.g. a 'noble background' would have a rank and social obligations that need to be described, or a Leadership feat cohort or 'mentor' might need to be built as a separate character. Too many advantages needing detailed specification can become wasteful of GM time; sometimes advantages might be designed to be interpreted more 'on the fly' to avoid this (maybe Fate Aspects).

Sometimes an advantage has an opposite 'disadvantage' - these might be costed the same (+10 for Precise Touch, -10 for Butterfingers) or a cost system might (as in the case of GURPS) reduce the points gained for a disadvantage on the grounds that a character is only likely to take one that doesn't have too much impact on their specialty/concept. Character points are sometimes related to some measure, such as 1 CP equaling a week of training. More likely costs will be related to utility of an ability, although some systems also set an artificially high cost for certain things to keep them rare (e.g. GURPS "Unusual Background" advantage).

A disadvantage system (as pointed out here (http://gamedesignfanatic.blogspot.com.au/search?updated-min=2009-01-01T00:00:00-08:00&updated-max=2010-01-01T00:00:00-08:00&max-results=50)) has the goals of compensating characters for flaws (which they might've taken for RP purposes anyway), and encouraging characters to be more interesting. These two goals are slightly at odds with each other since the second requires a PC be encouraged to load up on disadvantages up to a limit, which is more likely if they aren't actually that much of a hindrance, while the first suggests cost should be allocated fairly.
Systems while have extensive 'super power' subsystems may avoid needing distinct advantages since most effects can be modelled using powers (e.g. Marvel Super Heroes), though more commonly there are two distinct subsystems.
Binary-cost advantages which require checks may piggyback off another rating for use - skill, stat or another check - thus making the other rating slightly more valuable to that character. They can also just add bonuses to other checks in some cases. An interesting sort of example of the possibilities of design here might be the 'Wealthy Relative' advantage in DC Heroes 3E - the character gets a wealthy relative to sponge off who has a Wealth rating of (PC's Wealth +3) if they can be persuaded to part with their cash. A similar effect could be modelled by letting a character just buy a Wealth rating with a cost multiplier to account for the limitations here - parallel to how it modifies power 'factor costs'. (As designed, the advantage has a cost flaw in that there's a Wealth minimum before the advantage is cheaper than just buying a Wealth 3 points higher; this is a general problem with advantages that are fixed-cost, fixed benefit when ratings have nonlinear costs).  

Older game systems can also have "disadvantages" and "advantages" that function in an ad hoc fashion - without their being a single, unified way of choosing them, or costing method. For instance, Palladium lets some mutants buy up/down mutant features ("Speech, Looks, Bipedalism none/partial/full) using BIO-E, plus has random background tables, insanity tables, % random psionics, and other specific rules governing edge cases for other classes and races: a mutant could roll 'ambidexterity' as a mutation abnormality, or a phobia of the insanity tables, but they're not generally buyable. A "cyborg soldier" (Ninjas and Superspies) can 'sell off' body parts for more bionics $ budget, but most characters can't (the way a GURPS character could). A 2nd Ed. D&D wizard can trade spell schools to 'specialize', something that could've been (but wasn't) a feat in 3E. Talislanta has no 'advantage/disadvantage' system, but has a huge list of archetypes that are very specific - these may include a number of abilities that would ordinarily be separate options as built-in features.
(It is also quite possible, of course, for a player to choose to have problems or flaws without there being explicit mechanics for this at all. In a sense disadvantage systems distrust players to not naturally do this.)

Disadvantages usually have an up-front benefit i.e. extra character points are gained for taking a disadvantage, such as in GURPS. In some games, e.g. Savage Worlds, the character just selects an additional advantage for each disadvantage or equivalent other benefit (Savage Worlds does however have more powerful advantages which just have higher prerequisites, like 3.x D&D feats do). Other systems have more complex costings - GURPS has variable costs for everything; MasterBook divides advantages and disadvantages into multiple levels, with a disadvantage allowing another advantage of the same level but not usually one of a different level, so there is no exact comparison between levels possible. HERO distinguishes between fixed-cost advantages/disadvantages (“adders”) and those that apply proportional cost increases/decreases, with multiple disadvantage ratings added to give a cost divisor; DC Heroes (3E) uses a “factor costs” table (i.e. a factor cost 5 skill/power with a +2 cost advantage would become factor cost 7, and would use the "7" column to determine total point cost for N points of a skill or power). (See in the powers section here (http://www.therpgsite.com/showthread.php?p=503267#post503267) for more on advantages/disadvantages for Powers specifically).
As noted under attributes, attribute points might be purchased as a separate step to advantages/disadvantages (typically before), or there may be a single 'pool' used to buy everything. The second approach means that a disadvantage can potentially generate attribute points (not just advantage points, or skill points), or that a character buying an advantage is potentially giving up attribute points to do so. Using the same pool therefore makes advantages more measureable in terms of what they're worth, and hence the added flexibility comes with need for more detailed analysis of costs, to avoid min/maxing problems. 'Young' in Savage Worlds for example, comes with the problem a character gets one stat point for it (as a Major Hindrance) -but it has an effect of immediate loss of two stat points. Or SenZar has advantages like 'attractive' or 'keen senses' that add +1 to stat per level, which often cost the same as adding +1 to the stat, for stats less than 11. Segregated subsystems would make this sort of cost comparison impossible or at least indirect. Likewise advantages and skills being bought with the same points makes advantages giving '+x to a skill' potentially broken cost-wise (as seen with GURPS Eidetic memory, but also an issue with advantages that let characters apply skills to duplicate other skills, as either the advantage or the other skill may be overcosted).

Instead of gaining or costing points initially nWoD Storyteller and FATE instead provide xps or 'Fate points' when a disadvantage comes up in play; in FATE this allows the same traits (Aspects) to function as both advantages and disadvantages - although being freeform (instead of from a defined list) they are limited to only adding a bonus or penalty, instead of having defined effects.
Aspects in FATE are generally very open to interpretation- a few examples may be given but unlike e.g. GURPS, they don't need detailed mechanical differentiation (some FATE variants have 'stunts' however, which may have their own little subsystems). On the other hand as it is said here (http://forum.rpg.net/showthread.php?474043-You-don-t-like-Fate): Aspects can easily be bland; when "Trained by Swordmaster Vortex," "Strong," "I'll do anything to help my true love," and "Woosh!" all have the same mechanical effects, it's pretty easy to see why some people might think the mechanics all feel samey. (Anyone complaining that Savage Worlds is 'bland' should go check out FATE).
Aspects do seem to go beyond what normal advantage/disadvantage systems do, being integral to or replacing a lot of game systems in some Fate versions (e.g. Legends of Anglerre). They are sometimes criticized for requiring 'fate points' to be spent for bonuses the GM would often just give for roleplaying in a traditional system (e.g. post by Obeeron here (http://www.therpgsite.com/showthread.php?t=28736&page=2)).
Miscellaneous WTF: rpg.net thread on 'negative compels' (aspect compellable due to being inapplicable) here (http://forum.rpg.net/showthread.php?551222-Fate-quot-Negative-Space-quot-Compels-huh). Aspects being 'paid for' anyway perhaps may also encourage strange aspects to be allowably invoked, GM willing e.g. a player might be able to invoke a weird aspects since its essentially a 'reskinning' of just invoking another aspect they could have used instead. That could give rise to weird narrative scenes (like where in Mad Max: Fury Road a sudden hallucination makes Max block an arrow to the face just in time - which you could see happening in FATE easily).

In most games how advantages/disadvantages can be tested with checks or interact with dice probabilities is fairly nebulous compared to, say, the standardized bonus systems for how attributes or skills give roll modifiers. GURPS has a '+1 per level of trait', while Cortex as noted above uses die codes (d2, d4,d6, etc.), and Fate has a blanket 'Aspect gives a +2' rule (although its usually fuzzier than that, perhaps since aspects are typically special traits that are often more qualitative than quantitative). Systems with detailed predefined advantage lists sometimes are built with a general guideline ( e.g. +4 for D&D feats, +2 for a Savage Worlds edge), but with individual exceptions where a trait is more valuable.

Other Elaborations
*World of Terath (http://www.datapacrat.com/Art/Fiction/STORIES/FUR/WORLDRPG) has an interesting disadvantage costing system that involves step dice. Disadvantages are rated from d4 to d20 (rarely d100) rated in severity; a rating in it is assigned (giving bonus points) and in game a roll against the rating with the appropriate die indicates that the disadvantage applies. Hence the more debilitating the disadvantage, the more points are gained from maxing it out. 'Deep Sleeper' is a d10 disadvantage and could earn up to 10 points (the actual # being rolled against to wake up), while illiteracy is only d4 and so worth a maximum of 4 points (roll against actual rating to read something). Some disadvantages also had variable severity and could have various die types.

*Gamma World 3E has defect mutations (like inability to feel pain, a need to be immersed in water occasionally, etc) - these have a 'defect score' rolled on 3d6, similar to an attribute score (or mutant power).

*Instead of there being a general points pool or having each advantage chosen balanced by a disadvantage, advantages/disadvantages could just cost attribute points. e.g. 5E D&D lets humans trade stat points for a bonus 'feat' (and later, feats replace ability increases). 'Milleniums and Mutations (http://wizardawn.and-mag.com/game_mm.php)' supplement for T&T lets mutant animals pick up to 4 special abilities, but with each costing 25% of an attribute score (rolled randomly; additional rolls of the same score are ignored). Attributes are usually fine-grained enough that this would allow multiple degrees of advantage/disadvantage. This setup makes the relative cost of advantages/disadvantages very measureable as noted.

*ROAR (Rick’s Own Adventure Rules; a free rpg, now extinct) did not have a separate purchase of advantages; instead attributes provided pools of “faculty” points if high, or “flaw points” if low, which had to be spent on appropriate advantages/disadvantages. A high DEX character might be ambidextrous, while a low CON character might be a haemophiliac or sickly; a low CHA character might have social issues, pox scars, etc.

*Synnibarr 'skill points' (which can actually be used for a variety of things e.g. purchasing mutations and bionics) are based off [2x total of initial stats] rather than being a fixed pool separate to stats, or bought from the same pool as stats. The issues here are basically that a character is doubly boned by low rolls - a low stat and less skill points - and its questionable realism as well in this implementation (higher STR = more knowledge skills, or mutations?). Characters can get bonus skill points for choosing defect mutations, and also get bonus skill points by levelling, with more powerful classes not getting bonus skill points from level until higher levels in some cases.

*SenZar has a point system used to purchase advantages and attributes (from a budget of 100 points), which unlike say GURPS is wholly separate to its experience system. Characters can earn points for good playing, while XP from killing monsters adds to level (which has basically no effect on attributes or advantages). In essence it works as GURPS + D&D running side by side, instead of the usual hybrid where character level gives more points. AD&D 2E with 'skills and powers' is distantly related in that characters could buy a number of traits as well as having a class/level, but didn't combine the attributes and traits budget or allow traits to improve after character generation.

*Random systems may have random disadvantage determination i.e. HarnMaster characters can gain bonus attribute points by rolling for defects on the Medical Conditions Table, with some races trading out specific results e.g. elves gaining sterility instead of pox scars.
Gamma World (older versions) has mutation tables which includes both positive and “defect” mutations.
Mutazoids has random-roll mutation defects, but characters can spend points (=Power attribute) to buy off some of these, instead of purchasing powers or general mutations. (Mutazoids is also interesting in that it rolls descriptive mutant features area-by-area; a character rolls on a specific table for each of head shape, nose, mouth, teeth, tounge (sic), ears, eyes, arms, hands, torso, legs, feet, hair, skin texture, body colour, reproduction, diet, markings, head ornament, tail and wings. This does prevent characters rolling duplicates, but is a bit slow given that most rolls are 'normal' and can give mild-mutants that roll badly and get severe mutations.
 
*Unisystem has a number of advantages that are packages of minor advantages e.g. a Slayer in the Buffy game gets some levels of 'hard to kill' and stat bonuses, as well as enemies and obligations; an "Occult Investigator" in Army of Darkness gets a skill bonus and mental attribute points, as well as a drawback of curious about occult things. It does this sort of pre-packaging in an apparently ad hoc way, as compared to say GURPS where packages (like races) are bought as packages.

*Pathfinder has two separate advantage systems, Feats inherited from 3.x and an optional system of "traits (http://www.d20pfsrd.com/traits)" which fill a niche for lower-powered abilities (since feats are large/granular and there's no varying costs as in for example GURPS).

*3.0 feats could arguably have had a role in replacing subclasses/multiclassing, but ends up being redundant with 'open' multiclassing.

*DC Heroes 3E is also interesting in that it modifies bonus points for disadvantages when taken by a character with a higher point total. If a character is built with x2 normal starting points, a 25-pt (base) disadvantage would be worth 50 points, while a Superman-type built with x10 normal starting budget would get 250 points for it. Hence RP-based disadvantages that are always somewhat of a nuisance (like Married or Secret Identity) don't become less attractive as the number of points splashing around in chargen goes up. 3E has a specific problem with this and the "Pet" advantage, which should be exempt from scaling IMHO as the pet already has an inherently variable cost based on how awesome the pet is (1/2 what it would cost to build as a character).
A (sort of) similar idea is found in the Invulnerable RPG, where characters of higher Awesomeness Level can take more points in disadvantages [8+2/level], whereas GURPS has a GM-specified limit that may be some multiplier of a characters' total initial points. In these cases characters can take more disadvantages, but the individual disadvantages are still as bad. Some might be partly offset by some skill or power that becomes more affordable, however.
Some  classes of disadvantages relating to powers, alternate forms, etc. may be limited to superhuman characters (for instance, BESM notes this is the case for some of its disadvantages) - if a character is limited to a maximum number per category, this as a result indirectly increases the allowed size of the 'disadvantage pool' for supers.

*HackMaster has random-roll disadvantages but with results each providing different numbers of 'build points' (BPs) based on severity, or lets players 'cherry pick' disadvantages for set (lower) numbers of BPs. It lets BPs be spent to reroll some random rolls as part of chargen (e.g. ambidexterity, family heritage, social status).

*HERO I think allows for advantages to have separate modifiers themselves like limitations that will modify their cost. Adding a 'requires a roll' modifier for instance could create a sort of lower-value 'partial advantage' that works sometimes, instead of reliably.

*Advantages that require skills to use: Mutant Bikers of the Atomic Wasteland [2nd Ed] has "Gifts" (including powers), and then has skills to use those, which default to Good instead of having to be bought up with skill points (a "Good" rating normally costs 3 points out of 30 initially; so the intention is to make it possible to roll against Gifts without these actually handicapping skills separately, the choice of the Gift itself being the resource). Similarly, Savage Worlds powers (such as magic) have a skill-rating bought separately; this does default to untrained and so costs skill points in addition to the Edge to get the power.

*The 'Golden Open Gaming' D20 system variant expanded the basic D20 stats by including feats which allowed characters to roll up additional attributes (Appearance, Sanity/Insanity, Luck, Education, and so on). Unfortunately while having the attribute was often a prerequisite for other feats (like mechanical skills requiring Education, or seduction feats requiring Appearance), paying the feat and then rolling often generated scores that were less-than-average that shouldn't logically meet prerequisites. Hence a character might pay a feat to be ugly due to a poor roll (e.g. rolling "Appearance" with 3d6 and getting a 5), but could still select the 'stunning cleavage' feat based off Appearance. There was also a "Limited Education" negative feat which was bought after the Education feat, limiting maximum to 8 - 'so your salt-of-the-earth mechanic type can purchase assorted technical feats without becoming a brainiac' - but with a negative feat granting a bonus feat, taking this made Education actually free. This sort of mechanic could work if the game had also had a 'disadvantage limit' on how many disadvantages could be taken - if so while Education was still free with that disadd, the disadvantage would at least be taking up a 'slot' that could be used to take another disadvantage that could fund any feat, thus being an (albeit minor) limit upon character-design.

*Tristram Evans' *Venture Bros (http://pariedolia.weebly.com/exegesis), has a random-roll system where a character can refuse a randomly-rolled trait, but then has to roll 2 random traits instead, giving some player buy out if they especially don't want some character feature but at a cost.

*Low Life for Savage Worlds has a weird race (Bodul) which has a 'strange' racial ability letting them choose as many hindrances as they want (getting an edge for each) instead of the normal 1 major/2 minor. Low Life hindrances tend to include physical weirdness traits like no arms, making it work as a mutation system particularly.

*As noted earlier advantages can be purely either/or, or come in multiple 'levels'. D&D 'feats' sometimes automatically level up, or sometimes a player needs to select another feat to improve them. 13th Age lists specific tier-based benefits for each feat ( a character automatically improves their specific niche rather than being able to shift their focus).

Psychological defects may include absolute limitations (“the character can’t do something/must do something”), trait values that are rolled against (i.e. SenZar has “karmic saves” i.e. roll over your arrogance score to resist being taunted), or may use an attribute check such as a Willpower check to avoid disadvantage effects (this last may be abuseable). Disadvantages with their own trait scores may overlap “Personality traits” systems found in games such as Pendragon. Similarly, Dying Earth builds mental disadvantages into characters automatically by assuming characters are susceptible to most forms of temptation (requiring a roll), unless specific resistances are purchased to traits i.e. "resist Gourmandry" or "resist Pettifoggery". Unisystem lets characters buy off RP-based disadds with good roleplaying, rather than just spending points. A game may sometimes sell a disadvantage for having to play a character in a derpy fashion separate to actual INT score e.g. SenZar's disadvantage "Total Stupidity" (which characters with high Int could actually take - meaning they're just especially thoughtless). (This is handy in SenZar for giving PCs some human foibles, as its relatively cheap to put up every stat to human-max at at chargen).
 

Scope of Advantage/Disadvantage systems
The scope that advantages and disadvantages covers depends a great deal on how the other main components of a character - attributes, race, class, and skills - are defined e.g. we can look at  
*advantages vs. attributes:
*advantages vs. skills
An extreme case is the PDQ system: characters have 'qualities' which are advantage-like, although they vary in rating rather than being yes/no; these can be skills, racial features, etc. A quality is rated -2 to +6; they can be anything but are 'spun' in that direction. If a character is "Hook-Handed" at +2 it can be used as a weapon or threat or etc, (unlike FATE) only if rated negative does it generates complications.


-Advantages vs. Attributes:
*advantages vs. attributes: An advantage in one system might be an attribute in another - for example compare the 'Handsome' advantage in GURPS vs. Physical Beauty in Palladium (a statistic which can be randomly rolled). Conversely, Palladium psionics are rolled off a table as "none; minor; major" and then powers provide ad hoc bonuses, whereas another system might have a Psionics attribute (e.g. Space Master), and the modifier provided by a power (e.g. Dodge bonus from a Danger Sense type power) might be based off the Psi attribute modifier. FATE variants often only have 'Aspects' and no attributes. Special abilities such as 'ambidexterity' might be advantages in one system (perhaps with a stat requirement to purchase), but occur automatically off a high attribute in another system that doesn't use advantages.
In a point system, Advantages/Disadvantages may assist a system in reducing its number of attributes and/or keeping its attributes balanced e.g. GURPS treats various levels of “Appearance” and “Will” as advantages, leaving it with only 4 core stats. Unisystem has advantages which often add bonuses directly to stats (despite these being rated only 1-5).

Advantages can also overlap the same sort of ground as 'subabilities', though often defined advantages will give larger bonuses than are given by attribute and/or stack with attribute bonuses. There can be problems with overlap between advantages/attributes if one is cheaper and better - e.g. Champions (some versions) selling off END to buy 'End Reserve' instead for half the cost.
Disadvantages can be useful in e.g. supers games for adding limitations /weaknesses to characters - a human element - even though the system might be set up so that heroes have stats higher than human normal in every way (DC Heroes).
Statting a game element as an 'advantage' vs. an attribute perhaps affords a little bit more flexibility with it - in some games advantages can be further modified with other enhancers or situational limiters. Multiple options might be built in more easily than with attributes (at least, ad hoc defined attribute effects are relatively rare) - for instance HarnMaster has a Voice attribute which specifically improves Singing and Persuasion type skills only, whereas a Deadlands character could choose 'The Voice' edge and take one or more of a 'soothing voice' (Persuasion bonus), 'threatening voice' (Overawe), or 'grating voice' (Ridicule). Advantages/disadvantages being descriptive instead of just numbers sometimes means creating extra rules ("a character with Monstrous Appearance cannot also have Attractive" for instance, as opposed to different numbers which are mutually exclusive - a score can't be -1 and +1 at the same time).
Potentially if a factor affects another attribute - such as Size increasing Strength - probably buying of both will work better if handled at separate steps, although it is possible to instead have a rule where both must be within X points of each other.

-Advantages vs. skills:
What is a skill in one system might also be an advantage in another, or vice versa.

Advantages may be distinguished from skills for a number of reasons:
-skills being in multiple levels vs. advantages being purely you-have-it-or-you-don't.
-skills representing learned abilities while advantages are innate (WoD merits)
-different level of abuseability e.g. combat/noncombat (3E).
Or they might not be. HERO skills are a separate category but may as well be a sort of 'advantage' within context of that game, for instance (purchased the same way).
Mercenaries, Spies and Private Eyes has things that probably should be 'advantages' including "Title", "Secret ID/Double Agent" or psychic talents but that are just part of the skill list; the latter while purchased as a skill also require extra checks (Int roll) to see how useful it is. Rolling advantages into the skill list this way does mean it doesn't cover 'disadvantages' (all skills being positive), and for MSPE means INT (which gives # skill points) is paying for a character's title or secret ID.
Some abilities can be framed fairly ambiguously as either skills or advantages - contortionist vs. double jointed, seduction skill vs. 'attractive'.

Characters may also get fewer advantages than they do skills, which means that making something an 'advantage' makes it rarer. A good example of this would be Advanced Fighting Fantasy: in the first edition of this, the special skills 'Dark Seeing' and 'Strength' (giving +1 damage rolls) were both skills, but so powerful that nearly every character would have them, bought from a number of Special Skills equal to starting SKILL (of 7-12). The second edition of AFF added rules for 'talents' (=basically feats) and made the equivalents of these - 'Strongarm' in the case of the Strength damage bonus- both talents. 2E AFF characters have only one talent initially, and a larger list of talents to choose from, make these capabilities much rarer.
Advantages handling skills badly; Gurps 3E has a 'literate' and then also a 'semi-literate' advantage; I gather it halves reading speed.
*Quite often a game with detailed skill ranks will have some learned abilities that are yes/no, e.g. languages in many games, or 3.x D&D Feats.
WHFR has 'skills' including a number of things that would be specific abilities in other systems. MasterBook lets a character take 'unable to speak campaign area language' as a specific disadvantage, while another game would define that with (absence of) the relevant skill, in a more consistent fashion but greatly under-rating the impact of lacking the skill choice. Summerland uses 'tags' that can include either advantage/disadvantage or skill type abilities, which then modify the attribute checks used to resolve all game tasks.
*advantages vs. classes: Savage Worlds has 'Professional Edges' which are part of the advantage system but (on top of the skill system) replace classes.
*advantages vs. class features: what's possible here depends on how valuable a 'class feature' is, vs. an advantage (e.g. feat).
The relative value determines in which direction this can go. For instance, a 3E cleric has "domains", which include bonus feats, making a domain largely as or more valuable than a feat. That mostly disallows there being a feat called "Extra Domain" (unless its argued that the specificness of the feats available with the other domain powers offsets their actual value).

The presence of disadvantages may act as a factor driving consideration of how skills or attributes are scaled. For instance, skill may default to 0% in one system while another has a higher default, with complete inability still possible for characters but modelled as a Disadvantage (e.g. 'All Thumbs' in Savage Worlds for the truly 'Savage' primitive, unable to use mechanical devices).
Some 'advantages' can be duplicated by built-in systems. Some games for instance have an advantage raising a characters' purchase limit for an Attribute; in a sense this is not much different from just costing more points for a very high stat, apart from any psychological effect to the player (they know their character is considered superhuman).  

Disadvantages frequently have some sort of cap on how many points can be taken (e.g. GURPS has a variable 'disadvantage limit' set by the GM, while Savage Worlds automatically sets a limit of 1 major/2 minor). A disadvantage limit reduces the necessity of having +1 advantage be worth 1 disadvantage, although making disadvantages not-really-serious does handicap characters who opt not to take any.
Disadvantage limits may need to be higher if fairly ordinary build features require disadvantages to select e.g. is disadvantages are needed to 'buy down' attributes or skills, vs. what would normally be allowed with free distribution of points.
GM oversight may also be required; a game may assume that either the GM will monitor abusive combinations in character generation, or that they will adjust game play so that Disadvantages will be engaged in-game no matter how bizarre they are (this last is incompatible with some playstyles, and may require more GM oversight of hindrances taken). Some games cost hindrances based on frequency of occurances (i.e. Fuzion on an ad hoc basis, or HERO -4E anyway - had a random roll for each disadvantage on 3d6 to see if they would occur in a session, with higher frequency meaning more points) - this is incompatible with some playstyles where the GM engineers situations to deliberately exploit character weaknesses (the higher bonus points for commonplace hindrances is irrelevant - you may as well have taken the uncommon weakness to Kryptonite for more points if the GM was going to work it in anyhow). Disadvantage lists sometimes include minor things such as 'quirks' which really have no major negative effect, but act to reward detailed character concepts with more bonus points.
Disadvantages may sometimes (like some advantages) have some sort of prerequisite to select; this can be counter-productive if the prerequisite's cost uses up too many of the points generated by the disadvantage.

Characters might be allowed to add advantages or disadvantages after character generation, or not. Most allow disadvantages such as missing hands etc. to be gained from play, with no gain in points; Unisystem allows characters to voluntarily add disadvantages with GM approval for points in addition to this ( e.g. 'gaining levels of deafness due to off-screen practice in heavy metal bands'). If some can be bought off or gained also depends. In some games e.g. Supernatural the game specifies that some advantages will require 'story' reasons, but with the assumption the GM will make adjustments to the story to facilitate this.
Some systems might also allow characters to replace a disadvantage that no longer works with a different one, likely with GM permission that this makes sense - the character who doubts the supernatural taking a vow to destroy demons after realizing they exist, a character who loses a ward instead having depression, the battle killing a superheroes' arch-nemesis being violent enough to get federal agencies after them. Probably this works more easily in a game where many or all disadvantages have the same cost (e.g. Savage Worlds with its minor [=1pt] or major [=2pt] disadds. Buying off a disadd is relatively easier if it generates fewer points compared to character advancement i.e. if a character could pay it off in a session or two (again SW) instead of six sessions (a serious GURPS disadd being maybe six sessions of CPs) although the GM might be forced to allow prespending of future CPs if removing it has to match in-world considerations.

Potentially a damage system could tie into disadvantages/advantages, with X damage giving a character a -X flaw (particularly for something physical like 'scarred' or 'one eye'). The closest equivalent in a system I know of to this, however, would be Drain in Champions, which reduces stats or powers with an effect measured in character points. (One quirk of this method being that presumably abilities bought with cost-reducing limiting factors would be drained more quickly).

General Note: From a player POV, advantage/disadvantage systems can be a useful way to 'buy out' of aspects of a game system with which they are not entirely comfortable. Something like 'charmed existence' can reduce 'botches' if a player doesn't like that, or advantages can eliminate wound penalties, perhaps increase base HPs, and in various other ways let a player play a character similar to a different system's PCs. Avoiding advantages/disadvantages completely might let a player deal with less complexity, if desired.

General Note II: what a system's advantages/disadvantages are built around is (as with any character ability) determined by the level of detail in other aspects of the rules, in areas which can include things from movement/miniatures to skill use/advancement to game world physics to personality traits. The more detailed the rules, the more advantages are possible/needed for an area and the more likely a character will require mucking around with advantages to build it properly, particularly if its unusual.

General Note III: advantages are generally more useful to provide 'fine-detail' customization of a character. I think if a game has a huge diversity of options, people are more likely to play more 'steoreotypical' characters, whereas if there are only a few they are more likely to want to adds some mods and customize them.

General Note IV: as can be seen in some examples above (Synnibarr, ROAR) advantages are sometimes bought with abstract points, and sometimes may have a number based of e.g. an attribute. Non-abstract purchasing indirectly limits what can be put in as a reasonable option - the advantages will be something someone who is higher in XYZ should have more of - if most advantages are skill-like and purchased with Int points then a 'toughness' option there looks weird for instance.

See post 120 (http://www.therpgsite.com/showthread.php?p=515934#post515934) for some more notes on point systems in general.

The subtler the sorts of effects that Advantages/Disadvantages cover, in general the more of them an individual character will have to have, in order to be well-described within the game mechanics. Of course, this is also affected by how much heavy lifting is being done by other aspects of the character, like attributes and skills.
In simpler systems or those without a lot of rules, advantages/disadvantages may be just rated descriptively, with GM fiat applied to determine penalties or effects. For instance, a 'colour blind' disadvantage might just note that a character has trouble seeing colour; it would then be up to the GM to determine that the character has trouble on a particular check, for example cutting the correct wire on a bomb defusing attempt, or that a given target stealthing past them will be harder to spot because their colour contrast vs. the background is less significant.

A list of GURPS advantages [4E] is here (http://gurpswiki.wikidot.com/ind:advantages) as part of the GURPS Index - and maybe useful as somewhere to look in designing a list of advantages.

Games with advantages/disadvantages probably usually list 'advantages' first, then 'disadvantages'. Savage Worlds lists Disadvantages first - probably because to take any Edges you need the points from the disadvantages to do so (apart from human bonus edge) unlike other games where by default there's a large pool of points to begin with. It would be interesting to see what effect the order has psychologically on new players - disadvantage first may be a disincentive to advantage buying, since players won't be likely to not see anything they want and haven't yet seen what goodies can be bought with those points, although there would be some flipping to-and-fro.

Advantages/disadvantages might modify attributes, but its not necessarily a good idea since such an option is 'redundant' (maybe generating cost breaks which are undesirable). For instance, Gamma World had a "mentally defenseless" mutation that could be rolled and gives a character a Mental Strength of 3 - a character could just roll a 3 for Mental Strength normally, so it doesn't add much to the game.

[As sort of noted under 'controlling bonus and penalty accumulation'] Tag-based definitions like 'advantages' sometimes give better control of results than abstract numbers. For example, if a monster has the "hideous" flaw, then its hideous. On the other hand, if a monster rolls a d6 for Physical Beauty (vs. 3d6 for humans) then it'll be usually hideous, but a player might be able to stack some random bonuses to make it normal looking, like how Palladium supplement Mystic China has a martial art giving a +1 to PB for good poise and acting skill, etc. - probably this shouldn't work if you're a slime-dripping alien worm, but this and if you could find a few similar things could fix a low result. The problem being that a thing intended to give about a +10% to PB, instead give a bigger proportional shift, and enough could fix a low result.

Design Note: Like other character features, advantages/disadvantages can be written as more- or less-specific in order to represent a wider range of possible characters. (e.g. Pisces d20's Negative Feat Awkward Body Shape [the main game effect being preventing a character from wearing some items e.g. armour] - "Maybe you're portly. Maybe you're shaped like a letter of the alphabet. Who knows.". Another game might have a specific obesity disadvantage which also has Endurance modifiers, etc.

Backgrounds
Backgrounds are another facet of the character e.g. in games such as Storyteller, or FantasyCraft also has a detailed system (for renown, lifestyle, contacts, etc). In games such as Storyteller backgrounds are separate to attributes, merits/flaws and advantages/disadvantages, although in other systems they may just be a part of the advantage/disadvantage system.  Backgrounds such as resources, mentors, followers, items, reputations, and so on in a separate 'pool' of points is I think a worthwhile concept, if its tracked mechanically, since these points are potentially gained/lost more easily - through campaign events - than are stat points, and perhaps skill points. Compare this to say, GURPS, where reputation changes and so on must be 'bought' with character points. White wolf didn't however handle negative backgrounds (being hunted, having a nemesis, etc.) as part of the background system, they were simply normal 'flaws' (disadvantages).

Apart from these many games simply do not have a background system - the player can write up a background that makes them nobility or wealthy, or even grants them a magical item or similar, and its fine as long as the GM approves it. The GM might also add 'complications' to balance things of their own accord i.e. an ancestral magic item comes with an evil group who want to steal it. The overall effect here can be the same as if points were used (Wanted hindrance used to buy a special magic item) but with less accounting involved. Even in point systems, things such as nemeses and being hunted are perhaps questionable balance-wise - the game is likely going to have some sort of nemesis, so it makes little difference to the character if this is due to their Flaw or just assigned to them/the group by the GM. Sometimes a particular background feature is represented by a system without an overarching system for this e.g. a game might roll/let the player choose the number of Contacts that a character knows initially, or randomly determine Social Status (AD&D); HackMaster has a detailed Honor system (which also modifies attribute improvement rolls).
 
Some systems also have non-point-based backgrounds which are essentially random roll e.g. Cyberpunk had a series of LifePath tables (IIRC, fairly good). Paul (Jennelle) Jacquays authored a series of 'Central Casting' books which had guidelines for conversion to various systems, which were quite interesting. These could strongly affect the character including random boosts, impairments or extra skills (one of our games we got demigod once...), or results could be odd or contradictory.

13th Age lets characters choose 'one unique thing' (being a special snowflake is mandatory). This can't be combat-related or offer a 'hard mechanical bonus' (without costing other character resources at DM option, such as trading in class or race features) and could include odd physical features (clockwork hearts, opal eyes, human-eared elves, cutting off own arm to show how tough they are), odd racial affiliations (only halfling knight, human cleric of the dwarf gods), or an unusual relation to one of the settings' major NPCs (fated to kill the lich king, probably in a future age).

Apocalypse World /Dungeon World has players choose 'bonds' which define how the PC is connected to other PCs (a formal system for something that probably often happens in other games unprompted).

Both advantage lists and background feature lists for a given game will be designed to support the style of play for the game in question - preventing creation of characters that are unsuitable to the expected genre and playstyle, and costing options in keeping with their likely usefulness. If a campaign's style of play deviates from that expected, then, options will be miscosted, inappropriate, or the lists will fail to cover options (as unsuitable) which actually would be helpful.

(Note that the section above was written before 5E D&D, was so my use of 'background' is slightly different to what 5E means by a 'background'; I might classify that as being simple 'lifepath' system, cf. next post). 5E backgrounds are noteworthy however: it provides a very general sort of background pre-adventuring, as well as including some skill picks, a special ability and a set of possible personality traits to choose or roll. Mechanical dividing up skills this way would perhaps be a good way to reduce the amount of 'stuff' gained by multiclassing -  though they also decided to do that by not giving out all abilities when multiclassing.
See here (http://www.therpgsite.com/showthread.php?t=30395) for therpgsite's big list of homegrown 5E backgrounds.  While the background is a package, it is possible to build your own, and its also possible to 'swap out' specific features - for instance some adventures provide an alternative special power that can replace the standard special ability, that also being convenient if you are building a do-it-yourself background.)

Character Backgrounds in a general sense - rules interactions
Here I may talk a bit about general background design. To have a particular sort of thing written into the character's backstory, is affected by other rules. Fairly often even if there are no mechanic options, a GM can kludge something, but mechanics can streamline a process or even more so, can accidentally prevent an idea from working. Below is a list of a few fairly typical high fantasy ideas along with what makes them work. For example a character that's "secretly a necromancer" might be perfectly OK as a Savage Worlds character (one I've actually seen, since the magic skill costs only a few points and an Edge) but isn't so feasible in 4E, where a character uses magic nearly nonstop in combat.

Character background or trait      Mechanics/rules probably required (built in or GM fiat)

Adopted by other race------------   Swap native language for other races' language
Monster e.g. demon ancestry----- Monster powers e.g. demonic abilities
Conscripted to army-----------------Weapon proficiency (classes like 'mage' may cause problems)
Wanted / Hunted---------------------Disadvantage or GM fiat
Hunted by BBEG for owning object-----Hunted-type disadvantage, purchase magic object
Found/inherited a pet ---------------Animal companion rules
Scarred in accident-------------------Check Regenerate rules interactions (i.e. not worth free points)
Other physical defect-----------------Justified via stats (e.g. low Per - glasses), or specific defect
Noble title-------------------------------Advantage or ad-hoc GM permission.
Secretly a magic-user-----------------Viable without using magic i.e. low-cost/low-effect, or point discount for usage limitation
Personality issue   -----------------------Disadvantage, or XP for roleplay bonus.
Cursed-----------------------------------Disadvantage or GM fiat
From other region----------------------Invalidates region-specific skills.
Illiterate----------------------------------Disadvantage or point cost to learn reading   
Unusual size-----------------------------Size rules, or modelled via stats e.g. high STR


Allegiances
Characters can also be signed up to various organizations as part of character generation.
This can be a purely roleplaying or background thing, likely to have an impact on the campaign;
Or it can have a game-mechanical effect, sometimes directly and sometimes indirectly (that is, a particular background will set some limits on what can reasonably be bought, or at least raise questions or require additional explanations for some choices).
Some games where there are game mechanic effects have allegiance occur as a part of character class (e.g. in Mage the Ascension, your starting Mage group determines your style of magic and free Sphere dot); in others the choice of allegiance is a separate decision with minor perks e.g. in Gamma World, a character of most classes can choose from various Cryptic Alliances; in 2nd Ed. AD&D Planescape, planar characters could choose a 'faction', instead of choosing a 'kit' (class specific class add-on) like 'prime' characters.


recent edits: added 'allegiances' section(*); extra note on DIY'ing 5E backgrounds; reorganized adv. vs. skill/attribute (*)

Class and/or Skills
The known methods of determining PC capability include class-based (1), skill-based (2), lifepaths (3) and archetype (4).
 
1) Class based; a character’s class determines their capabilities and give characters “niche protection”.  The main benefit is to encourage diversity in characters, and it tends to encourage teams of characters (most often class systems work optimally with about 4 players). 2E D&D did often encourage the GM to run single-class campaigns (e.g. where everyone is a fighter), and potentially even where characters all have the same 'kit' (all barbarians, all gladiators, etc); this in retrospect seems peculiar in that it made characters very similar with only slight differences in ability scores and/or proficiencies and/or race. Advantages cited for that in Creative Campaigning is that it avoided 'spotlight time' problems where say the thief 'could do little in wilderness games', and that it was 'more challenging' (players needing to find innovative ways around areas of ineptitude); I'd note it also somewhat 'balances' a party e.g. everyone has similar ACs/HPs (something achieved in later editions like 4e/5e by fine-tuning numbers between classes), as well as limiting the effect of 'optional rule' rules variation which often had class-specific effects.

In OD&D, Dragon Warriors or other skill-less systems, each class can be thought of as a single very broad “skill”; skill systems are frequently added in later editions with some classes getting free skills, altered costs of skills, or banned skills. In Talislanta, each “class” is defined almost wholly by which skills it gets either as primary skills (at the character’s full level) or secondary skills (at half level) (though classes are also racial, and so have different racial abilities). Class can be very simple (e.g. a Tunnels and Trolls character in the adventure Dargon's Dungeon can have their class magically replaced with a different one and -aside from spells- be ready to go virtually immediately) or can support extensive arrays of dependent numbers and specific ability selection trees [e.g. FantasyCraft]. Hollow Earth Expedition has 'archetypes' like Academic or Big Game Hunter selected from a list as the first step in chargen, but with no game mechanics, even recommended skills - they exist purely for role-playing. Savage World 'Professional Edges' and FATE 'defining Aspects' also sort of give some class-like definition. A set of classes might be designed with standardized features (...they all get one bonus skill, a +1 to a particular stat, etc.) for balance or whatever reason, though taken too far this might cut into differentiation between the classes (it could be argued that 5E D&D does that it ways, with class features designed to e.g. provide unarmoured AC, or healing via second wind vs. spell, etc. reducing differentiation). Classes might have a sort of taxonomy or tree structure where several classes form groups; one interesting thing about this is that what goes where varies from system to system e.g. Techno is a Tunnels and Trolls 'warrior' subclass (Sorceror's Apprentice) as warriors can't use magic, while in Gamma World the equivalent (Examiner) is a main class, alongside Enforcer as pure warrior. Bard might be a rogue sub-variety or basically a singing wizard, or rogue itself might be considered a warrior subclass (e.g. 4E D&D has rogues as 'Strikers' using the 'Martial power source').
Classes might have various numbers of 'special abilities': a 1st-level character might get only one ability (Star Wars SAGA), 3 or 4 'powers' [4E D&D], or a large array of special abilities (or spells)(Rifts). More abilities relates to more competent PCs, but also make multiclassing more powerful and hence problematic.
 
Classes may have minimum stats to select (sometimes including requirements in e.g. social class, such as in 1st ed. AD&D with Unearthed Arcana, or alignment - this last possibly needing to be maintained to continue in the class), or be limited to certain races.
A racial requirement might be waivable in some cases - for example, if cultural and they're raised by a different race, or have a specific advantage/feat.
More rarely, classes can have attribute maximums e.g. a 1E AD&D barbarian can't have a Wisdom of 17-18 (the 2E barbarian class from Complete Barbarian has no max., but instead has a penalty to Int and Cha checks outside their homeland), while a Deluxe T&T character who rolls triples is a 'specialist' and so can't be a 'citizen' (the peasant class). The need to roll triples, rather than any particular scores, also means specialists can't be created with point-buy.

Attribute minimums can work to randomize whether a character can belong to a particular class in a random-roll system. Some ability scores may exist almost solely as a way of determining if a character can belong to a class (e.g. Wis in AD&D), being useless to other classes; this is probably a problem once point-buy or rearranging of stats is possible since characters of other classes can 'dump' these scores.  A low score might fully prohibit becoming the class or just make it a subpar choice.
Other random rolls can also be used to determine 'class' (usually fully yes/no rather than merely handicapping):
- Warhammer does this to an extent (although this is less of a problem in WHFR since a character is expected to change profession several times).
- Synnibarr uses random rolls to determine what classes a character can select from initially, but gives a character 3 rolls (rerolling results for which the character can't meet class minimums); it is also interesting in that it has characters becoming multiclassed when they become immortal at 51st level (even though it uses race-as-class), with the new class progressing instead until level 100; rare 'immortal born' characters (with 20 in every attribute) can start with two classes initially. Characters can pick their 2nd class at 51st level freely.
-Dungeon Crawl Classics generates 'profession' randomly although this really mostly just determined 'skills' and limits access to racial classes; the initial random system paired with random dice roll and anomalies such as Str 3 Blacksmiths, although fixes were proposed such as a set of tables, rolling based off highest score or (a compromise) weighting a roll toward the highest attribute(s) and then branching out to a separate table for each score - see http://www.goodman-games.com/forums/viewtopic.php?f=72&t=34279&start=25.
-Spawn of Fashan randomly rolls a 'parents' choice occupation' and then has a player choose an occupation, before stats are rolled; i.e. if stat rolls would make a character terrible at the chosen occupation, they can instead choose the random one (only). The exception is that if 'misfit' is rolled, that's automatically the class.
-in other systems, random rolls may modify class choice in exceptional cases, such as a character in 2E D&D Complete Celt rolling a 'gift' that let them be a human multiclassed wizard (humans couldn't normally multiclass, only dual-class); a low Social Status in Unearthed Arcana 1E D&D would prohibit being a cavalier (or force the character to start at "0-level", but not most other class choices.
-if race limits class choice, randomising race will then also randomize class choice (no known examples).
A class might have a feature with randomly-determined power, as well. One sort of example here is the Dilettante 'kit' in Dragon magazine for half-elf fighter/mage/thieves, which rolled 1d6 for how many 'secondary skills' were known (characters normally get 1 or very rarely 2). For me at least the point of the kit would be more skills, meaning the characters total resources (overall character design) can be wasted on a poor roll. That sort of thing - with major class features - can be an an issue in that since the main purpose of classes is to offer 'niche protection', they either fail to fill the niche or may be overshadowed by other characters on the basis of the roll. This sort of randomization isn't that different to having a # based off a stat (e.g. the kit would've worked if it gave Int/3 secondary skills) in that this provides variability, but known in advance. I suppose the counter-argument for this sort of randomness is that any extra variation could appear in a low-stats character and make them more viable.

Classes often have a single key attribute. Some systems deliberately weaken some classes by making them deliberately multiple-ability-dependent (MAD); many 2E D&D classes have higher requirements in stats which aren't 'prime requisites', while 3E D&D tries to weaken some spellcasters (favoured souls, archivists) by splitting spellcasting functions across multiple stats. In random-roll games this sort of thing makes MAD classes harder to roll up (rarer), while in point-buy it leads to characters that drop 'dump stats' significantly. Having a classes' abilities be heavily attribute-dependent e.g. the 2E D&D psionicist which uses ability checks for power activation, the 3E D&D marshal which gets auras adding +Cha mod to various things, and the the SenZar rogue - see next post) can be a problem as this front loads abilities rather than having them be level-based (at least its a problem unless all classes are designed similarly and multiclassing is restricted). Sometimes there may 'workarounds' for some ability score dependencies - a couple of 2e kits in 'Champions of the Mists' changed a characters 'prime requisite' (so letting characters get +10% xp more easily, if the class had more than one), or 3E has some feats or racial features that can change key abilities for attack rolls, skills, or class features. These are sometimes designed to make particular races (with a penalty) or multi-class combinations more workable.
One thing to note when considering classes' design is that the usefulness of a class is often determined very much by general rules of the game, rather than the rules of the specific class itself e.g. consider how loose skill rules helped the AD&D fighter work as a general adventurer without needing many skills, or how a Savage Worlds "rogue" is potentially very effective since its relatively easy to one-shot opponents. Conversely a class can be crippled if its shtick is heavily opposed by other game rules or factors (e.g. how 3E swashbucklers lack significant 'swashbuckling', due to tight system constraints on movement, and unusual combat options requiring feats to perform).
A few (older, especially) class-based systems are set up as such without providing enough diversity or niche protection to justify this - Rolemaster for instance distinguishes classes mainly by skill purchase cost; Palladium's Ninjas & Superspies has classes differentiated only by bionics budget, number of martial arts, and number of skill programs - classes resemble just different purchase arrays of those, and could be replaced with a single purchase system, if not for compatibility with the rest of Palladium.
More recently, Star Wars SAGA (the more recent of the d20 Star Wars) has classes with similar numbers between them and somewhat overlapping skill lists. The main differentiator are 'talents' specific to classes but the game uses 3E multiclassing anyway -choose a level of whatever class you want whenever you level up- so overall you basically are just picking whatever talent you want when you level up anyway. Classes with more skills have less weapon proficiencies (e.g. Soldier) but as both are purely yes/no (skill training = +5 to a skill) rather than 3E D&Ds varying # of skill points/level, this could also be duplicated simply by making a weapon proficiency cost a skill.

At the other extreme, classes in a complex game can be designed so that different classes interact with/get power from different game 'subsystems' e.g. FantayCraft (Courtier: currency systems, Keeper: skills, Soldier: feats). Heroes Unlimited's different power categories might be another example of this. This sort of structural difference - tying into various subsystems instead of one or a few - makes little difference ultimately, with how well this works depending a lot on the specifics of the implementation of the subsystems. One game might handle several things with the same subsystem that are distinct in another - a character might get the same game benefit from an attribute raise in System A, a skill in System B , or a feat chain in System C e.g. compare having to choose between more skills and having psionics, vs. psionics being a skill (classes can also use different 'rolls' or subsystems for checks to other characters - frex. some later classes in 2E like the psionicist rely on d20-under-stat ability checks moreso than other classes, which were designed mostly before there was an ability check system).
Classes may be differentiated by specific handicaps as well as special abilities (e.g. poor hit dice, weapon selection, etc.). T&T (e.g. Deluxe) gives a named negative feature to (most) classes (weapon inability, magic blindness or half powered magic). D20 glut era Pisces RPGs had a series of classes which each had one bonus feat and one balancing 'negative feat'. 3E D&D barbarians had illiteracy as a special feature, while Pathfinder Oracle's have significant debilities (e.g. blindness); 3E prestige classes in particular struggle with this a bit - characters are meant to want to aspire to join them so one eye [Eye of Gruumsh], a writ of outlawry [Outlaw of the Crimson Road] or sudden loss of all knowledge ranks [War Hulk] is a hard sell.  
The overall design of a class across its various aspects may generate significant differences between different classes (warriors being good at one thing, wizards at another, etc - as in 'old school' D&D/AD&D, or classes can be deliberately designed to be similar enough that they essentially only provide different "flavours", while all being equally able to contribute to combat, skills, etc. [4E D&D strongly, 5E D&D to some extent].

Multiclassing is tricky in class-based games. Sometimes multiclass characters fairly normal with up to several classes e.g. 3E D&D, while in other games they exist only rarely (AD&D dual-class) or under special circumstances (e.g. Rifts' retired juicers or T-men from Atlantis). Multiclass characters might be equivalent to a more powerful/higher level character, have ability requirements to qualify, or be normally against the rules except in very rare cases [e.g. NPCs]. Multiclassing can also be balanced by giving it to everybody i.e. Gamma World 7E inherently gives a character two 'origins' (something like racial classes); original Recon gives characters a 'primary Mos' and 'secondary Mos' so they're also sort of inherently multiclassed. (In this sort of setup you can design extra classes that let someone emulate being single-classed by just giving more benefits to the primary class, say if Expert/Artefact User is 'fighter with magic sword' or Expert/Paragon the just really strong fighter ).

I think generally you could say there are three models of multiclassing depending on overall structure: 1) you get one class and can pick up a couple of minor abilities as a sideline (4E multiclassing); 2) the character splits their capability between both classes fairly evenly [4E hybrid characters]; or 3) you get the full set of powers of both classes but with other drawbacks, like slower levelling [AD&D characters]. (3E is somewhere between 1) and 2) depending on how you split up the levels).

Multiclassing is sometimes done by splitting XP between two classes (AD&D, Palladium Fantasy), or splitting levels between classes (Japanese RPG engine 'SRS', translation here (http://neko-machi.com/extra/srs_basic.pdf), mentioned in this thread (http://www.therpgsite.com/showthread.php?t=33851), gives all characters 3 levels to split up initially). A more well known example, 3E D&D splits a variable character level between classes; some combinations ended up very weak in this setup, giving rise to patch options in Prestige Classes like Eldritch Knight, or feats that allowed specific classes' levels to stack for some abilities;3E also had an entirely different optional multiclassing system ('gestalt') in Unearthed Arcana which however powered up the game significantly and worked only if everyone played gestalt characters. A level-splitting system also has a 'feedback' effect on class design - it severely constrains the number of abilities that can be given out at 1st level, since front loading encourages characters to multiclass excessively (a problem with the 3.0 ranger).
Other systems deliberately added new classes to cover particular combinations, though this eventually leads to a lot of classes. Rolemaster (which let characters of any class choose any skills) sometimes just allowed characters who 'multi-classed' to alter development costs of skills to the average of both classes. Multiclass options are sometimes limited by race or ability requirements (in original Palladium Fantasy multiclassing is slightly tricky as a character needs to meet both sets of class prerequisites; AD&D dual-classing or 5E D&D multiclassing has extra-high stat requirements). Multiclassing may also have serious limitations due to game balance concerns; in some cases it may be perhaps deliberately not be included as an option (e.g. Rifts, where character abilities are heavily front-loaded compared to level-up benefits; multiclassing is sometimes necessary e.g. for slave-borgs or retired juicers, but is handled on an ad hoc basis. Characters can also sometimes pick up individual archetype abilities like psionics, super powers, martial arts forms or cyberware; each case has its own custom rules).
If multiclassing is relatively common or easy, character concepts can be handled with the multiclass system which would otherwise require more complex & specialized individual classes to cover them. As in Synnibarr or Apocalypse World/Dungeon World, multiclassing (at least picking abilities from another classes' list) can also be used to avoid writing as many abilities for one class (e.g. in Synnibarr, as noted above, the character gets a second class at level 51 with 1st level abilities; this then has a 1-50 progression in the second class to cover up to level 100 without having 'dead levels').

Sometimes multiclassing does not grant all benefits of a second class (e.g. in Fantasycraft, the 'core ability' of a class is only gained if its the characters class at 1st level). 5E reduces number of skills gained by multiclassing by splitting them between 'background' and 'class' - a 1st level character has 1-3 skills +3 from their background, giving them 4-6 skills total but only another 1-3 if they multiclass again (since a second background isn't gained), as well as (in the final version) not granting the full set of save proficiencies for multiclassing.
Chris Perkins's "AD&D3E" has primes (derived from C&C, I think) - a character has two primes (three for humans), one of which corresponds to their class and gives +5 on relevant checks; multiclass characters will just have their focus areas (equivalent somewhat to class specialties) preset, rather than gaining any extra bonuses.
Very limited multiclassing may give only a single ability from the second class, as in 4E D&D power swap feats, Conan D20s 'Arcane Dabbler' feat, or in 2E Skills & Powers via some of the alternate class options like 'warrior-priest'. A GM may also let a player just 'swap' an ability from one class, for one from another (Skills and Powers did show that this could be a problem when a class ability didn't always kick in - for example, if a class feature requires a high ability score to use like 'fighter bonus to HPs', trading it out might be giving a 'freebie' bonus power). Sometimes a single bonus ability comes with handicaps relating to the original class e.g. Skills and Powers would let a fighter get a ranger's animal empathy, but they would then need to abide by all a rangers' ethos restrictions, or a character learning a single spell but not being able to wear armour with it (like a mage).
Games while are partly skill-based may let some classes branch out into other areas at a cost by buying skills at greater expense (Rolemaster; 3.x D&D to an extent). Rarely multiclassing might add a specific disadvantage to a specific combination: in oWod Storyteller, Vampire and Werewolf types - while not 'classes' exactly - could be combined to create an 'Abomination', but this required a Gnosis roll botch to avoid death, largely limiting it to NPCs, and was later noted to also cause a deep depression limiting dice pools, 'hirano'(sp?).
Sometimes classes are only available as a multi-class option e.g. 3.x Prestige Classes, the 1st edition AD&D Bard, AD&D OA Ninja, or Palladium Fantasy's Alchemist class (NPC only, requires prior wizard and diabolist [rune guy] levels). Such classes may be designed as add-ons and not have the full range of abilities normally given to a class, e.g. AD&D bards don't increase their 'to-hit' values.
4E D&D has "paragon paths", "epic destinies" and "themes" which are expansions of the class system: every character may choose a 'paragon path' which gives extra powers at a appropriate level. Likewise a character can choose a 'theme' (e.g. Athasian Minstrel, Dune Trader, or Gladiator) and gets one theme-related power, plus at higher levels can select further 'theme' powers in place of normal class powers. Some themes, like classes, also have associated paragon paths.
A specific problem to avoid with multiclassing is to make sure MC characters’ aren’t better than single-class characters at their niche (or generally). (Watch out for dual-class fighter/illusionists who can keep fighter HPs and also get bonus HPs for phantom armor or whatever other spell)
Classes with more built-in flexibility can work better in multi-class combinations, e.g. the 5E D&D Warlock can be taken in a few different directions that would complement other classes, e.g. either combat or skills or magic. OTOH, adding flexibility to a class makes it need multiclassing less - adding Skills & Powers rules to a fighter/cleric, the cleric gained most of the fighters abilities (e.g. two weapon use, fighter Str/Con bonuses, using non-blunt weapons) making fighter/cleric less useful.
A couple of games have multi-classing as a power of characters with 'multiple personalities'. Spawn of Fashan treats each additional personality as having a separate (rolled) class, and gives each d4 'trigger phobias' which if a save is failed moves the character to a new personality. 3.0 D&D has a 'Thrall of Demogorgon' prestige class, giving a character multiple personalities that lets them multiclass without a favoured class penalty [arguably this would've been better as a Feat, since its giving a character a class than then lets them take more classes...when total levels to split are still limited].

Supers games sometimes use class systems for powers too with classes like Alien, Cyborg, Mutant, Psi..  - this is seen in Heroes Unlimited, Superbabes and a couple of D20 variants. One thing to note with these is that they can make 'secret origin' stories like the Savage Dragon turning out to be of alien origin rather than a mutant more difficult to pull off in-game, as well as making 'multiclassing' necessary for characters like Wolverine (i.e. mutant w/ bionic skeleton). The 'Invulnerable' RPG (point-based rather than class-based) specifically adds rules for 'mysterious origin' characters, possible since most origins are bundles of powers) with the note that a character whose origin is revealed may 'tweak' their stats. Aliens in HU are sort of inherently multiclassed, with a mix of alien-specific special features based off physiology + limited additional powers from the super-power, bionics, magic-user or other categories (one category per character only). Gamma World 7E is interesting in that characters inherently always have two origin types that they combine, making them fairly weird and inherently multi-classed.

Class systems are somewhat inflexible - a player might actually want just something simple like more skill points, more attribute points, more mutations or super powers or Edges/advantages which in a point-based system could just be purchased directly, whereas in a class system have to be purchased indirectly, through a 'class' created to allow that. From this standpoint, some 'classes' in a class-based game list will possibly be just kludges to get around the limitations of a class system (e.g. perhaps 'Experts' in 3E D&D). There is also often a 'class' created for characters with no particular training (i.e. 3E commoner, Rolemaster 'No Profession'; earlier D&Ds instead normally used Fighter as the default, and/or assumed inept characters were 'Zero level'. Games where class rules apply specifically to PCs only, such as 4E, don't have to include an 'unskilled' class).
Classes inflexibility also tends to make them more genre- or setting-dependent; most universal or multigenre games are skills-based rather than class-based (the exception being Palladium, which instead just writes a new set of classes for each game). Specific class abilities like 'turn undead', 'favoured enemy' or etc. can set world expectations, or force houseruling to replace features if a gameworld doesn't match the default.
Games can sometimes include rules for making up your own 'class' (2E AD&D); although even being able to do this, somewhat undermines the idea of their being classes. This resembles skill-based chargen a bit, except that building a DIY class tends to set advancement options permanently; skill-based characters tend to be more flexible. One site here includes a randomized DIY class generator for BECMI D&D. http://www.apolitical.info/webgame/class/becmi.php (http://www.apolitical.info/webgame/class/becmi.php)
Classes sometimes overlap 'attribute' as well as skills - D20 modern's "Fast Hero", "Smart Hero", etc. or Tunnels and Trolls has 'specialists' who are super-good at particular attributes. This can also be a multiclass option so someone could be a fighter/superstrong say (even 3E D&D in DMG II has a  prodigy special ability that isn't a class but replaces levels of one by having a level adjustment, and gives a +4 on checks). This can be a fairly cumbersome and fiddly way to let players be exceptional at stats - it may be better to design attributes to be purchasable at higher levels and innately provide whatever exceptional abilities you want.
Barring multiclassing class selection is either/or, so classes are usually balanced against each other (also barring particularly strong classes having attribute or race restrictions). Making something a class - things like 'merchant' or 'noble' for example - can therefore involve a lot of work to build extensive somewhat wacky abilities to balance them against pure warriors or wizards. That does make these work as 'pure' options, but its also possible a player would be happy having such abilities made into an advantage, skill, or other 'add-on' option. 2E AD&D for example has a number of merchant 'kits' (so a merchant will also have a class and so other abilities) while AD&D (Dragon #136) has a merchant class for AD&D which is available as a dual-class option regardless of race. FantasyCraft Courtiers or Star Wars d20 Nobles exemplify the other approach, where a full class is constructed for these. Providing 'niche protection' for classes designed around non-combat use can also make it harder for the combat-based characters to interact outside the combat minigame, leading toward the Shadowrun problem where game play is split between the Face, Street Samurai and Decker dominating different scenes.
Class variations sometimes split into 2 classes over time: the Rifts Borg includes 'partial conversion' and 'full conversion' options (much more powerful); Ultimate Edition instead makes the Borg class exclusively full-conversion with another class, Headhunter being an example of partial conversion.

Class abilities can form different amounts of the 'pie' of total character power in different games. Its interesting to compare 3E D&D and 5E D&D, in that limiting feats and making them optional in 5E tends to mean most of a characters' power is built into the main class level progression in 5E, whereas in 3E customization varied a character's power more depending on what feats etc. they chose. (5E characters vary much in skills since those are 1/2 based on background, but are more standardized by class in terms of damage output and strategies by which their damage might be generated)

Some games tend to not want much 'niche protection' in which case skills are a better option. An obscure example would be 'Monsters and Slayers' (reviewed in Dragon magazine) where NPCs might be just thieves or fighters or mages but player characters are 'Slayers' all trained as fighters, wizards and assassins - each has its own set of skills or spells and this is actually a skill-based game; it generates characters sort of reminiscent of (1E) Advanced Fighting Fantasy, where characters chose various special skills up to their Skill and always always including some thief skills, combat, and probably magic.  

2) Skill selection: characters purchase skills (a fixed number of skills or using skill points).
Simplest examples of this are almost similar to class systems e.g. Barbarians of Lemuria gives a character 4 'careers', rated at +0 to +4 (adding to 2d6 along with an attribute bonus, likewise 0-4). What tasks a career helps on is largely a matter of GM fiat ('hurtling toward a giant pit, Krongar makes an agility task..luckily the GM is in a good mood and decides his natural Barbarian instincts come into play, allowing the character to add Krongar's barbarian rank of 2 to the die roll').

Some systems may sometimes use "skills" for non-characters - e.g. Fate Core [the 4th edition of FATE]. See discussion of the Fate Core "fractal" here (https://plus.google.com/108546067488075210468/posts/WBuMyZ1H1yT): the short version is that they define a skill as representing the ability of a "story element" to influence a scene, with story elements including potentially characters, locations, Aspects, or whatever).

3) Lifepath: characters roll a character background which determines their skills. GDW systems such as Traveller are the classic example of this; a modified version of this is Warhammer Fantasy where in play, characters continue to add new “careers” (despite characters basically being adventurers as an occupation i.e. class acquisition is pushed off to a slightly metagame level). Some terms of service may have prerequisites e.g. Starcluster 3E has stat or skill minimums, though with a 'waiver %' chance for a character to scrape in regardless (someone thinks they have potential).
(Edit 3/12/2014: see later in thread for discussion of non-random lifepath systems in e.g. Volant, where templates are layered up without random rolls: see page 22 (http://www.therpgsite.com/showthread.php?p=801903#post801903)

3.x D&D can be thought of as layering a 'lifepath' system over the basic class system through its multiclassing rules.
Palladium in places combines random-roll skills with classes - mutant animals in TMNT roll up various skills, while 'Survivors' in Dead Reign (fairly uniquely among the classes there) roll to determine their prior occupation/skills. Survivors also roll d4 to determine their level in occupational skills, due to prior experience, unusual since Palladium OCCs instead get a flat percentage bonus.
Mutant Epoch has a single background roll rather than a 'path'; it has a row with different %s for each species, but ignores direct attribute effects (you're as likely to be a courtesan with Appearance 1 as 100). Customizeable species get multiple entries (you roll up 'bioreplica military' or 'bioreplica pleasure', or likewise military or 'comfort' clones, and each then get separate profession tables) rather than races being more customizeable or giving a profession-specific bonus.
A particularly over-the-top Lifepath system was found for HOL in its lone supplement, BUTTery HOLsomeness. This starts a character off with a 'totem' giving base stats and a roll on the Homeworld table, then characters roll on the "Chart Chart" to see which chart they end up on, including options such as Crime, Family, Generally Bad Choices, Specifically Bad Choices, Cornholed by God, Sidekicks, Mutations, Night School or Pressed Ham. Each chart entry gives an effect then directs to another different chart; generally good charts cost a point from a pool of starting pool of 'kudos'. A character can return to the chart chart by spending 2 points (a really good idea should you be about to go to the "Cornholed by God" table), or more to go to a specific table. Results give bonus skills/stats until a character falls below the last few points and is mustered out (converting any final points into stats or skills).

4) Archetype: as skill selection, but a pregenerated character with an array of skills is provided, ready to play (TORG, Shadowrun). Archetypes usually place no limits on how characters may progress after character generation.
Systems with extensive skill rules sometimes also have 'packages' of skills (perhaps a sort of 'sub-archetype). Rolemaster for example does this, with each packages having a different costs to buy for each class (because each skill has a different class-specific cost).
 
Interaction between Skill System & Class System:
A basic 'class' system functions as a set of extremely broad 'skills' which largely avoid the need for a skill system - basic task resolution can use saving throws and attack matrices, or more rarely player skill.
0D&D had no skill system; Tunnels & Trolls had originally no skill system per se, but still occasionally had skills as unique, one-off abilities - in its solo adventures a character meeting the Shoggoth can make an IQ and/or Luck attribute saving roll to be skilled in playing the piccolo (useful against shoggoths), or can be taught improved bow skills at the Archer's Guild in Gull.
AD&D through to 2nd Edition developed add-on systems for minor skills (e.g. Secondary Skills, Non-Weapon Proficiencies) which made it possible to run the game either with skills or without -  potentially even with a mix of skilled/unskilled characters, since a character not using NWPs might have access to abilities that would normally cost a proficiency slot at GM discretion (reading, swimming). On/off skill systems are also a topic of 5E D&D discussion, with about three possible systems that may be of interest discussed here:
http://forum.rpg.net/showthread.php?687366-5e-D-amp-D-Next-Q-amp-A (http://forum.rpg.net/showthread.php?687366-5e-D-amp-D-Next-Q-amp-A)
The final 5E also has optional rules for running it skill-less (DMG) - giving characters 'proficiency bonus' with one stat check based on class + one for 'background' (=actually free choice). Needs GM tinkering to allow for racial bonus 'skills' like elf perception. Similarly but less extremely, 3E D&D had optional rules that eliminated skill ranks and just had yes/no skill proficiencies (Unearthed Arcana).

Other class-based systems such as Rolemaster and Palladium used skills to define the classes, making them integral to the game - for Palladium magic remained unique to certain classes but a majority of class features including stealth (Prowl), hand-to-hand combat abilities, and weapon proficiencies were built as "skills", with different skills distinguishing e.g. the Mercenary from the Soldier.

Rolemaster took this further again with hit points ("Body Development"), magic use (spell lists) etc. all described as skills, and with characters having some ability to pick up skills from other classes.
In Rolemaster the main difference between classes was that development costs were different, making it more expensive to pick up unusual skills for a given class. RM classes are fairly similar, with specific class features modelled via particular skills or "spell list" options. Spell lists were however particularly expensive (e.g. RMC semi-spell-users such as Rangers paying 4x as much for a spell list) making (IIRC) wizard/fighters a better option than fighter/wizards (so to speak).

2nd edition D&D Skills & Powers has a system of 'character points' which actually gives a final result fairly similar to Palladium Fantasy's skill system. S&P has menus of class abilities for each of the main classes, with point costs for each - equivalent to picking skills within each class, although with finer detail in cost based on utility, and the same ability having different costs between different classes. S&P also 'prepurchased' future skills with the initial points at first level i.e. at first level a character might buy followers for 9th level (with a point discount for the delay), or paladin spells at 4th level, instead of getting extra points/skills from levelling and using them to buy the skill at level 9 or level 4.

3E D&D had skills covering primarily 'adventuring' skills, but with magic and fighting ability being outside the skill system. Classes provide large numbers of unique benefits at various levels, while skills are either 'class' or 'cross-cross' - classes vary somewhat in skill due to expected ability scores, and rarely due to class features giving extra bonuses, but largely a class is good at a skill or not (compare to Palladium where classes could get between +0% and +40% skill bonuses, or "Archetype" systems where a character might be built with some or a lot of a particular skill).

Notes:
*SenZar gives out different skills to different classes, but skills use only an attribute check and so never improve from levelling up. Consequently skill-based classes such as Rogue are traps, particularly as part of a multiclass combination - exacerbated by XP being split in half by multiclassing when skills are learnable just by training in downtime, so you can pay 50% of your XP forever for skills that someone else got by taking a few months off and spending some gold. The same basic problem of scaling is found with AD&D 2E bards, who regardless of level perform with musical instruments no better (as far as raw skill check goes) than a proficient non-bard with the same Charisma; and with a number of the NPC classes in 'Sages & Specialists' like Scribe or Blacksmith which for the most part are redundant to a character with the right non-weapon proficiency. This sort of setup can be made to work, however, if attribute increases are built into a class progression: for instance, Warhammer 1E/2E has a specific 'advancement scheme' for each profession.
*Earthdawn (1E) assumes all characters are 'Adepts' with magical powers. Characters can choose talents from other classes, but these are received as the non-magical version of the talent ("Skills").
*Savage Worlds has 'Professional Edges' that look a bit like character classes. These just add a bonus to skill checks (skills sold separately). I quite like this approach as being primarily free-choice but with a nod toward classes.
*A few games distinguish between classes, which usually provide level-scaling benefits, and "kits" or "specialties" which are one-off packages relating to character concepts. 2nd Edition D&D calls these "kits" and has separate lists for each class (and some multiclass combinations), while FantasyCraft has a single list of "specialties" which serves a similar role. D&D 5E has very broad mega-feats which might also sometimes be used to define subclasses.

Systems sometimes have problems modelling particular character concepts because these concepts rely on 'skills' which are outside what the system normally handles. For example, a "Tanis Half-Elven" character in 4E D&D could have a 'warlord' type class, whereas in 1E, tactical skills rely on using the player's wits, while motivating other PCs would likewise be roleplaying (or just use of Charisma). The thief class in 0D&D has some issues with its abilities duplicating things other characters could probably do to some extent anyway, such as finding traps by describing how this is done or sneaking; likewise diplomatic classes aren't overly useful in systems without diplomatic skills. The Demon Hunter in Mystic China is another interesting case since the class is meant to use trickery and deception to overcome demons, though there are no skills for this in Palladium; the class gets extensive roleplaying notes on possible tricks, plus some interesting items and a few other skills which are left there so a clever player *might* be able to leverage some advantages over demons as written, including super-drinking, play dead, and arm-wrestling skills, and a minimum Int of 10 so a player being cunning isn't role-playing too badly. Another interesting case is the Riddlemaster (Bard kit) for 2nd Ed. AD&D; this supplements player skill in riddle-solving by allowing two 'tries' -the first unsuccessful guess by the player didn't happen and is 'retconned' out as far as the game world is concerned- or double the normal OOC time to solve a problem.

[Edit to add July 2018] Where class affects skill availability, there's a subtle difference between point-buy vs. binary skills. With point-buy (e.g. 3E D&D), a character will tend to slowly pick up various skills covered by their class, while with 'binary' skills they're defined as knowing a skill or not; if your 5E ranger didn't pick Knowledge (nature) initially they'll probably never know it. The binary skills approach works well for classes which include several varieties (the rogue with a focus on being a con artist, sneak, lockpick, or pick pocket) but can also create sometimes peculiar permanent knowledge gaps.

Other
Vivsavage's Tower of Adamant RPG in development has a system of 'roles' separate to classes - representing a literary role like protagonist, guide, supporting personage, (a la Sam Gangee in LOTR), or anti-hero - these give various benefits (often metagame, like a guide being able to narrate change to a terrain feature). Roles can change/be exchanged after adventures.

Edits: Note on overall design (*); primes(*), classes & different core mechanics in 2E (*) note on Star Wars SAGA as having a poorly-designed class system, extra multiclass note; 7/7/17 multiclass structures overview. 19/11/17 - parties of all one class

Number of skills known by characters
Number of skills/skill points a character receives may be determined by
*character point expenditure (GURPS)
*fixed # points (Storyteller)
*character age (Ringworld) - usually higher age meaning more skills. Age can also have a 'lifepath' effect e.g. Systems Failure for Palladium gives younger characters different skills due to growing up after the Apocalypse; FGU's Daredevils, set in the 1920s or 1930s, has rolls for age with characters of enlistable age at the start of the Great War (depending on campaign) having to fail Health rolls or be drafted.
*attributes such as Intelligence (and/or Education or Willpower). (e.g. 3E D&D). 3E D&D modifies the class-based skill points from each level by Int. More directly a stat can just set # of skills: the Buck Rogers Cliffhangers game (according to a Dragon review) rated each stat basically 1-4 which determines how many skills for that stat are learned. Mercenaries, Spies and Private Eyes gives a character 'skill points' equal to the Intelligence attribute, with more learned only when a character raises the stat with levelling up (though known skills can also increase level up by earning XP).
Int bonus is more likely to apply if 'skills' are largely intellectual; heavily skill-based games where things like e.g. hit points are a skill, are less likely to give skill bonuses for Int. "Education" may also be a random roll that isn't a stat (Palladium, Heroes Unlimited) and/or affect if you can buy a skill (Medical doctor in TMNT requires a Masters or better education).
"Class" can affect which stat determines skills e.g. Amazing Engine generally uses [Intuition+Learning]/10 but with Once and Future King having castes which either use this normally (Technologer), Psyche+Willpower (Acolyte), Charm+Position (Courtier) or Fitness+Reflexes (Knight), somewhat justified by access to different 'skill groups' in each case.
(# skills based off stats can be argued to be reasonable/realistic, with the drawback being that terrible stats mean a character also has terrible skills. This may be unfairer in a random-roll system, then, but OTOH having skills based off a stat in a point-buy game allows for character customization to give a player the number of skills they want. Its a potentially complex question that has to also consider what the game calls a 'skill' - weapon proficiencies, spells, body development, stat raises [HARP] - as well as if/how much attributes otherwise modify skill checks. Variable amounts of scaling are possible based on stat ranges and formulae and can make or break the idea. Note also that pregenerated archetypes become more complex if skills vary since any stat change will need skills added or dropped [Alternity], and racial attribute modifiers e.g. to Int become more important [3E D&D]. ).
INT or similar typically doesn't affect number of 'skill points' in point-based games where you're just spending from a pool e.g. GURPS, HERO. This would be because points are split between skills and stats and so points spent in Int would be counted twice as it were. These games actually have the reverse - more INT means less points left to spend on skills, although only subtly and for GURPS, stats affect skill rolls so much it doesn't much matter. GURPS also has a pretty broad definition of what a 'skill' is, including fighting skills and the like where being a brainiac isn't necessarily super helpful.

*# based on class/level (3.x, Rolemaster/MERP; the latter has adolescence skill ranks, as well as those for gaining levels).
or a combination of these.

*Random rolls can also be used directly in various ways i.e.
-random roll to determine skills known (Marvel Super Heroes/FASERIP). 5th Ed. Tunnels and Trolls determines languages randomly (1 roll per Int point above 12) ignoring duplicates; Common is 50% likely and telepathy 1% likely. Early Gamma World had no skill system, but some randomly rolled mutations were sort-of really skills, like "economic genius capability".
-random roll for # points (e.g. CHILL).
If both # and which skills are random, a high roll might end up wasted if a 'roll twice' result generates one or two crappy skills.
-RECON (1st ed.) also determines skill levels randomly - after picking a skill a character rolls d100 to determine their skill bonus (no attribute modifier). (IIRC this looks painful in Recon with checks also being d100 against the skill rating?; linear rolls for skill 'rank' would be more balanced if Rank 1 is the base and extra ranks each give limited bonus).
- Synnibarr has characters roll to see if they have the talent to Sing if they buy the skill, with skill points spent indicating a 50% chance of gaining the skill - otherwise the points are lost.
Overall a random chance of some characters having an unusual number of skills can be given if characters either roll to see # of skills known, roll to see which skills are known with some rolls giving a 'roll twice' etc. result, or roll to determine the rating of a skill with some rolls exploding (e.g. crossbreeding Deluxe T&T's random skill ratings with Maelstrom's roll-up system: you could roll d6 to determine skill bonus, with a '6' instead being a d6 roll for two skills).
-lifepath type systems can sometimes determine initial skills indirectly. The generic Task Force Games "Central Casting" books are an example here, where characters would roll various background events including for birth, childhood, etc: this could include skills ("learn head of household occupation at rank 2"; "apprenticed when a talent for a skill is discovered" (more ranks if an apprenticeship event makes the character's master legendary in his craft); conscripted learn a weapon skill at d2; etc., as well as items, injuries, or curses. The CC books tend to slightly power-up characters if bonus skills were allowed. One game system that seemed like it would dovetail nicely with the system there was Mercenaries, Spies and Private Eyes which encourages the GM vaguely to give out a few skill points as part of character background, if its particularly good; hence, the CC book could plug in just by replacing ad hoc GM-permitted bonus skills with the random roll results.
-cost modifiers might be generated by random-roll. 'Dark Fantasy' rolls handedness randomly; left-handed characters get attack bonuses vs. dextral characters, but also training cost of skills from right-handed trainers is increased by 10%.

(Player knowledge can also influence a character's abilities in some games (such as roleplaying/player social skills where no explicit skill mechanic exists for convincing NPCs of things, player tactical acumen in games with fairly tactical combat, or trapfinding in games that rely on player description of how the problem is solved). Player abilities are not readily testable with game mechanics, so a default to player skill usually happens outside the game system. Character background and actual skills selected (if these exist) could however influence how much knowledge a player can legitimately bring to bear without this being seen as hugely or invasively meta-gaming.)

Depending on system a starting character might have 1 skill for example in Deluxe T&T (for a 1st level character), AD&D 'secondary skills' [in 1E DMG/2E PHB], or DCC character 'profession', half a dozen broad skills (5E D&D), up to 15 or so skills (Savage Worlds - 15 points, so a varying number of skills depending on their rank), or 30+ individual skills (e.g. a Rifts Coalition Military Specialist, for skills they have; or a Call of Cthulhu character has a character sheet listing their rating for every skill in the game, but with many being at a base rating representing being untrained).
Often if a character only gets one skill, it is very broad and its impossible to learn more skills; generally it becomes easier the less meaningful individual skills become.

At a systemic level, how many skills an individual character has is partly driven by:
-length of the skill list and hence how specific skills are (cf. also 'skill lists' below).
-untrained default system: if a default is very low (or conversely e.g. in BRP, very high - i.e. attribute check) this acts as a driver of a large number of skills so that most skills are trained.
-whether there's a major 'jump' between trained/untrained i.e. 0 and 1 rank of a skill. If "competency" is at say about rank 5, a character will be given more points (and might instead have lots of low-level skills). This is something in part determined by 'granularity' of the dice mechanic. (this is something I noticed converting characters between lots-of-skills and few-skills games; one way to do it is to just select the few highest-rated skills).
-what aspects of the game system are covered by mechanics e.g. what things are instead covered by player skill.
-whether skill-type functions are covered off by 'class' (or even attributes); some class systems use skills to further define what classes can do exactly, in which case # of skills may skill be quite large (Palladium).
-if skills automatically scale up with level, then characters may get fewer extra ones as they level up (the automatic scaling is the primary method of advancement). It might be possible to add a patch skill that instead gives more low-level skills, i.e. instead of one skill automatically at +X someone could take a 'Skill Group' skill that gives X minor skills at +1.  Although, automatically scaling skills may also pair with especially big skill lists (see Skill Lists below).

Scale of Skill Numbers
Unlike attributes damage is not usually assigned against skills, and they are not usually 'rolled up' randomly (in part I suppose characters are usually assumed to have some control over their career choices, whereas they don't over how healthy or smart they innately are).  Consequently (as there's no need to design the range to buffer high random rolls) skills are normally scaled to function directly as a modifier to rolls, (along with any other applicable bonuses). (One example of skill 'damage' would be games where the core mechanic is resource-based e.g. Gumshoe, Dying Earth. Skill modifier may also be used to derive numbers like 'magic points' or 'body development' hits indirectly).
Sometimes a skill number may be used as a bonus to damage, bonus to 'soak', or other effect, (needs fairly granular skills to do directly).

Skills may be binary (you have it, or you don't;  limiting divergence in bonuses, and preventing players focussing all points on the most powerful skills; it can also be for simplicity e.g. if skills are also being costed based on how useful they are), or be buyable in multiple levels.
If binary, usually a skill either defaults to a flat attribute check (e.g. 2E D&D NWPs, Warhammer, Amazing Engine) or has a bonus that's a flat number (4E D&D's +5 for skill training), or may have a fixed class/level determined value (e.g. Palladium, though classes also get % bonuses). Languages may be treated as binary even if other skills aren't, with other skills applying for checks (e.g. Persuade).
If a raw attribute check represents 'trained' use, then untrained use might be impossible, a 1/2 attribute roll, default to player skill, or largely unspecified? (2E AD&D). World of Dungeons (http://www.onesevendesign.com/dw/world_of_dungeons_1979_bw.pdf) (simple Apocalypse-world variant) has a system where a 'skill' (really, class feature) adds no bonus to a raw stat check, but a character with the skill can't fail skill checks, instead receiving a worse 'succeed but with complications' result; already high rolls get no further bonus.

5E D&D is interesting in that skills are yes/no but with an automatically scaling bonus - a skill gives a bonus equal to the 'proficiency bonus' (hence tying into other rules); saves and hit bonus also grant bonus equal to proficiency, making them essentially equal to skills for most purposes (though a bonus that can be applied to 'any skill' couldn't be added to a 'save').
Minor kludges on basically 'binary' systems can be seen in 2nd Ed. AD&D (where an extra 'slot' gives a pitiful +1 to the check) and Magitech for Amazing Engine (which lets characters buy 'half skills' for roll-under-1/2 stat, instead of full). Sometimes a binary skill can be boosted with an advantage e.g. 4E D&D skills are trained (+5) or not, but characters can also take the 'Skill Focus' feat for an extra +3.
Level-based games with binary skills have trouble checking core class functions (i.e. they don't scale with level, or don't consistently use the same mechanic, or could have complex 'trees' of very specific abilities with prerequisites - I think Deathwatch is an example).
Binary skills also don't work with skill-based games, leaving them a choice that best suits attribute-driven games. Some exceptions here are 5E and Palladium - in both cases while the skill itself is purchased Yes/No, but it gets an automatically-scaling, level-based bonus.
Talislanta [3E, I think] gives characters a number of skills that automatically scale (a class skill may be 'primary' and increase +1/class level, or 'secondary' and +1/ 2 class levels), but can also buy 'rudimentary' skills with XP.
A primarily-binary skill system might let some characters effectively scale up a few skills with advantages or even powers that boost the score.

Skills are also sometimes set up on the same scale as attributes; for instance Savage Worlds rolls either stat or skill (which are the same d4 to d12 scale), or FUDGE where both use a ladder of ranking adjectives like Fair, Good, Superb, etc. In both cases the skill roll is unmodified by attribute. Storyteller is somewhat similar (1-5 dot scale for both skills and attributes - or almost, since skills can also be 0 dots) though it does apply stat modifiers since a skill check rolls [stat+skill].
Overall, this approach can open up some options for more efficient rules, like for fair stat vs. skill opposed rolls or even stat vs. power checks (Savage Worlds' powers e.g. from Arcane Background have skill ratings), for giving free default skills (e.g. free native language skill rank = Int score). Or, from Exalted: 'Linguistics rating counts as Appearance for written social attacks'.
This is largely incompatible with binary skills (apart from the 2E NWP method), as well as significant level-based skill scaling (as attributes are usually fairly fixed).

Other specific oddities related to scaling:
Modifiers: an exception to the rule that skill rating = skill modifier, in Rolemaster a character buys skill ranks and the rank then provides a modifier to checks - +5% per rank up to 10, +2% for each rank 11-20, and +1% for ranks 21+; this diminishing return tends to encourage characters to branch out after maxing their key occupational skills; at the high end, attributes provide critical differences since that can add an extra +25% or so regardless of rank. Generally, the same effect could be duplicated (with less use of character sheet space) by increasing the cost of ranks instead of modifying their bonus, although that would give different results on any other rank-based effects (# free levels in 'related' skills?). The diminishing returns occasionally generated undesirable results for melee skills (with difference from level for combat abilities of non-spell-user characters becoming too small).

Skills scaled without regard for dice system: 'The Future Belongs To Us' apparently uses a skill system where skill rating (up to 1000 for some skills) is used to determine what tasks a character can do automatically. This (reportedly) does not tie in much to the general check mechanic of d20 + proficiency score.
Negative skills: HERO 5 (The Ultimate Skill sourcebook) notes that a character can buy 'negative skill levels' - actually a Power, or part of a power -that then applies to opponents' rolls, e.g. combat or for resisting mind control.

Combining level-based skills and 'ranks': the Pathfinder 2e playtest has a level-based skill, plus has 'ranks' that add another bonus i.e. can improve to Master or legendary. An ability to let a character be 'legendary' has a level minimum, so level modifies the check in two separate ways. Its interesting to contrast with Palladium where characters instead normally get large OCC bonuses to raw skill %s - similar in that there's a level bonus and a flat bonuses; but PF2's definition names lock bonuses into later levels in 5E (it seems wrong to have 1st level character be labelled 'legendary' when total bonus is small), whereas in Palladium bonuses are instead always front-loaded.
More often names are just based on a rank (e.g. White Wolf would say 5 dots is 'master'). Or Fireborn list 'primary skills' and 'secondary skills' for each background, which just determines base 'rank' for each - rank 4 for primary and rank 2 for secondary.

Cost of Skills
If buyable in multiple levels, skills may have linear or non-linear costs.
A non-linear cost system in a sense helps balance by adding an incentive to raise lower-rating skills - if your Waraxe-Megadeath-Killing skill is already huge, you might be able to add multiple points of a Craft or Profession skill in place instead of an extra +1 to it, for the same cost. This works as a corrective factor, making it less critical that all skills are equally important/valuable (compared vs., say, d20 System skills that are always +1-per-rank). Non-linear costing can be implemented directly via having costs increase with each skill point, or a similar effect can be a result of the core dice mechanic itself (e.g. for 3d6 roll under, the dice roll's bell curve means later points added increase the total probability by less than earlier points).
Nonlinear costing can occasionally have odd effects e.g. if a game lets a character know one language per Linguistics dot and ranks increase in cost, it takes longer to learn a characters 3rd language than their 2nd (if cost increases but # languages also increases with each dot, cost becomes irregular).
While basically less balanced than nonlinear, the primary advantage of linear costing is that it is simpler. Another compromise to get this effect is to add 'prerequisites' in order to break certain caps - say if raising a skill beyond +10 requires another skill to be likewise raised 1:1, the effect is of a doubling in cost beyond +10. Or a skill raise might require special abilities be purchased separately. The FATE Pyramid is another related, more elaborate example.

Individual skills may all have the same cost, or may have different costs based on the usefulness/specialization of the skill -or IRL difficulty to learn it e.g. in Palladium: powerful skills such as Martial Arts may count as 3 or even 6 skill choices; in 2nd edition D&D, non weapon proficiencies cost between one and three "slots" depending on usefulness of the proficiency. Systems where skills have variable costs rarely have an individually purchasable skill levels as the math is more complex (though examples do exist - HERO, or DC Heroes has a 'factor cost' chart for allowing this even though cost/level is nonlinear). Also note that the game effect of variable cost, and of individually purchaseable levels, is somewhat similar - see 'Modelling Skill Difficulty", below. BESM 3E (and "Dx"?) reportedly have skill costs which are adjusted by game genre. Skill costs -or number of skill points- can also be affected by attributes.

Where skills all have the same cost, skills can sometimes be balanced by having skills that are relatively important (due to coming up frequently, or helping in particularly dangerous tasks) or may be balanced by being divided across a set of narrower skills e.g. instead of one fighting skill individual weapons may be distinct skills. Tasks that are really important are sometimes also split off from what the game formally considers its 'skill' system - for instance a level-based game may have combat abilities directly based off level with no skill involved, or the storyteller game Mage has magic actually use the character's 'Arête' statistic, rather than being a skill.
Systems may have multiple 'pools' of points for buying different sorts of skills e.g. 2E AD&D had separate 'Weapon' and 'Non-Weapon' proficiencies, while Barbarians of Lemuria gives a character separate allotments of combat skills (4 points across Brawl, Melee, Ranged, Defense) and Career points (also 4 points across Alchemist, Assassin, Barbarian, etc.)(Attributes are also generated the same way across Str, Mind, Agility, Appeal).
5E D&D separates out broad 'skills' from 'tool proficiencies' that are much more niche e.g. including musical instruments, gaming sets, or vehicles.

Skill Programs: Modern Palladium games (Ninjas & Superspies, Heroes Unlimited) allows either individual skills to be purchased or allows characters to choose 'skill programs' which are sets of several skills (sometimes, still including some choices). Some of these may form major 'chunks' of classes, with a program sometimes selectable instead of e.g. a major martial arts power (N&S). A program might contain a few good skills, or a larger set of weaker skills. Heroes Unlimited included 'professions' for Alien characters, which became alien 'skill programs' in Aliens Unlimited - aliens had few skills but still these were particularly large, counting as 2 skill programs and with extra skills thrown in if it was the 'profession choice'.
Somewhat similarly, Shadowrun 4E had 'skill groups'; these covered 3-4 skills each, and let a character increase all the skills in the group more cheaply (by defaulting to the skill group score instead), but preventing the character from buying specializations.
Some characters may get an adjustment to skill cost for some skills - e.g. in Exalted based on caste, in oWoD possibly by type [Vampire, Mage, etc.] just as the system evolved from book to book, or class-based in Rolemaster, 3.5 D&D. In generally I would view this as a bad idea (cf. post on point costs (http://www.therpgsite.com/showthread.php?p=515934#post515934)).
Champions reportedly (https://web.archive.org/web/20110309040638/http://www.afeather.net/~archer/hero3tohero4.html) had a Martial Artist skill which had a cost equal to a characters STR, i.e 30 Str = 30 points, higher attribute being higher cost.

Skill Improvement Limits: high skill values may be restricted initially by a hard cap for initial characters (can't exceed level X), a soft cap (cost is double above X), a stat-based limit (e.g. Savage Worlds when score > stat costs double), increasing costs that put some values generally out of the reach of starting characters, a limit that a character can only exceed for a couple of skills due to needing an advantage to do so. Original Storyteller had higher skills bought from a smaller budget - skills being limited to *** initially, unless 'freebie points' were used. See 'skill improvement' post below for more on this.

Modelling Skill Difficulty: How difficulty of skill use is modelled also varies between game systems; difficulty modifiers can be 'built in' to the skill score itself, or are expected to be situationally applied. Roll-under systems like RQ set varying base percentages for skills - that is, the base value for a 'routine' skill use factors in that some skills are normally more difficult. Similarly, Synnibarr sets a characters Piloting skill for trained characters at a base of about 100% (before any additional difficulty penalties) so that characters can drive to work without crashing.
On the other hand, D&D sets all skills at the same 1-point-per-skill-point value, and difficulties are instead rated for many tasks, or set by the GM, as target numbers. Consequently while all skills look like they have the same cost superficially, buying 'competency' in some skills where base difficulties are quite high (e.g. Use Magic Device) is much more expensive.
In other words, variable cost of skills, can be replaced by variable 'task DC', if characters are free to spend as many points as they like. That is, brain surgery could be a DC 10 task (but learning brain surgery costs 10 skill slots), or using brain surgery could be a DC 20 task (but your bonus is the same as any other skill). When a player is building a character this gets similar results either way, but how the system works should be understandeable by the player, so they don't under/over specialize their character.
Of the two approaches, variable DCs probably handles untrained skill use more realistically without further kludging; it ideally requires a list of task difficulties more comprehensive than "Easy-10, Moderate-15 Hard-20" however, and caps on skill purchasing can prevent some skills (and hence character concepts) being useful. Variable purchase costs mean characters must buy 'competency' as defined by the system to get the skill (no medical school washouts or semi-competent rocket repairers!) and can't break the skill-bonus system, but the skill purchase system becomes more complex (i.e. probably a longer list of detailed skills).

Attributes & Skills
Frequently, skills are modified by one or more attributes. Some games limit this to one (sometimes which one varying from occasion to occasion), others apply more e.g. Runequest often adds two or three. Keeping skills with the same # attributes keeps it perhaps more consistently scaled, though its perhaps not unrealistic that people vary more in capability with certain things. Games can sometimes have skills which have no stat modifier (again often realistic in context, but dependent on what stats the designer has already decided to include).
Attributes generally modify skills by either:
 
*adding a bonus to the skill roll (either a flat number or extra dice).
Elaborations here - systems may allow for cross-matching a skill to a different attribute depending on circumstances (e.g. the Storyteller system, or the original Cortex);or via advantages/feats letting characters switch controlling attributes (which works as long as attributes have a fairly consistent scale i.e. some can't rate twice as high as others, albeit that it may lead to different-cost i.e. unfair methods of maxing out skills).  (See also 'Weapon Proficiencies' later for weapon-based adjustments). Some situations might penalize characters by preventing them applying an attribute bonus, e.g. limited mobility preventing a character from adding DEX to attack.
Mutazoids has multiple possible defaults for some skills, but with some being lower i.e. Administration is either Cha/3 or Int/4.
Systems may also unhook skills from attributes for certain characters, e.g. FATE variant 'Bounty Hunters of the Atomic Wastelands' often has Skill ratings equal to attribute score, or a special ability can disconnect it/make it a step higher if the attribute is maxed fully: e.g. "Keen Senses: a Bounty Hunter's perception is treated as Great regardless of his Thinking score. If his Thinking is already Great his perception becomes Superb"; similarly an early D&D Next playtest let thieves default to a stat mod of +3 for some skills.
Quite often games will double stat for raw stat checks (e.g Unisystem, Magic Quest, Talislanta). Done well this lets the same difficulty scale apply for both raw attribute and [attribute+skill] checks. Making this work well is one argument for having large stat numbers (e.g. 1-10) instead of just modifiers rated around average 0 with correspondingly lower target numbers.
Some skills as noted above may lack a controlling attribute. If stats are random (particularly if adding stat directly), it might work to add extra dice as if generating an attribute to each skill roll (i.e. stat rolled on 3d6+skill 2d6 - a bit like Tunnels and Trolls? - just roll 5d6 for skill). Or oWoD Storyteller could use a Luck Roll's successes l to generate a # dice if no attribute applies, then add skill dice and reroll.

*being rolled for skill checks directly (i.e. Warhammer 1e/2e, 2nd Ed D&D Non Weapon Proficiencies/ Basic D&D General Skills). In these cases what to roll for 'untrained' use is generally vague (2E) or defaults to e.g. 1/2 stat (WHFR 2). (And World of Dungeons as noted above has no bonus for having the skill at all, but worsens failure results for untrained use).
Hackmaster often has skills based off two attributes, with the lower of the pair used unless an extra 'build point' is spent. Beyond the Wall (reportedly) uses stat rolls and adds a +2 to a stat check for a relevant skill, which (if PCs generally pick skills for stats they're also good at) makes the die roll nearly superfluous (http://forum.rpg.net/showthread.php?760416-Old-school-ability-check-odds) (near 100% success rate).
This is possibly useful in allowing a skill to use multiple stats simultaneously, by averaging the stats. Forgotten Futures is interesting here in often using avg. of multiple stats, despite having only 3 stats - Body, Mind, Soul.

*modifying skill cost (usually assumes skills are purchased in multiple levels). E.g. in Savage Worlds, an attribute's main effect is capping when a skill goes to double cost. As Edges and skills are bought from a single points pool, a low attribute can thus give an incentive to pick up an Edge that would normally be suboptimal instead of raising a skill further.
A few systems (WEG's Star Wars, Feng Shui) give skills non-linear costs based on total attribute+skill, i.e. a high attribute raises purchase cost. JAGS and DC Heroes provide the option of "linking" a skill to an attribute, or having a wholly separate skill score.
The downside to this approach is with regard to balance - for example, a high stat may or may not be a benefit depending on which skills you pick. ( See post #121 on point buy variable costs for related discussion).  
A 'cost' modification can also be done by first assigning points, then adding a bonus to them based on attribute; so, Basic or AD&Ds' 'bonus XP for high prime requisite' is another version of this.

*modifying improvement rolls (if skill gains are random). HarnMaster has a 'skill base' calculated by averaging up to three attributes, with improvement rolls getting a bonus for high stat (see next post).  
 
*determining the number of skills (or skill points) a character gets initially. This is fairly clumsy and awkward compared to modifying the purchase costs of skills for the relevant attribute - it has a similar overall effect (i.e. high stats = more skills), but makes it much more awkward to represent how different attributes give benefits to different skills.
Synnibarr and SuperWorld both add together a set of attributes to give a total number of "skill points" to spend on skills, meaning a high STR can give you the points you need to learn Rocket Science (...or for Synnibarr an extra cool mutation) ; Buck Rogers High Adventure Cliffhanger game gave 4 skills to the top-ranked attribute, 3 to the next higher rank, and so on down to 1 skill for the character's worst stat.
 
A couple of games have stats modifying per-level skill points as well. Rolemaster has 'development points' based off a characters several random-rolled statistics, while 3E D&D has a simplified version of this modifying points by INT modifier each level. With random roll this can have unfortunate effects, with higher stats continually drawing ahead (though RMs' diminishing returns on bonus from rank may slightly ameliorate this). (HARP had a particularly bad system for this where stats determined development points, but development points could then also be spent to raise stats in a feedback loop).
 
*a skill check may default to an attribute check if the roll fails (so the skill gives an extra separate roll). For instance, in Gangbusters a character with Boxing can roll their Boxing skill to hit an opponent; if this fails they receive the normal Agility check to do so (success on the boxing check indicates two hits, rather than one).
 
*default to attribute check if no skill, otherwise unmodified skill check (DC Heroes, Shadowrun 1e-3e: see following section). This relies on players' being aware of the system and building around the 'trap' option, as a character with low skill may be better off defaulting to attribute anyway.
HERO [4E] uses the opposite system - background skills default to a base chance, but can be upgraded to a 'characteristic roll' for a character point if desired.

*skill and attribute may do different things e.g. in Legend of the Five Rings, skill determines number of dice rolled and attribute the number of those (starting from the highest) that may be kept and added together. In Wolsung (see reference here: http://forum.rpg.net/showthread.php?628579-Interesting-Attrribute-Skill-interactions ) a d10 system is used where skill increases the threshold at which dice explode (e.g. Strength 2 higher than normal allows a reroll on 8-10, instead of only 10) while Skills just give a flat bonus. Arrowflight 1E has dice pools where stat determines number of dice rolled and skill determines target number.
 
*'Edge of Midnight' has all tasks using separate [1d10+trait] rolls for skill and attribute, with effects on how the success is narrated (i.e. complete success if both succeed, total failure if both fail, partial success by skill, or partial success by raw talent).

*occasionally (Palladium; FUDGE) attributes may have more or less no effect on skill scores. (Fudge evolved into FATE, using Aspects to plug this; Palladium actually does it in reverse, with skills modifying attributes instead of the other around e.g. "Running - +1 to Endurance and +4d4 to Speed"). To an extent I suppose Palladium's system is justifiable if it is assumed that a character develops particular talent in aspects of an attribute related to their skill (climbing muscles for the guy who climbs alot, strong right arm for a baseball pitcher, etc) which then overflows into their general attribute). FUDGE does suggest that characters stats and skills be built logically by the player i.e. there's some expectation that the player might assign good physical skills to a character with good physical stats.
 
*potentially, in a system where attribute modifies advantages/disadvantages (cf. ROAR where a high stat gave 'faculties' and a low stat gave 'flaws' e.g. a low CON making a character a haemophiliac, low STR dwarfism or low CHA scars or exile) attribute modifier could be dropped entirely to solely use ad hoc modifiers from advantages/disadvantages. You can again compare this approach to say 0D&D, where different (but not game-mechanically-defined) ideas of how a stat works could affect checks, such as a character with Dex 3 being 'as blind as a bat'. This approach also operates slightly as a secondary mechanism for adjusting checks in Savage Worlds, where a particular stat may be a prerequisite for an Edge (Spirit d8 to get Charismatic, for example).

*Other weird: Fireborn is interesting in that skills are buyable in multiple levels, but are basically a raw attribute check. What skill ratings do is that characters can move dice from another stat onto the main stat roll, and this is capped by the skill. (Perhaps its almost-binary since the system can't account for different skill ratings in action sequences, see 'actions' post). Higher skills' then give extra dice, but generally at a cost e.g. more melee means higher attack but less defense (the exception being non-combat scenes where the reduced stat likely won't come into play). Skill rating also limits how many associated manuevers can be piled into an attack sequence e.g. a character with Athletics 3 could [Climb+Climb+Climb] but if they had 5 actions, couldn't spend the last two climbing.

As noted under attribute modifiers above, skill and attribute vary considerably in their relative weighting on tasks, due to how much of each contributes and the relevant variation in each (...if everyone has an 18 for a +4 bonus, its real 'weight' is limited). Skill labels are often added to skills (Whitewolfs' 5 = master for instance) but this labelling can be deceptive if attribute weighting is high.
Relative weighting of bonus from attribute, vs. bonus from skill is something to consider carefully especially if you intend to allow purpose of attributes and skills from the same pool of points instead of suballocating pools, since it may be more optimal to spend points on one over the other, like how in GURPS its usually preferable to go for attributes. In any system watch relative stat/skill gain costs from earning XP or levelling, which is usually a common pool and may have problems too.

Overall: Attribute modifiers can boost low/untrained skills particularly, boost high-end skills particularly, or boost everyone equally. Which depends on method chosen, and probability curve of the core mechanic itself e.g.
Savage Worlds [High-end] - stat raises 1:1 purchase limit.
Storyteller- [All Equal] - albeit for many checks if 1 success is all you need, the stat helps low skill ratings more.
D20 [Low-end] - bonus outweighed by level bonus at high level.
Star Wars D6 [Low-end] -increase cost for skills is based on total score.
HERO [Midrange]- low values increase more due to 3d6 curve, then hits scores cap.
Overall character-benefit of a high score (for skills based on it) - will depend on its cost, and how common low or high skill ratings are.

Talents
Game systems can also try to give characters skill modifiers from innate ability separate to those defined by the games core attributes.
This may be for more realism for instance or because the game has a limited number of attributes (or no attributes), to supplement attribute modifiers where the effect of those is low, or add more variation to skills if these are fairly fixed. Subabilities, feats or merits/flaws can do this, or 'talents' might be determined randomly, either in a generic or very specific case-by-case fashion. Skill specialties (or just higher skill purchase) could also represent talent, if the game system doesn't want to differentiate between innate and learned skill boosts.
Fantasy Games Unlimited's range of RPGs (e.g. Daredevil, Aftermath) included a set of modifiers to skills from "Talents", each of which covered a skill category, as well as attributes. Dice rolls generated base talent ratings from -4 to +4, with a pool of discretionary points also added. Talents could also provide special advantages (but are presumably not usually tested individually, the way attributes are). deadEarth had characters roll for each skill for inability/ability (it uses an Xd6 dice pool with ability letting 1s be rerolled and inability makinig 6s reroll once - abilities and inabilities are by default rare -2 or 12 on 2d6 - but the mechanic is also used by mutations which may give particular abilities or inabilities). Synnibarr has an optional roll to determine if a character's learning rate for skills is modified. GURPS has a number of specific advantages/disadvantages; it showcases one problem with these, that being skill boosting merits mainly just create ways to alter effective cost of skills (and create less balanced characters) in context of its point-buy system, a problem difficult to fix when skill costs are non-linear.

Other subsystem modifiers to Skills:
Not infrequently advantages/disadvantages may modify skills as well as raw skill point expenditure.
Savage Worlds has a lot of these, for instance. FantasyCraft is interesting in having feats that alter 'crit range' of skills (raw bonus doesn't affect this).

Skill categories & specialties
Some skill systems also include rules for specializations in skills e.g. Shadowrun. Similarly, LegendQuest has multiple skills of varying widths which are potentially stackeable onto the same roll - "group skills" including Melee and Rogue and potentially fulfil the same sort of role as 'classes' by giving basic ability in a set of skills, including cancelling the default -15% untrained penalty. (Kerberos Club for ORE has a similar arrangement with Broad/Flexible/Influential skills, with broad skills useable in various profession-related ways and likewise multiple skills potentially stackable). CORPS has (reportedly) stackable broad Primary skills, then Secondary and Tertiary skills - secondary rating can't be higher than Primary and Tertiary no more than half secondary.

DC Heroes lists various 'subskills' for each skill; a character can buy just one or two subskills if desired, with a cost discount [Though being good at particularly niche things can also be the "Scholar" advantage, which is more expensive, e.g. Lobo is a 'Biology' scholar with some scientist skill]. Most specialization rules reduce cost to buy higher ratings or add a bonus, though deadEarth has specialization skills used to roll against a lower difficulty (useful though it doesn't help with opposed rolls). Another variant for a dice-pool-step-die system might be to have narrower specialties have larger dice for tasks.
Specialties might be purchased with skill points as skills are, or, a skill might give a free 'specialty' when chosen (other related uses being penalized), or a specialty might be gained automatically at a higher rating - oWoD Storyteller gives a free specialty (reroll of any 10s) to any skill at 4 dots, while HarnMaster lets a character get a specialty (+10%) in a skill at 70% and again each further 10%.
Freerpg FURPIG (http://fast-times.eldacur.com/Furpig.pdf) lets characters who reach 'perfect mastery' of a skill or 100% (limited to one character per skill in the universe) create new super-skills building on their mastered skill.
Alternity had 'broad' skills which were yes/no - without the broad skill a stat check to use the skill was halved - then "specialties" which added a bonus to more specific actions (e.g. broad skill Athletics, specialty Jump). It had rank benefits for higher specialty ratings, with characters also sometimes being allowed to spend skill points to gain a benefit prematurely e.g. brawl 8 gave a damage bonus with unarmed attacks, but a character could spend skill points - based off the rank difference - to get this earlier).
Hero has 'penalty skill levels' letting a character purchase reductions to situational penalties, such as range modifiers, called shot penalties, throwing unbalanced objects, or being prone/encumbered/underwater. (As well as possibly 'rapid use' penalties). Some powers or advantages could also modify skill use (e.g. "A character who buys his legs and/or mouth as Extra Limbs suffers no penalties for performing Agility Skills with them" - The Ultimate Skill supplement for Hero).
Original Cortex reportedly had broad skills which could be improved up to a threshold; beyond that a character had to choose and individually improve specializations.
Skill specialties are handy for adding depth to characters while still having very broad skills, and thus a short skill list (a normal problem with broad skills being that characters can end up with odd competencies due to skill conflation, like Pathfinder paladins being good at Gather Information (a Diplomacy function in PF).
5E D&D has very broad skills  at a quite low bonus - being trained in a skill at 1st level is a +2 bonus or +10% - with 'subskills' generated via specific class/race abilities -e.g. rangers double their proficiency bonus in a particular terrain, while dwarves and gnomes double their History skill with stonecunning or 'artificer's lore' respectively.
In a sense raising attributes has a similar effect to having 'broad' skills in most systems though even broader (assuming a +attribute bonus to skill checks, or default to attribute - it doesn't apply in e.g. Savage Worlds, and barely in Runequest).
Skill specialties can overlap somewhat with "complementary skills" (see later). For example, Mutazoids would let a character roll a Jury-Rig skill check to get a bonus on a Mechanics skill roll; Storyteller would instead have a mechanics-type skill with a 'jury-rig' specialty. Mutazoids here has the advantage of being able to define different levels of jury-rig skill (not just yes/no; although, other games do have specialties that aren't just binary) and allowing matching of Jury-rig with other skills if need be (though that might not really be required either, the principle could apply to other cases).

Skill-based special abilities
A simple case of this is where some threshold lets a character skip a check e.g. oWoD vampire lets Drive * handle automatic vehicles and Drive ** for manuals. That can sometimes happen automatically as a result of e.g. 'take 10' type rules [cf. post 28, excess rolling].
4E D&D (in PHB-3 and Dragon magazine) has "skill powers" which are available to characters trained in a skill, and which can be taken instead of a normal (class) power when levelling up, giving extra abilities related to a skill (like 'fast hands' for thievery, or ability to substitute Knowledge checks for raw Int checks). These count as alternate 'utility' powers which are only gained at e.g. level 2, 6,10 etc - fairly artificial and they can't be used to make more diverse or skill-focussed starting characters.
3E D&D (in Complete Adventurer) had "skill tricks" which cost skill points but which worked similarly, giving characters special abilities for skills like 'whip climbing'. A game with advantages can similarly limit access to some of these to characters with an appropriate skill (no doubt GURPS has done this at some point). Effect-based systems (see the super powers section) can model this backwards sometimes - M&M (I think) allows characters to take a 'requires skill roll' as a limitation on a power to represent something being skill-based which by default needn't be, although this is problematic since buying enough skill ranks makes the actual detriment of the limitation questionable.

Skill Lists
Skill Lists may be described as edge-defined or centre-defined.
(see thread: http://www.therpgsite.com/showthread.php?t=18250 )
 
Skills are sometimes player-defined (e.g. in Teenagers from Outer Space); in other systems basic skills may be defined but characters may have some leeway in inventing specialties (e.g. Storyteller).
Length of skill lists: Length of a skill list usually flows from other concerns (i.e. definitions of the individual skills) though Fate Core attempts to work the other way, with length of the list chosen to generate enough diversity between PCs while still giving parties access to most things. Skill lists are also sometimes rejiggered to balance out number of skills relating to each stat, and hence relative stat importance.

Games can have shorter skill lists if 'class' normally covers that purpose, or if characters are largely differentiated in other ways, for instance in a supers game where powers largely differentiate characters:  early Champions for instance was said to have had a fairly simple skill list until the HERO system started to cover the non-supers genre with other games, and many others e.g. MSH likewise gave out only a handful of simple binary Talents giving +1 step to stat checks. Overall simpler games also have simpler skill systems. Another interesting case is drama-based Cortex+ game Smallville, where personality/relationships somewhat assume the role of skills for checks.
There is some discussion here (http://www.therpgsite.com/showthread.php?t=32835&page=7) on the merits of 'narrow' vs. broad skills (broad being the current trend, with PF/4E and 5E D&D having skills designed to more or less cover every possible eventuality).
Skill 'tiers' (see below) also make for longer skill lists - (e.g. one Mathematics skill vs. separate 'Basic Mathematics' & 'Advanced Mathematics' skills).
Games with fairly vague skill definitions, leave the GM some leeway in deciding how 'broad' a skill list is. As a weird example Gamma World D20 is actually fairly defined (=d20 modern), but also claims in the GM guide that the GM can or should alter skill 'breadth', e.g. whether Craft skills also include "related bits of lore" depending on if they want a pulp hero feel vs. gritty feel in the campaign. Fiddling around with this significantly also alters the balance of power between classes that are largely skill-based vs. those that aren't.
One mechanical factor affecting length of a skill list may be if skills automatically scale (e.g. with level) or not: having skills scale up automatically is more compatible with a longer skill list (e.g. Palladium), whereas allocating points is more likely to be unbalanced the more skills there are (it becomes hard to keep up with all expected skill requirements and generates significant areas of incompetence for characters - maybe 3E D&D).

Skill tiers
Skills may form tiers where one skill is required to buy another skill. Palladium uses this a fair bit (i.e. Math-basic and Math-advanced are separate skills, instead of Advanced being the same skill at a higher rating). An approach such as this can let characters be built that can achieve specialized tasks easily without being generally competent in other areas i.e. the rocket scientist who has Rocket engineering, vs. the rocket scientist with Mechanical engineering at super-high levels and can also fix anything else ( although with a more detailed skill system required compared to just having 'specialization' rules).
Skill tiers in this case may be a consequence of binary skills e.g. for Palladium while characters have varying %s, purchase is binary so you can't choose to be good at something, except by buying multiple distinct skills (apart from OCC bonuses to skills). Dark Heresy may be another example of this.
Lords of Creation built tiers into skills explicitly, with each rank of a skill group being a new skill - which did mean characters couldn't be good at some skills without learning vaguely related skills. deadEarth had complex prerequisites which sometimes accidentally formed 'trees' - Armor Repair requires Smithing, Construction and Chemistry, Smithing in turn required Metallurgy and a Weapon Skill, resulting in some skills having large point costs to buy. (everyone has herb lore, but Haggle is rare due to having 5 prerequisites; Intimidation requires Resolve which requires Running).
 
The free rpg JAGS has an odd rule which seems something like skill tiers; characters buy a skill level for rolling against on checks separate to a rank description ('level') of the skill - Beginner, Professional, Expert, or Master. A character suffers a -3 per level beyond their own, and usually a discount on difficulty penalties, but a character with a high score may be able to do routine low-level tasks more reliably. This sometimes represents changing tiers of skills (Level 3 Lockpicking is 'safecracking') but its not always clearly designed.
 
Skills which 'overlap' sometimes use different task difficulties for the same task. Risus for example describes this as 'subjective difficulty': tasks become harder the further removed they are from a character's "cliche" (the Jungle Lord can swing on vines automatically, the Swashbuckler easily, while other types find this more difficult). A more formal version of this would be skill defaults (below).
Risus also very generously allows characters to substitute "inappropriate" ratings for checks as long as the player can describe it, and rewards this by giving "inappropriate" ratings additional damage in contests - i.e skill misuse is encouraged for the humour value.

Skill defaults and untrained penalties: [attribute+skill] systems generally default to just [attribute] for skill checks. However, a key concern is often to give a character with some training a hefty bonus for knowing a skill vs. the character with no training hence additional penalties may apply. If a game uses skills for combat the decision for this will also obviously impact untrained weapon use.
Some examples of default systems:
*In oWoD a character rolls [stat+skill] but the target number may also increase if the character has zero skill, or a check may not be allowed.
*A few systems may have base ratings for all skills e.g. BRP/CoC/RuneQuest - lack of an easy default system in BRP means it needs fairly long list of skills to cover most eventualities; a raw attribute check would have a much higher chance of success than a skill check. Here there are no extra penalties for not having a skill, but 'competency' represents a large investment of skill points for many skills.
*D20 system: this gives characters x4 skill points initially (so a 'starting' skill level is +4). Pathfinder instead gives any trained class skill a +3 extra bonus.
Normal 3.x has some characters unable to use some skills untrained, or for some skills just not use certain functions (others are fine). FantasyCraft by comparison has a DC-based ban (if untrained, can't pass DC >15) instead of specifically task-determined. IIRC.
*The D&D 5E playtest of midyear 2013 added 'skill dice' to a d20 roll i.e. a roll is d20 + stat modifier, +d6 if the skill is trained. This gave diminishing returns on skill points spent as the largest bump is at the initial skill level (+3.5), while successive improvements in skill to d8,d10, or d12 have less effect (+1 on average each time).
*GURPS has a complex system where each skill lists several other skills that can be substituted at varying penalties - a character might be able to attempt a combat move using Dex-6, Karate-3 or Quarterstaff -2, or something. Metascape similarly has varying penalties based on how similar a check is, but penalties are GM-assigned; it also recommends the GM reduce penalties or make tasks easier if there are no skilled characters.
*Shadowrun 1E has a complex flowchart, the "Skill Web", indicating how many "steps" any skill is from any other skill or attribute (=what penalty), which fulfills the same function as GURPS defaults. This could make defaulting a better option for characters with low skill and a high related skill or stat, depending on target number and how many successes a task required, but with which to use being fairly non-transparent. Characters usually got no bonus from stats to skill checks in 1E unless using them as the default (although in combat a character might get extra dice from 'action pool').
Shadowrun 3E replaced the Skill Web with a default rule that if a character with no skill could roll attribute with a +4 target number penalty; 4E dropped this as TN was fixed at 5 and as rolls went from just skill in dice to [skill+attribute] in any case, but had an extra -1die untrained penalty.
*Default to stat roll. DC Heroes does this; characters either use a bought skill value with no attribute bonus, or default to [attribute score] with a column shift penalty. It has the problem that characters with very high attributes should not buy skills, or only if they buy large amounts of them. DCH characters can buy points in a skill equal to the attribute exactly, no higher or lower, as a 'linked' skill, with a cost discount, but overall costs are fairly ad hoc.
*Palladium (according to one Rifter) suggests d100 under stat instead of the normal percentage which gives very low default chance -unrelated to how difficult the skill normally is to perform, which sets the base percentage.
*Skill-based dice pools with low attribute mod: here the task mechanic is very deterministic based on skill level, inherently making untrained rolls difficult or impossible anyway. For instance, Central Casting suggests a skill system where a character rolls d6s equal to skill level (additive), plus or minus d6 for a high or low attribute.
*Default to 1/2 stat instead of full stat: often used where a skill would ordinarily be a stat check e.g. Amazing Engine, Dark Heresy/Deathwatch. Note that '1/2 Stat' gives a very different probability depending on whether a game uses a linear die like d20, and multiple dice like 3d6 roll under (much less than half).
*ZeFRS (originally in the Conan RPG from TSR) - here there are no attributes but a characters total ranks in groups of related skills ("talent pools") are added together and divided by 10 to give a default talent rank. The idea is interesting but this requires a fair amount of granularity (ZeFRS uses a d100 table lookup), with base chance of success being quite high even for zero talent; while being more realistic in some ways than say GURPS despite the latter's complexity, the bonuses involved are small and fiddly (unlikely to be more than +6% or so).
*D&D 4th edition has binary skills where a character gets +5 if trained in a skill. Characters can take a 'jack of all trades' feat giving +2 on untrained checks (i.e. half the trained bonus).
*Talislanta rolls d20+stat+skill level, but uses d10 instead of d20 for untrained rolls.
*Savage Worlds uses a default roll of d4-2, and the -2 also applies to the Wild Die (normally a d6 reroll with no other adjustment). It also allows a "Common Knowledge" [Int] roll for areas not really covered by skills, with modifiers for character background. As noted above, stat affects purchase limit for skills, but doesn't modify untrained skills.
*LegendQuest has a fixed penalty (-15% for untrained use), but with the interesting idea of 'cross-matching' untrained penalties i.e. attempting to use archery from horseback without Ride applies the Ride unfamiliarity penalty to bow use.
*The GDW House system (Twilight 2000 2nd ed, Cadillacs and Dinosaurs, Dark Conspiracy) is a skill-based system with no defaults. Skills are bought up from zero and an easy task by default gets 2x rating; hence characters are by RAW often unable to attempt many basic tasks unless they've put ranks in them including shooting guns, shooting bows, Perception checks, and Persuasion checks. The skill system covers most tasks quite comprehensively, which makes the problem with Perception harder to houserule fairly (adding a default rule likely disadvantages those who took the skill, whereas if no one had Perception skills it wouldn't). T2000 edition 2.2 of the rules changes to a D20 roll under [stat+skill] to address issues such as this. Cadillacs & Dinsosaurs does often give a couple of ranks in skills for free based on background, including shooting - the "free skill" sort of works for shooting in that some characters (e.g. the Wassoon tribe) are quite primitive and wouldn't have any knowledge of firearms, though its a little too easy to accidentally create characters unable to fire a gun. The 'free skill' approach does make maxing-out those skills more expensive than raising the benchmark performance for untrained characters would have.
HERO similarly has 'everyman' skills, where every PC may pick up some specific skills. Giving everyone a skill is probably less useful than adjusting default difficulty and whether 'untrained' use is allowed.  
Giving out 'free' skills could sometimes be an easy way to generate some base values or fudge numbers; for instance, if everyone has a few ranks of 'Running' skill or 'Body Development' skill, this could be used to generate movement rate or HPs without overcomplicating a formula (having to add an extra base value) and while keeping maximum divergence in ratings low.
*The HDL system uses (basically) stat+stat for stat checks and stat+skill for skill checks. The 'good looking' merit makes a seduction roll from a skill check to a stat check (so that the merit effectively gives free skill points equal to stat number). Its interesting, though this has a couple of problems: free point shortcuts like this can create multiple ways to build a character some of which are cheaper, and the merit is conceptually redundant with the games' actual Looks attribute or at least poorly named.
*in 2E AD&D, skills (NWPs) have no defaults, but what skills cover isn't well defined and untrained use isn't expressly prohibited so, GM-permitting, an untrained character may still be able to pull off the equivalent of successful "skill use" with an 'old school' approach, getting the GM to describe the situation exactly and reacting with player skill.
*In Warhammer 2E characters typically had a skill or didn't (rarely it may get a +10% or +20%); WHFR-4E instead distributes 'advances' that are +1% increases. Similar to 3E not all skills can be used untrained and a character needs to put 1% into an 'advanced' skill to use it, but 4E looks more annoying in this regard in that the points are more more fine-grained. Which is to say, trap options exist in that a character can choose between a +1% that increases their stabbing skill from 30% to 31%, and a +1% that lets them use e.g. a Lore skill at all (from 0% to 31%).
 
A couple of games have skill 'defaults' but still let characters drop below default - e.g. 'The Agency' (as mentioned in Attribute Effects), or Genre Division 3 (reportedly) where characters can have 'incompetencies' rated at -1. Original FUDGE also usually defaulted skills to 'Poor', but with characters able to reduce some to Terrible in exchange for a skill rank elsewhere. Games with disadvantages can also have disadds that ruin particular skills e.g. 'All Thumbs' in Savage Worlds. Whether this is really necessary depends a bit on how competent having any ranks in a skill makes the user.

Special: a couple of systems have no specifically defined mechanic for skill use. A primary example would be Secondary Skills (from the 1E AD&D DMG, but most often recognized from 2nd Edition D&D) which describes vaguely what a character is capable of but leaves the exact mechanic to us (ability check, GM-defined percentage, saving throw, etc.) at GM discretion. Similarly Superbabes defines how to resolve some specific cases (usually with d20 roll under ability checks) but has no defined method for using skills overall.
Reputedly, Traveller also originally used different resolution systems for each skill.
 
Extended Checks: A few systems (Alternity, 4E D&D, Shadowrun, White Wolf) have skill mechanics for complex or extended skill checks - see more in future sections dealing with e.g. Crafting. These tend to work most easily with dice pools. An extended system tends to be used in RPGs for representing lengthy actions, although they are better really for cases where a single die roll is too polar, where multiple characters can help/cooperate, or possibly (it is argued) when useful for building dramatic tension.
More successful versions of this give some way to have a higher success grade on a single check make more progress e.g. by counting successes (dice pool); Alternity had a system where a good success (under 1/2 skill) counted as 2 successes and an amazing (under 1/4 skill) counted as 3.
 
Skill-less systems (see also post #21, derived attributes): older versions of Tunnels and Trolls have no skill system; rarely in play a character may get to roll to see if they have a particular skill (e.g. an IQ roll to see if the character can play a piccolo when fighting a Shoggoth). It does have a language system.
0D&D/ early 1st edition AD&D has no skill system, with class determining most of what a character can do and player skill often used to resolve other actions (i.e. describe to the GM how you would do something and they determine the result).
Gamma World (4E) gives skill points to spread among 'class skills' but handles most tasks with derived attributes, except for a % by class to know Reading/writing, Riding and Swimming.
Maelstrom mostly defaults to pure attribute checks with occupation giving some special abilities. While there are no general skill points, 'preaching' ability is based off # of years spent studying the ability.
Skill-list systems can also require GM arbitration of tasks based on character background to determine what a PC can do.
 
Complementary Skills: FUDGE lets a character with a (GM-determined) secondary trait add a +1 to the task if Good or better. Fuzion lets a character roll one skill in order to get a +2 to another skill roll (e.g. using a successful Fashion roll to get a +2 on a follow-up roll to Seduce) again GM-determined. This rule can be used to generate e.g. attack bonuses for successful stealth rolls and the like. (Note that this system where a roll not an extra skill rank adds a bonus, a character might be able to leverage extra benefit from a high attribute, and/or involve extra attributes - e.g. in the above example, both Fashion and Seduce might be Cha-based, letting the character who passes the synergy roll due to CHA effectively 'dou

The "Play Rifts" skill starts at 15%, but you get +7% per level.
So by level 8 you can be successfully playing Rifts fully 50% of the time."
-OptimusZed, penny arcade forums.

Skill improvement resources in many systems are linked to other character improvements e.g. based off level, or points may be spent on either skills or other improvements.
 
*RQ/HarnMaster usage-based improvement- significant skill use gives a character a “tick”; they roll over the skill (i.e. the skill check must be failed) to get additional skill points; this slows down increases in skill values as the score increases (conversely to this, Synnibarr gives improvement for a skill only if it is used successfully and subtracts if a character fails checks, meaning high skills get higher and low skills get lower (!)). RQ doesn't handle gaining advantages/disadvantages etc. as RQ doesn't traditionally have a major advantage/disadvantage system; some attributes in RQ may be boosted with training. IIRC RQ doesn't modify improvement rolls for high attributes, so benefits from these erode over time; HarnMaster however uses a roll of d100+ Skill base (the average of three 3-18 controlling attributes for the skill) so that higher attribute characters keep ahead on relevant skills.
Risus likewise has usage-based improvement - a "cliche" rating improves if all its dice are rolled and come up an even number, so again higher scores are less likely to improve.
Skyrealms of Jorune is noted here (https://refereeingandreflection.wordpress.com/2014/04/18/referees-bookshelf-skyrealms-of-jorune/) as similarly having rolls to improve skills, however, rather than being vs. the skill score, a roll is made against a characters' "Learn" attribute (linearly rolled!), so characters with a high stat have a permanently much faster advancement rate.
Gamma World 5E has a usage-based system for psionics (each time you use a power, gain +1, a character can spend bonuses to try to learn a new power), despite other advancement being XP/level based.
Mercenaries, Spies and Private Eyes has characters earn XP separately in each skill they know, e.g. 50 per round used; this uses the same table as character advancement in level, but that earns xp more slowly. New skills can be learnt only by raising the Intelligence attribute, which gives more skill points.

*time-based e.g. the ALIENS Adventure Game (Leading Edge Games) gives a skill roll to improve after each year of game time. StarCluster adds a skill improvement each year at the cost of an attribute decrease (Immortal characters in Outremor get neither, but can shift a skill point around).
 
*Training/money may be used to purchase skills, rather than experience points (RQ again; SenZar; Languages in AD&D (if not using NWPs) or in Dragon Warriors.
 
* the GM may award ad-hoc increases. Similarly to this, Amber uses points, but with the GM tracking advancement of the player without their knowledge of the PCs exact capabilities.
A sort of example of this- although not a skill improvement per se - may be fairly obscure freerpg FuRPiG, where the GM is allowed to give permanent "Bonus Hit Points" to characters who "have been particularly valiant in battle" and "continue to fight against extreme odds right up to Death's door". In similar vein, some Tunnels and Trolls adventures would grant stat raises for with little or no explanation ("you spend several hours conversing with Lorac...add 3 to your IQ for absorbing some of the much and varied knowledge of this man"), and in other places grant bonus skills for some event (visiting the Archer's Guild in City of Terrors, making an IQ SR to know how to play a piccolo in Arena of Khazan) - the Deluxe T&T rules formally recognize this, giving the GM ability to reward PCs with new 'Talents'. In many systems ad-hoc GM adjudication handles fuzzier cases outside the main rules e.g. gaining reputation and the like - though GURPS would probably charge characters points for adding the "Welcomed as a hero in Turdhaven" Advantage after saving the town, of course.
 
*XP: Characters may be awarded XP, which are spent to either increase the characters’ Level, or to buy up specific skills. (Talislanta allows XP to be spent either on putting up Level – which increases all a characters career-related skills - or buying up specific skills individually; among other things this meant the GM can stat up a generic NPC of a high level quickly, while still giving PCs using the same system the flexibility to add skills beyond their character class).
In a level-based game, there might be have abilities based off exact XP total as well i.e. in Basic D&D demihumans eventually would cease levelling/getting hit dice, but still would gain combat abilities at specific xp totals; 1E AD&D Barbarians gained a 'Horde' with 1 member per 1000 of their XP. Savage Worlds gives "advances" (a new skill, pair of skill increases, Edge, or stat bump) every 5 xp and a full Rank increase every 20 xp (which mainly gives them access to new and better powers or Edges).
Skill-based systems that use XP (but not levels) may still have other limits to how far skills can be improved. Limits can be attribute based (Savage Worlds); FATE has a 'skill pyramid' whereby a character can only have so many skills of a certain rank without having more skills at a lower rank. This occasionally annoys people ('I can't improve my Drive skill until I've gained a new skill in Interpretive Dance') (perhaps letting players create new subskills would help here, so they buy a separate 'Handbrake Turn' skill instead).

XP or equivalent rewards may be awarded for various actions including defeating monsters, delivering the final blow on a monster (MERP), bravery, surviving, clever ideas, avoiding unnecessary violence (Palladium), roleplaying a character well, self-sacrifice, annoying other PCs (picaro (http://www.therpgsite.com/showthread.php?t=33686) rules, with thanks to Shipyard Locked), rolling critical successes, rolling any saving roll with an amount based on dice roll/level of roll (Tunnels and Trolls), failing rolls (Dungeon World), travelling a certain distance (MERP), just attending sessions (Storyteller), keeping diaries or writing backgrounds for characters, helping other players (particularly newbies), making the GM laugh, making magical items or furthering their god's ethos, performing other class-related actions (2E D&D), finding treasure (Basic D&D), or squandering all of your treasure between sessions (Barbarians of Lemuria). Extra bonuses are sometimes awarded to lower-level characters (3E D&D) or characters with high ability scores; AD&D gives XP bonuses for a high 'prime requisite', balancing classes with more powers by giving these multiple prime requisites (or no prime requisite) to make it harder to gain an XP bonus (XP bonuses for high stats started in 0D&D, where stats gave few other modifiers - at most +/-1). An otherwise largely useless stat, e.g. Charisma in D&D clone 'Dangers & Dweomers' can also be balanced by giving XP modifiers. XP penalties may also be applied to characters of certain races or race/class combinations. XP is usually GM awarded; Teenagers from Outer Space suggests a XP ballot where all players vote.
 
AD&D multiclass characters had separate XP pools for each class (one early AD&D class, Entertainer in Dragon #69, has three separate sub-classes that can advance separately, with two needed to improve to 10th level and three to 11th, plus optional magic-use and complicated HP determination system); a system could also theoretically have multiple XP pools for different things (roleplaying vs. combat).  Fireborn has characters that are humans reincarnated from dragons, and so advancement points are divided between 'humanity points' and 'heritage points', given by the GM based on the nature of characters' adventures, but can trade between types at 2:1 (this sort of thing could also be patched on fairly easily in AD&D, by treating human/dragon as a multiclass combination and giving class-specific XP awards for each).

Systems may be paranoid about xp awards leading to discrepancies in character power; Savage Worlds hands out xp at basically a set rate of 2/session, with good playing being instead rewarded with 'bennies' (luck rerolls). 3.x D&D hands out extra XP to low-level characters to allow them to catch up. This is particularly a concern where xp progresses at a linear rate. AD&D instead has xp requirements that double from level to level so that low-level characters in high level parties will advance faster - if they survive. Palladium gives only minimal power increases from levelling, and has very slow advancement (Palladium like AD&D slows down character advancement for more powerful characters with a worse xp table, but its debateable if this works since level advancement is so slow/benefits limited - a legacy mechanic; its power curve is also low enough that its hard for the GM to make super-NPCs or BBEGs, meaning that they have either massively inflated levels or bunches of ad-hoc perks as well to compete - 'is secretly a dragon' happens pretty often in either the fantasy or Rifts versions).

Superbabes starts characters at 0 xp, with only 1 xp to 2nd level - characters level up at the end of their first session automatically if they did anything, then progress fairly slowly.
German game Midgard reportedly has three sorts of XP awarded for combat (damage output), spells (energy invested), and general skills (successful use) respectively, which are reinvested back into new skills of the same type.

XP may be individually awarded, or XP may be calculated for the group then divided. Original Recon for example does that, even though XP is awarded for things like 'using skills' individually (maybe they learned something by watching, but without GM oversight on expenditure afterwards this could be weird).

XP varies between being given out in very small amounts (like 1-3 session) to huge amounts e.g. 2,000+ for a single monster. (Sharp Swords & Sinister Spells actually rates level in terms of number of adventures, e.g. 2 adventures are needed to go from 1st to 2nd level; Arduin Adventure also does this, much earlier).
Large XP amounts traditional in early D&D were used so that XP = GP could be awarded. Challenges such as monsters may have a fixed XP reward (2E D&D), a subjectively-allocated award (Palladium, 300 for a 'major menace') or 3E uses an awkward table of CR vs. character level to award XP - which is designed so that a set 13.33 encounters is needed to advance in level with the XP per level also advancing evenly (level x 1000 to get to the next level) i.e. there's a calculation required every time XP is awarded, rather than once in class design, although it also sets the relative value of XP so that XP losses from magic item creation or spellcasting are enforced.

XP may be directly spendable to give boosts to rolls or rerolls which may be another factor in determining how XP is scaled, although IMHO this design has some serious problems (cf. 'safety valve (http://www.therpgsite.com/showthread.php?p=496547#post496547)' discussion later).
 
Level-based systems where maximum skill value depends on character level create a ceiling to character abilities which controls unbalanced skills i.e. weapon or magic skills very well. In contrast, systems where characters are free to distribute points as they wish are much more min/maxable. Level-based skills systems struggle somewhat with languages (usually these operate outside the skill system, as otherwise a skill level equivalent to "fluency" might not be available to a starting characters!)
Usually in a level-based game, higher level is better. There are a couple of games where a lower number for level/rank represents more ability (Weapons of the Gods, Lejendary Adventures; Generation in Vampire). This unfortunately makes character progression more awkward in terms of calculations (i.e. a minus gives plusses to other factors) and puts an upper limit on ability. Though Weapons of the Gods has one bad guy NPC who is "below first rank" anyway. (The term 'tier' seems to imply this sort of reverse progression, although Numenera uses it anyway with a regular start-at-one-and-work-up level system).
A couple of other level-based systems that work in unusual ways:
*Tunnels & Trolls 7th Ed. generates level from attribute scores connected to their class i.e. a wizard could use their INT or mana/power attribute (/10) to calculate their level. Level affects magical ability and also increases other talents. Characters spend XP to raise attributes directly (current score x 100). Note the system is quite different to earlier versions of T&T, where level gains improved attributes instead.
*Slightly similar in Lords of Creation, XP was spent to add dice to ability scores, with total ability scores determining "Personal Force" which then gave level, number of skill points and powers.
*Elder scrolls (the computer game) has direct skill improvement through training, books and skill use. Each class has a set of skills which must be raised to increase level, putting up stats/HP/mana. Characters can put up other skills (e.g. a wizard putting up fighting and armour skills) but don't get levels for that. In a sense the effect of this parallels the Talislanta system.
*while in most systems there is usually simultaneous 'vertical' (numerical increase) and 'horizontal' increase (number of specific abilities), the Lone Wolf gamebooks were interesting in having increases in Combat Skill or Endurance as a secondary effect of choosing particular abilities.

Systems can have multiple advancement tracks e.g. SenZar separately awards character points (to raise stats or gain special abilities) and XP (putting up level).
The "E6" mod for 3.x D&D caps characters at 6th level, but allows 6th level characters to earn bonus feats with XP, i.e. it radically changes progression system.

Class-based systems that use XP can have very different "advancement tracks" for different characters. Point-based systems are more inherently standardized, though the game may try to work around that by having extra skills etc. that are fairly race or type specific, by having some skills etc. work slightly differently for some characters (perhaps extra bonuses), or by a 'tax' where you need to continue to buy particular feats or edges or whatnot for some concepts, or by purchase limits for some characters (e.g. synthetics in d20 Gamma World can't buy feats relating to 'personality development' after character generation, without first taking a 'Spontaneous Algorithm feat; this also generates costing problems since the same feat effectively costs 1 feat if selected at 1st level, or 2 feats later, while other feats are unaffected). Costs can also be modified for some characters (which I wouldn't really recommend). Unintentional differentials can develop if one character type has a continued need to 'pump up' a particular stat or skill to keep up, when another doesn't.

Negative Advancement: very rarely (at least, aside from ageing) a system is seen where some characters have some sort of negative advancement i.e. gaining experience lowers a characters abilities. (This is different to the case where level counts backward but actually still improves the character; by negative advancement I mean a character actually weakening as they gain XP). A couple of examples of this would be the Reformed Demon RCC in Mystic China for Palladium, which becomes less demonic and physically weaker as they level up, eventually retiring and becoming a new 1st-level human character, or the Risen Martyr in 3E D&D Book of Exalted Deeds, which returns to the heavens (forcible retirement) after reaching 10th level in the class. As noted earlier, Rolemaster has checks for stat improvement that can sometimes result in characters losing stat points instead, but rarely. Basic's divine ascension rules made Level 1 deities worse than Level-36 basic characters in some areas (see 'Divine Ascension (http://www.therpgsite.com/showthread.php?p=645535#post645535) post). Palladium also has a "Juicer" class, which had a limited (7-year game time) lifespan; the Savage Worlds' Rifts conversion reportedly replaces the fixed cut-off with a mechanic of "burn", which rolls for decrease each session (and can potentially be spent) until a character reaches 0 and dies.
Somewhat related to this but less extreme, a system can have level 'benchmarks' where a character is still perhaps getting bigger numbers, but not as fast as monsters or other characters do. This is something that was especially noticeable with e.g. 4E D&Ds sample Skill DCs in some places, or monster defenses if Expertise rules were not in use.
A few games have skill atrophy rules for disused skills, e.g. Rolemaster optional rules in one of the Companions IIRC.

Skill Costs: in games where skills are purchased, the skill cost can be based off class skill list (3E D&D, Rolemaster), current rating (with or without adding in attribute bonus e.g. Star Wars), a controlling attribute (Savage Worlds), or skill inherent usefulness (2E D&D, Synnibarr, GURPS). Tri-stat reportedly adjusts costs of skills depending on genre e.g. combat skills will be more expensive in a combat-driven game.

Retraining: as well as adding to skills games sometimes let characters 're-train' existing skills. D&D-4 has built in retraining of powers, with higher level options replacing lower-level options while D&D-3 had it as an optional rule in case of bad choices only, and in the Expanded Psionics supplement has a psionic power that lets a psion spend XP to adjust skills and feats ("Psychic Reformation"). Legend of Anglerre reportedly also has skill readjustment rules. In some cases 'retraining' can make sense if an ability overlaps another ability gained (a character spent a feat to learn battleaxe and then multiclasses to fighter. Likewise a character with Toughness gets several HP from levelling up, or a character with a +1 to hit from Weapon Focus who increases their attack bonus with all weapons when levelling could 'retrain' without this resulting in any values actually dropping).

Training/practice can sometimes be mixed with an XP approach - levelling up can require training. Particular skill use or circumstances can alter level up options e.g. Mutant Epoch allows a character who has attempted unarmed combat during gaining a level to switch their level up bonus (normally rolled randomly) for an extra Brawl skill point. 4E characters who met some FR NPCs (Drizzt, Jarlaxle) could learn specific reward powers taught by them in place of the normal class choices.
Another version of "fiction" around levelling is the contest approach - AD&D 1e in a couple of cases (Assassins, Druids, Monks) required a character advancing to a new level to beat up and replace someone of that level in a duel. The approach probably works badly with its multiclass system in that someone who's multi-classed had a major advantage over a single-class character in a duel (though magic items, ability scores, or other unique features like psionics could also swing the balance).
Another skills-based freerpg, FURPIG, allowed there to be only one 'perfect master' of a skill (100% rating), so someone advancing from 99% had to defeat the current master.

Energy Drain: (A)D&D is almost unique in having it possible for characters to lose levels from "energy drain" e.g. from undead such as vampires, wights or spectres. This is something that works in the older context where all new characters start at 1st level - as a setback less serious than character death - but by 3E D&D is literally a fate worse than death since a dead PC would be replaced by one of the same level. It works better in the context of AD&D since a) replacement PCs would instead generally begin at level 1; b) the XP costs/level double each level so that lower-level characters generated either way can catch up and c) abilities are less level-dependent, and players had opportunity to participate based off player skills rather than character abilities in many parts of the game anyway, making level less important.
D&D energy drain occasionally managed to create characters with greater-than-maximum hit points, due to rolling low when levelling-down than high when regaining a level. [a particularly combo with 'Gifts' from 2nd Ed. Complete Viking, giving a bonus on die rolls of a particular die size, potentially including HP).

This sort of "level loss" can produce weird problems or cases at times.
For example, Gamma World d20 has a "Mastermind" class which at level 10 ["Apotheosis"] lets a character take over bodies to use them as 'nodes' backing up their personality. If a node is killed they lose [total level/# of nodes they have], meaning they would technically lose the apotheosis feature while still having other 'nodes' left.

Ageing: characters may suffer changes related to ageing in addition to earning XP (though some systems, including LEG's Aliens game and Clash's Starcluster/Outremor system, have advancement primarily through ageing e.g. the former has an improvement roll each year, the latter lets characters lose stats but gain skills with age). D&D notably has aging adjustments for each of 1/2, 2/3 and full 'base max' age, where characters lose physical stats and gain mentals; other simpler RPGs omit this and a characters' initial stat array can be assumed to imply their age (e.g. high mental and low physical rolls = an old character). Palladium/WHFR have primarily penalties for ageing (including to Int or equivalent), RQ has random stat losses rolled for each stat and where characters dropping to 0 die (including APP, so  characters can 'ugly to death').

Player Skill again: as well as mechanical increases, players in any system can improve in terms of using their characters' abilities better. This can be more pronounced in rules-lite games where the actual scope of abilities is unclear (e.g. Amber Diceless specifically makes mention of it - noting that characters with Shapeshift from different campaigns might meet and be surprised at what the other can do with the same power). Some player skill improvement may be 'in world' learning, some may instead be a matter of better understanding pure game rules (e.g. learning to take-10 more often).

Note: see also here (http://www.therpgsite.com/showthread.php?p=726855#post726855) for overview on character advancement-related topics.

Note that character advancement can sometimes also trigger or require improvements in other characters e.g. a replacement character or another player character. A replacement might be created at the same XP total/level, gain a portion of XP/levels, or gain an ad hoc bonus to base skill. New characters added to a party might also be made equivalent. Interesting systems here include Amazing Engine's "player core" and Dark Sun's character tree (mentioned briefly in attribute generation).

recent edits: 24/12/2015 - picaro thread link

Advancement note: with XP type systems, skills might increase immediately or require training as well. FantasyCraft has a feat ["I Can Swim"] which lets characters adapt on the fly by not having to spend all their skill ranks immediately after levelling. This is somewhat workable as a feat just since a character gets a new shipment of skill points with each level advancement, although its utility is limited compared to D20 since FC characters can't buy up cross-class skills at all.

Advancement systems can have implications in terms of character background design. e.g. a level 1 character is sometimes assumed to be fresh off the farm, with the assumption they haven't fought any monsters or done very much; this is worse if identifying traits like 'is a pirate' can't be gained until level 6 or 7. [3.x prestige classes]. I usually like to not take that too far, and assume that mechanics aside, a 1st level character can still have done a few things. Note that 3.x is also weird in that it has a very high power curve where some PrCs are limited to high level, despite play already having changed enough so as to make many of these less useful; these may really work well only for NPCs, or where a party ranges around in level.

Most of the character building process - attributes, skills/classes, etc. - seems to have relatively little effect on choice of core mechanic  (d100, dice pool, etc), and vice versa - games are fairly similar and follow similar ranges of choices. In very rare cases, an unusual core mechanic might force a strange adaptation e.g. Marvel Super Heroes' universal table system has rolls based off a single attribute only (not stat+skill, etc), and hence has a Fighting attribute; DC Heroes' system needs Acting, Effect and Resistance numbers from attributes and so has lots of similar-sounding attributes (e.g. Mind which gives a target number to avoid mental damage, plus WILL to absorb damage if it occurs).

With regard to skill and level systems, note that:

*level-based systems are not usually dice pool games - in part because the dice pool games appeared in the 90s when levels were going out of vogue, but also perhaps because dice pools don't scale to large numbers (level would have to set dice pool directly) and so can't as easily account for skilled/unskilled as well as level and attribute. Dice pool games usually don't have inflationary HPs either, removing another reason to have levels; soaking is easy to implement by counting successes so most do that.
I know of no true level-based dice pool games (aside from T&T with its multidie-additive combat system), although Storyteller games do have a level-equivalent primary stat such as Generation for vampires, Arete for mages, Rank for werewolves, Quantum for novas (Aberrant RPG), etc. Also interesting is 'Over the Edge' - here characters have an experience pool which acts as a reserve of points that can be spent to get bonus dice, rather than adding to every roll.

D10-based or systems using changing-die-type are also not usually level-based due to high granularity- the exception being Earthdawn (step-dice with rank determining sets of dice rolled) and DCC (which uses d14 -d30 as well as level bonuses). d10 provides almost enough granularity for level bonuses, except that skill bonuses from level would tend to be outweighed by attribute mods unless attribute scale is limited to a very small range.

The concepts of 'levels' and 'classes' usually go together - partly perhaps due to D&D traditions, though it has also been argued that skill-based systems do not generate "level appropriate" results, and in general games without levels rarely have 'classes' - they are more likely to use 'archetypes' or free skill selection. Most 'derived attribute' games are level-based too, so classless games are more likely to be skill-driven. Fuzion is sort-of an exception in having lots of 'derived' attributes that are averages, although its non-level-based and uses d10s (if not using the 3d6 variant).

Other notes:
Point-buy systems get increasingly unwieldy as stat scale goes up to larger numbers (for use with 3d6, d20 or d100), although to be honest this has never really stopped anyone.

Advantages/disadvantages tend to have more of an effect in dice pool games or games that are more granular - comparatively additive systems give out smaller bonuses (Compare White Wolf advantages or Savage Worlds' Edges against lots of the d20 system feats, which frequently give out very small bonuses). Racial stat bonuses are also more pronounced (e.g. Shadowrun 1E).

Usage-based improvement isn't usually seen for highly granular stats (step-die, d10, or dice pool) although a system could award 'xp' towards an increase from successful use. Random improvements are most common with d100 systems.

Highly 'abstract' statistics (D&Ds six attribute system) perhaps don't work as well with detailed skill systems -the skill modifiers limit how the player can interpret a low/high attribute (e.g. 2E might let a character explain their low DEX as due to being half-blind and so a lousy shot, but DEX in 3E doesn't modify Spot by default).

One-Value vs. Two-Value Systems
A core mechanic has a 'base chance' of success which could depend on a single number, or may be calculated by adding two or more numbers together. Table-lookup games for instance ( Marvel Super Heroes, DC Heroes ) typically use one value. FUDGE uses one value corresponding to a descriptor (Good, Great, etc.).  Likewise, roll-under games often use one value - d100 games are an exception in that while there are d100-based games that use just attribute checks (Maelstrom, Amazing Engine), a percentage is more often calculated in a more complex fashion (e.g. Runequest). GURPS (3d6) would be another exception as it uses a table to factor in # skill points as well as base stat, though stat still has a high weight). One-value games generally correspond to the 'attribute-driven' model [FUDGE being the exception] whereas two values (see next) relates to stat+skill.

One Roll Engine or Storyteller (or Toon) however inherently use two values (Stat+Skill) -in these games limiting to one value is effectively a major penalty. (Many other games can accomodate either one or two values - here having two on a check is virtually mandatory).
Toon uses 1d6 to determine stat and 2d6 roll under for skill checks, which gives very low chance of a raw stat roll succeeding with the same mechanic - less than half that of a skill check due to the probability curve of a 2 die roll. One Roll Engine chance of success likewise increases dramatically as dice pool increases, though as stat and skill are both 1-5 they could've used [stat+stat] rather than inventing new skills (Cortex is similar but sometimes uses stat+stat (cf. Serenity pg 142), although it also has a number of skills that might be classed as filler, such as Athletics and Willpower).
This therefore generates a need for extra values (or very broadly defined values) to ensure all tasks have a reasonable chance of success, or will have 'holes' where chance of success is too low...raw Str checks, perception checks for taste/touch, etc. Skills can be forcibly created to fill gaps if rolls must be [stat+skill] and never stat alone.  
Fuzion also has a number of skills which fill this niche; these usually default to 2 though with it being argued (http://www.therpgsite.com/showthread.php?t=23012) that scores should be higher for more competent characters e.g. =attribute (which would only work due to stat/skill being on the same scale).
Skills are also sometimes invented for the opposite reason e.g. if a raw stat check is much more likely to succeed than a skill check - this may be the case with BRP, where stat roll is usually [stat x 5% or around 50%] whereas skill is a small base score % + stat modifier)(often under 20%).
From a character-building perspective, two-value systems may be slightly harder to build effective characters for, since making a PC good at something involves putting up both values, possibly in conjunction with knowing the relative importance of each (weight on checks, etc). Poorly costed build options could easily have a low attribute invalidate a large-ish skill point investment or vice versa.
Going from using 'one value' to 'two value' is if anything more difficult than the other way around. Sometimes a game will use averages (for instance, Tunnels and Trolls in some solo adventures averages two scores); sometimes a game will apply a small modifier from one stat to another that doesn't totally break the scale, sometimes a game will drop the core mechanic and go to a different mechanic (DC Heroes initiative of d10+sum of the three 'acting' attributes, rather than the usual table).

[Games with one-value can still add lots of small modifiers - e.g. Marvel Super Heroes' 'column shifts'.  There can also be games where instead of one main value, you are expected to reference and add up a bunch of bonuses  (e.g. say Cortex+ with its various dice), which you could call an n-value system. How well a character does might be harder to predict in advance since its a question of how many bonuses can be brought to bear, rather than how big one number is, though Cortex has safeguards to make sure some dice are always applicable. This sort of approach probably requires defining lots of specific aspects for characters; the idea might be to get around people breaking the system with extra modifiers by making the base value low so you need all the extra modifiers. Simple additive systems trying to use this can get fairly broken - maybe 3E D&D armour class at higher levels, where PCs had to deliberately stack various AC bonus types to reach the right AC]

Probability Curves & Skill Breadth
Core mechanic can also influence what breadth of skills makes sense for a system. Both D&D 4E and Pathfinder, for example, have gradually adopted broader skills in conjunction with their D20 mechanic.
With very narrowly-defined skills, randomness is less desireable, while for broader skills, how much the character knows about the exact sub-topic is a variable that's part of the random roll; in these games the random roll is skipped when/if likely to give inappropriate results. In another words, if you're playing GURPS then having a priest of Pelor make a Knowledge: Pelor roll would give probably reasonable results (since this uses 3d6), while for D&D 3E they could botch this and know nothing about their god, so it makes more sense to have a Knowledge: Religion skill and have the priest not roll for Pelor-related tasks.

Core mechanics with limited scaling potentially limit multiclassing (if benefits from levelling are low, then gaining a new package of abilities instead is more unbalanced).

High-order Considerations
Systems could be broken into 'Concept-first' or 'mechanics first' games with regard to character generation - in one you start with mechanics (an optimal feat chain, multiclass combo, etc) and interpret a character around those, in the other you start with a concept and find mechanics that fit. Which applies depends on how many mechanical 'moving parts' a system has, how balanced options are and how re-skinnable options are. Factors like how fuzzy attributes are, how broad classes are, and whether or not there is a feat system, are all contributors.

Systems also vary in how inter-connected various character options are. A highly detailed system can have rules where e.g. size modifies Strength directly, whereas another game e.g. Storyteller lets a character buy the Huge merit and Strength separately, and the onus is on the player to create a final character sheet that makes sense; this gives the player leeway to adjust for various factors, and to consider connections that might not have been accounted for by the designer, but also can be a temptation for players to build for optimum character power instead of matching a concept. Another example is the split between free choice skills systems and those with classes that are tightly defined; a character in one picks a class e.g. doctor and gets a number of skills with not much choice in the matter, while in the other a character just chooses the skills that match the concept (so they can fine-tune specific concepts, but could also overlook something important).
Detailed rules for modelling interactions between various bits on the character sheet can be very specific and fiddly, and can't account for everything, but maybe should be used where details are something that should be niche protected or relatively rare.

When designing, there are often multiple methods that can be quite different yet yield similar results. That is, the systems are structurally different, but functionally the same. For example, an emergent final result of "warriors typically have higher physical scores such as in Strength" could occur in a game where fighters get a bonus to Strength as a class feature, or as a result of some classes costing fewer character points to buy and the same points being used to buy attributes, or by adding an extra 'Power' attribute that's necessary for wizards but a "dump stat" for warriors. These options could differ in some specific edge cases, for example a bonus to Strength as a class feature will (barring extra rules) give multiclass characters more Str, the second option less Strength (having spent points on buying two classes) and a middling result in the third case. Similar results in play can also occur from different amounts of starting complexity, e.g. based on ad-hoc adjudication as opposed to numbers of formalized rules.
(Note: Here, we're speaking of comparing systems. Potentially there might also be multiple ways of generating/representing something within the same system [like HERO characters sometimes able to build the same thing more cheaply with Power X and some disadvantages, than Power Y), but this is probably a flaw since it can lead to 'right' and 'wrong' ways to do it).

Systems sometimes have specific 'order of operations' where you have to do say stats, then class, then skills - an example is AD&D 2E where you need particular stats to qualify for a particular race, then race affects class, then classes buy skills for different costs (Skills and Powers was particularly fiddly that way in that points could be moved across categories that way but only to later 'steps', with advantages coming weirdly late in the process after race and class purchase and so being easier to buy if you have a class/race with a larger Character Point budget). In another game skills, race etc. may form different 'partitions' but in no particular order - say Storyteller where a character buys skills the same regardless of what their vampire clan or mage tradition or werewolf auspice is, you could start anywhere really.
Order of operations (e.g. stats > race > class > advantages) tends to be more annoying if a character makes a decision and then finds it invalidates later choices, needing redoing - for instance, if stats are bought and then the player discovers they can't qualify for a feat or ability ('charm', etc.).

I think optimally choices should also be arranged such that they are a) independent (avoiding trap options where one choice early on, locks you into another particular choice later - classes and essential attributes for them would be an example, though one that's hard to build out short of using archetypes and b) not degenerate - for instance having a choice between A/B/C and then between D/E/and A again, such as if a feat duplicates a class feature. Probably better to narrow this to one decision point. The peril of duplication is that two different characters might have the ability, but with different trade-offs to get it leaving one in a worse position.
(in the past I did ignore that for one design, where a character could pick up 'Luck' later in character generation as a trait, or earlier as a Talent [Talent meaning not a skill but an aptitude for particular skills] which gives points in the trait: the main difference here was that Talents occur earlier in the order of operations, in this case with a random disadvantage-determining step in between: Lucky the talent like other talents allowed a character to reroll some particular results on the random disadvantage roll which Lucky the trait normally couldn't, simply because buying Luck is normally the last step).

Systems in some case might design a number that's an 'input' initially, and in other cases derive it as an 'output' at the end. Mainly depending on what you want to use each for; for instance 'Education' might be an attribute that at the start gives a number of bonus skill programs, or it might be a derived stat [/thing] calculated from what skills a character has bought or the bonus of them, with a bonus for other feats/advantages, then used to modify the reaction rolls of scholars or a character's default %knowledge checks.

Number control (abbreviated from later)
When trying to balance or control increase in numbers, a number can be set in various ways, essentially with a continuum of a variation that goes like this:
*fixed for all characters
*fixed, but with possible modification for a rare Advantage if bought/rolled.
*archetype-based numbers (meaning stats can be controlled in an archetype-specific fashion - if a character type gets massive extra value from CON e.g. some powers are based off it, it can be 'costed up').
*An attribute, which can be rolled or bought up at cost in other stats.
*A number which automatically scales up based off 'level'.
*A number which can be purchased upward with variable expenditure of points.
[this is rough, since there's actually two sorts of scaling - horizontal between characters and vertical with 'level' or experience - and something can scale by both or neither]

Niche Protection
Its debateable as to whether 'niche protection' is desireable in the first place, but something else to note is that games where roll bonuses are highly divergent between characters tend to produce 'niche protection' automatically (to be competent at something requires a larger investment). Generally, high variability in a roll cuts into divergence (anyone can roll high and get lucky). Basically then D&D can be thought of as creating niche protection 'artificially' where a skill-based system often does it innately.

Synergy
Options intrinsically work or don't work with other options. Competition for varying resources is usual, for example abilities that are based on different attributes; action-economy where you can either swing a sword or cast a spell, or so on. Abilities can directly synergize, be redesigned to synergize more or less. It can be possible to promote a synergy directly between A and B, or create an option C that helps both. Implementation of a specific ability can often be fine-tuned so as to promote synergy or not - compare 'elves get +2 to Spot' (3E D&D) and 'elves get Perception skill for free (5E D&D) - both making elves more perceptive on average.

Edit notes: niche protection (*), redundant options with system (*), different ways to control numbers (*), more on order of operations(*), n-value systems (*)

General intro on Resolution Mechanics
Every mechanic is going to have its pros and cons.
Any single-die mechanic will have very swingy results (including 'changing-die-type' systems, these being if anything more variable than die+mods systems).
(Often in practice, tasks may incorporate multiple rolls or allow a certain number of rerolls - 4Es 'skill challenges' for d20 being an example - going the other way to make 3d6 more swingy is a harder task!)
Any multi-die mechanic will be annoying to roll for lots of targets/foes at once (...though they may sometimes at least generate a couple of results simultaneously, as with One Roll Engine combat, Warhammer 1E/2E reverse-d100 hit location, or Heroic Golden Turbulence colour results; see later). It will also be less transparent with respect to probabilities (though it is sometimes argued that less transparency is desireable, to keep players immersed as opposed to calculating probabilities; quite often even linear dice rolls are made against secret target numbers to obscure probability, e.g. D&D hit rolls).
Take-highest systems are both swingy and clunky.
Diceless or card-based have their own issues, like being overly deterministic or needing shuffling.

An additive system means more math.
A roll-under system will be 'nonintuitive' (lower results are better, unless its a 'blackjack' system), gives extra subtractions instead of additions as soon as modifiers start applying, and are generally more work for opposed rolls (e.g. initiative).

There are also trade-offs between lower and higher granularities (size of dice). The finer your resolution (to handle detailed advancement such as level advancement, or multiple modifiers) the more the math multiplies (for e.g. adding bonuses, or converting rolls back to success levels at the end). At lower resolutions odds of critical hits/fumbles occurring, or alternately of needing an extra roll to 'confirm' your success or fumble, may get too high.

Choosing a core mechanic
Usually 'core mechanic' is something chosen based primarily by designer preference, rather than any objective reason.
Some interesting cases of why particular mechanics were chosen include:
-Dogs in the Vineyard; its dice pool system is built around specifically having social rolls that fail and turn into gun battles.  
- Savage Worlds the core mechanic (step die) was chosen just so mass combats run more quickly.
-DC Heroes uses tables that cross-reference scores to get results, as part of a universal result system designed for comparing logarithmically increasing attributes. It works great for figuring out how far a STR 15 character can throw a Size 5 object, for instance.
-One Roll Engine has its height/width counting which is used on every check, mainly there to do hit location as part of the attack roll (a bit gimmicky).

A note on distribution curves
A single die roll generates a flat curve, whereas a multiple dice roll generates a bell curve (e.g. 3d6). The single roll has the advantage of having odds that are easily calculated and understood (i.e. on d20, a +1 always increases a characters chance of success by +5%); the bell-curve on the other hand generates results that are more predictable - a dice roll will typically be an average result (i.e. 9-12 on 3d6 is much more likely than getting a 3 or an 18).
While the d100 generates a flat/predictable linear curve, the fine detail allows for considerable control, e.g with 'special successes' and the like set to a fixed (small) percentage (1/10th of regular skill, for instance). Or tables can be used. Such methods can transform the linear roll indirectly to get 'diminishing returns', i.e. a non-flat result pattern.
Some interesting discussion on the effects of how modifiers affect probabilities in true bell-curve systems (like GURPS) is here: http://forums.sjgames.com/showpost.php?p=1490660&postcount=7

Opposed rolls in additive systems where highest wins basically converts a linear roll into a curved distribution (e.g. d10-d10 = same spread as 2d10). Opposed rolls in roll-under systems where a number is a flat succeed/fail (e.g. Runequest for the most part) are probably more complicated.

See below for more on specific implementations.
EDIT NOTE: See also post #42 (combat manuevers and core mechanics (http://www.therpgsite.com/showthread.php?p=497808#post497808)) for further on combat system design specifically.

D100 systems.
A d100 system is finely detailed, meaning there are no break points/dead spots for attributes – every point is important, limiting min/maxing. Using a percentage can make it easier to consider multiple factors (such as several attributes modifying skills e.g. HarnMaster), or different weightings i.e. one stat could give +2% per point while another gives +1%. The very exact percentages may be useful for critical hits or fumbles, etc.

It is slightly slower for multiple rolls (as dice must be paired up as 10s/1s). (Potentially, a d100 additive system can be sped up slightly by rolling d10+modifiers, with a fail-by-1 triggering a reroll against the ones place.)
d100s may be used as roll-under or additively; see relevant sections for further notes...(post 12 directly below & post 14).
 
With values being expressed as a percentage, players can immediately see their base odds of success in a way they are not able to with, say, dice pools, and new players can usually grasp immediately that say, 85% library use is good. (Though not all systems using a d100 are necessarily this transparent - tables like in Marvel Super Heroes can make the %s less apparent).
% systems tend to be upward bounded at 100% (i.e. making it difficult to exceed this); so that penalties having more serious effects on higher skill characters i.e. a -20% drops a character with 95% to 75%, or a 1-in-20 failure rate to 1-in-4, while the character with 60% succeeding just over half the time drops to 40% or just under half the time. Bell curve systems are sometimes recommended to get around this sort of problem.

d100 systems occasionally generate additional information using the '1s place' of the d100.
-HarnMaster treats rolls ending in 5 or 0 as critical successes or critical failures, to assess these quickly (if non-intuitively)
-Amazing Engine treats the 1s place as the quality of the result; for weapons if the ones is less than weapon "lethality" it deals "body point" damage rather than "stamina point" damage.
-Warhammer 1E/2E inverts the attack roll (i.e. 39 would become a 93) and uses this as the hit location roll.
-early versions of HARP (discussed on Rasyr's blog wizlair) used d100 + mods to attack, then added together both dice to get a 2-20 number for hit location.
-Top Secret/SI uses the 1s place on attack rolls to determine hit location, and the 10s place indicates damage for melee attacks (higher is better i.e. blackjack success); firearms instead deal random damage (thanks RobM for this note).
-a number of games use 'doubles' on the roll to indicate a special result (Unknown Armies; Rolemaster weapon breakage).
-a few games (e.g. WHFR 'clone' Zweihander) can allow a switching of the 1s and 10s dice as a special ability - effectively an instant reroll (though with no extra chance of doubles). Unknown Armies has skills letting this happen provided the switched result is under the skill, so higher skills can increase chance of a flip (& multiple skills feed into one skill check).
-with a blackjack system where higher is better, flipping d10s/1s place could increase chance of success but at a cost in degree of success (Effect).
-If the 1s die is used to determine "effect" [e.g. HarnMaster, Amazing Engine type mechanics], then switching the 10s/1s becomes more frequently possible when the task succes percentage is high, meaning that there's actually an increase in effect from high skill value instead of it being effectively independent. For instance with Harnmaster's '5s are crits' a roll of [6,5] would be a success given 58% skill ('roll' of 56%) but would be a crit at 65%+ skill ('roll' of 65).
-PlanetAlgol on his blog has suggested having the player roll the 10s dice and the GM the 1s dice to preserve uncertainty (though this works only sporadically)

d100 systems sometimes have attributes that are directly set up to be used as percentages rather than being skill-based (Amazing Engine, Warhammer 2nd ed), or they may have ability scores rated on a lower scale such as the 3-18 of Runequest/Harnmaster. These last tend to use a formula of [attribute score x a difficulty multiplier] to determine a base percentage chance for attribute checks; HarnMaster sometimes just uses a 3d6 roll for ability checks instead.
DragonQuest (at least the 2nd edition of it) has a statistic scale that's slightly higher (going up to 25 for a normal character and includes fractional multipliers e.g. x2.5. To prevent characters going past 100% too readily, an additional rule gives a minimum chance of failure equal to (30-stat) i.e. a character with a 25 Strength would still have a minimum 5% chance of failure on a Strength check, meaning a roll of 96-100 fails even though the character would have a base 100% chance of success at e.g. [Str x 4].
 
d100 systems tend toward expansive skill systems with lots of tightly defined skills. My theory here is that either a) these systems tend to be built by designers focussed on gritty realism down to the 1% level, or b) these games need to export stuff that would ordinarily involve an ability check off to the skill system (like Listen in BRP) since leaving it as an ability check would make the % much higher than other skills.
This and the scale of skills to start with can mean juggling fairly large point budgets during chargen, e.g. Call of Cthulhu needing to divide 300+ points between various skills.
 
Another interesting rule for d100 is from J Arcane's Drums of War: this rolls 2d10 additively, but uses the same numbers to generate a percentage for the purpose of determining if a critical occurs (i.e. 9 + 7 would be a 16 to hit, or 97 for criticalling, compared against the characters % chance of critical).

While a %-based system's fine resolution means lots of small modifiers should be applied exactly (+1% circumstances like slight wind on your archery check) this is a bit fiddlier with roll-under than with an additive system. Modifier heavy games get slightly clunky with d100 (e.g. Deathwatch).

[Edit] Final Note: while it seems I'm against 'swinginess', it can be a legitimate design objective in and of itself - to generate a range of game outcomes - although it can be at odds with either minimizing lethality or generating balance. A case of a game deliberately designed to produce weird and swingy results is the DCC rpg - a good sampler article is here:
https://muleabides.wordpress.com/2010/12/13/glorious-swinginess-results-from-the-dcc-rpgcastle-zagyg-experiment-part-1/ (https://muleabides.wordpress.com/2010/12/13/glorious-swinginess-results-from-the-dcc-rpgcastle-zagyg-experiment-part-1/)

Additive systems are excellent for opposed tasks and provide intuitive results; higher numbers are better. Multiple dice can be rolled at once more easily than with dice pools (to allow the GM to, for example, roll several attacks at a PC simultaneously, or several saving rolls) but perhaps slightly less readily than roll-under systems. Level of achievement is more prone to inflation (usually, amount by which a roll succeeds gives effects of success). Probabilities are slightly less transparent than d100-roll-under but better than dice pool systems, at least if using a single die.
Some additive systems suffer from out-of-control bonus stacking.
Additive systems may be slightly better than most other types of mechanic (e.g step die, dice pool) for letting players roll without telling then for what.

Elaborations:
Additive systems can provide success levels as a proportion of success chance by having a natural die roll that is ‘confirmed’ by a successful check. For example a longsword in 3E D&D used by someone with a 60% chance to hit (e.g. +4 to hit vs. AC 13), has a 6% chance of being a critical; a natural roll of 19-20 triggers a possible crit (10% chance ) times a 60% chance of hitting (confirmation roll) = 6%.

Combination with other setups: 5E D&D uses d20+modifiers (attribute, proficiency bonus), and also frequently has a rolled-bonus for some class features e.g. sorcery points (d4), bardic inspiration die (d6 base) or fighter 'superiority dice' (d8 base)  - with dice increasing sizes at various levels. Increases are fairly erratic, and whether a class bonus is a flat + or a die is fairly ad hoc. In some respects reminiscent of Alternity (a roll-under system) but less structured. (Also compare 'action dice' in FantasyCraft - noted in safety valves). The main benefit of the rolled bonus here is that it can often [depending on the specific power] be declared after a roll is failed, still with some doubt as to whether the boost works...e.g. you could fail by 2, then roll a 1 on +d6 and still fail. This wasn't a feature of Alternity, where the step die was rolled simultaneous with the main 'control' die.

Variability: How variable the outcome of an opposed roll is, in an additive system, can be reduced by allowing all participants multiple rolls, taking the highest result (or the middle result). This skews up the average toward the maximum; the likelihood of the character with the highest bonus winning increases. This could be used for tasks where results are more cut-and-dried than normal (an opposed Strength check for an arm-wrestling contest, for instance).
This same method can be used in roll-under systems that use margin of success.

Whereas in roll-under systems the total chance can be multiplied (e.g. halved), an additive system instead makes it possible to multiply either the bonus to the roll, or the base target number (this is very rarely seen). Halving the target number is equivalent to averaging the percentage chance of success with 100% for a character with bonus +0. Halving the bonus on a DC 20 roll (for d20) is equivalent to halving success chance.
With a linear die + modifier, adjustments to chance of success have a fairly coarse effect (its easy for a modifier to push a success chance beyond 100%, and difficult to set exact %s as desired) : Timelords had a modifier table which cross-referenced bonus and difficulty to give a proportional reduction, so that highly skilled characters didn't automatically succeed at tasks, though similar effects are easier to implement with bell-curve systems (die pools or 3d6) or roll-under.

Modifiers: Perhaps as a general rule the upper end of bonuses should be about as large as the die range (i.e. +20 for d20) so that the upper end is an automatic success - less than that gives everyone a chance of failure on all tasks. This does depend on the DCs set, and means that at the high end d20 systems will need double-digit addition. Actually, expanding range of modifiers beyond [1x die range] may be desired to guarantee predetermined outcomes for opposed roll contests as well (+full die range  is needed to guarantee outperformance, between two benchmarks rather than entire top/bottom of scale, at least if assuming that the comparison is based off the margin of success and not some other effect system).

Here I include systems such as West End Games Star Wars and (for combat) Tunnels and Trolls. A pool of dice are rolled and the total calculated. A problem with this system is that a character’s result varies enormously depending on # of dice in a characters pool – making some tasks very easy or impossible for some characters. To ameliorate this, WEG Star Wars uses a safety value in that characters can spend Character Points/Force Points to add extra dice when needed; Star Wars also adds a “wild die”; one of the dice has a different colour, on this dice 6s are added and re-rolled, while a 1 takes away the highest roll and may result in complication/fumble. deadEarth (also multid6 additive) characters with the 'Unlucky' mutation roll a wild die with a 1 taking away the highest roll, then rerolling with a second 1 meaning 'something terrible happens'.
Theoretically, a 'roll again on 6' could be applied to every die (not seen as a core mechanic in any system I know of, though 2E AD&D's Masque of the Red Death has firearm damage rated 1D6 [Derringer] to 3D6 [shotgun], +/- modifiers, and all 6s add and roll over).
Some T&T characters may have powers that let them 'roll doubles' in combat again (Berserkers).
 
Star Wars/D6 system also added more granularity to its dice pools by having intermediate levels of +1 and +2 (i.e. attributes went d6,d6+1,d6+2,2d,2d+1,2d+2, 3d, etc...(similar to GURPS damage values by STR except that these also had a -1 step i.e. d6,d6+1,d6+2, 2d-1, 2d).
 
Legend of the Five Rings (and I think 7th Sea?) lets characters roll dice equal to [attribute+skill] and keep dice equal to [attribute].
 
EABA rolls, and counts highest 3 in the dice pool. # dice equal stat/3, with remainder added (i.e. 11= 3dice+2, 12=4 dice) (before difficulty adjustments). For some target numbers a +2 may be better than having the [next largest] number of dice, although characters can opt to trade a die for a (non-stacking) +2. Some talents can let a character take 4 dice.  http://www.therpgsite.com/showthread.php?t=31552&page=2 (http://www.therpgsite.com/showthread.php?t=31552&page=2)

The Framewerk system (Cthulhutech) has a more complex system where a character rolls several dice and may take the highest single die or a sum of a couple of dice, depending. A criticism of the system may be be that which the system is almost as complex as say Cortex+, it does not do anything a [d10+modifiers] system wouldn't do, except for making the probabilities weird and nontransparent - compared to Cortex's (e.g. Marvel Heroic's) various applications built into the system which assign effect, generate complications, recharge pools and so forth.
A detailed breakdown of the Framewerk system's probability issues can be found here:
https://web.archive.org/web/20100611041917/http://taharqa.org/?p=249

Over The Edge uses an additive d6 dice pool, with character advantages potentially adding bonus dice or subtracting dice. A penalty functions by adding a die, but forcing the highest roll to be discarded, so buffering the results from changing too much. It has an (optional) rule whereby any 6s rolled may indicate a 'partial success' despite an opponent having a higher total - the rulebook example being an exorcism that succeeds by trapping the spirit, but gives the ghost a slowly increasing hold on the character. Note: for reference, Over The Edge is (partially) cloned as the basis for free Thundarr the barbarian rpg Under the Broken Moon (http://www.rpglibrary.org/settings/thundarr/index.shtml).
Similarly, 'Don't Look Back' (reviewed in Dragon #220) has a system where a pool of d6s is rolled (3 + modifiers) and 3 are always taken, either highest if positive modifier or lowest with negative modifiers, giving a success rating of 3-18. 11+ translates to success, with weapon damage being (hit roll-10) i.e. base 1-8, times weapon damage multiplier.

Early versions of Imperfekt Games' Invulnerable superhero RPG (the 'Year One' edition) apparently used a multidie d6 system which included rolls of 'hyper-dice' which were [d6x10] alongside the normal d6s, and difficulty ratings going up to 600+. (The equivalent of this for a dice pool system might be e.g. Aberrant, where mega-attributes would get multiple successes per die hitting the target number). The modern version of Invulnerable (the 'Vigilante edition') is instead a combined additive/multidie additive system, where a normal roll is 3d6+stat+skill but with 'hyper-attributes' now adding extra d6s (the rationale given for having hyper-attributes be rolled being that it gives normal characters a slim chance of success). (A setup where powers, including 'hyper attributes' get extra dice like this could be a way to build a fundamental failure rate into powers, i.e. 1 = doesn't work, as a part of the core mechanic/a roll that would be made anyway, though perhaps with the dice roll perhaps still made even on normally automatic actions).
The lost free-rpg ROAR, related to T&T, was (IIRC) similarly a combined additive/dice pool system, with a normal roll being 2d6+attribute but with bonus dice sometimes given out; the two base dice were I think a different colour as doubles on these could roll up and/or a low roll could fumble.

Storygame My Life With Master uses a d4 dice pool, where any rolls of 4 are discarded before dice are added, possibly to give a fairly narrow range of results possible. This gives the same average as d4-1 per die. (A similar mechanism is seen in JAGS which randomizes 0-20 for roll under using 4d6, 6s count as 0, to avoid all rolls being 4d6-4).

A system I saw distribution charted for with the "Troll" dice roller, but not actually as part of any system I've seen, was "4d6, eliminate duplicates and add" -i.e. only different dice rolls are included. (Difficult to say how much more dice actually add to result- maybe best with a fixed-size pool).

A feature of multidie additive systems is that ratings can be used as either a # of dice (the default), or instead adding a flat bonus equal to rating (much lower weighting) - e.g. rating 3 could be rolled as 3d6 or just give a +3. This could be used to represent skill synergies, aid another, etc. This idea shows up in Infinite Power (e.g. the 'dead aim' talent adds Reflexes score, normally a # d8s added together, as a fixed bonus to ranged attack damage).

John Wick's game "Thirty" is a multidie d6 system which is somewhat like White Wolf in that it uses 'Trait' (2-5) + Skill (0-5) for number of d6s rolled. While simple, a lot of dice and results are fairly unrandom (unfair particularly in combat). An interesting rule is that it has "Backgrounds"; a background adds an extra differently-coloured die if it helps, and also any dice that roll less than the background die are raised to that (so if its a 6, all your dice now count as 6s; making the 'swordsman' background deadliest in combat for instance). So far so good, except backgrounds can also be negative, with the extra dice rolled and that setting a cap on other rolls. (With low dice pools however the extra d6, if high, can be higher than if the negative wasn't applied). Potentially making the background die negative could work somewhat if not added the same as if it was positive, and perhaps the background die could be less than d6, say +d4.

Combining Multidie Additive and other systems e.g. Count Successes, match-counting:
Later editions of T&T (7th ed.) include a success counting mechanism as part of combat as well (where 6s count as points of automatic ‘spite damage’, and may trigger monster special attacks e.g. enough 6s from the Medusa turns one PC to stone). This scales up results with increase in attacker ability, but is unaffected by defender ability. The main issue with this is that T&T sometimes uses very large numbers of dice (e.g. the largest monster in the Corgi solo adventures, the Shoggoth, had MR 1000 = 101 dice) and counting the 6s gets a bit wonky when trying to replace e.g. 20d6 with [2d6x10]. Although perhaps in cases like this, Spite could somehow be rolled separately, e.g. 6 dice could also give a roll of 1d6 for # spite 'successes'.
(My own house rules for T&T, years ago, included a star wars-type "wild die" which had a fumble on a 1 and automatic hit on a 6. As T&T uses 2d6 (doubles roll up) for most rolls outside combat, a later idea recently would be to roll the wild die but on a "1", roll a second die and treat this as a Saving roll, i.e. the other rolling being a "2" would be a fail [double-1 would roll up]).

Free rpg Twisting Tunnels ( http://beardedbaby.net/twisting-tunnels-rpg/ (http://beardedbaby.net/twisting-tunnels-rpg/)   )is slightly similar but uses a system combining additive dice and match counting: a roll is made with multiple d6 with either the highest single roll or the sum of all matching rolls giving the total (and compared vs. opponents total). The effect ("Impact Dice") is equal to the number of matching dice, and is often used as a modifier to a follow-up roll, either as a boost e.g. a bonus to attack following from a good Stealth roll, or a penalty e.g. netting an opponent would give the impact dice as a subtraction on rolls until they untangle themselves. Compare also One Roll Engine (post #20 below).
(The Twisting Tunnels system could be interesting with an add-on for giving ORE style hit location: since it uses 'sum' rather than 'count' to give total to-hit, it'd be possible to make head shots more difficult by having these be a lower number i.e. if '2s' are needed to hit the head, it becomes much harder to land a head shot against an opponent, if they can build a defense total from any matching numbers in their roll- a single 6 would block three 2's from an attacker.).

kosmos1214 proposed a system (see page 26 of this thread) where dice are added up to reach a target number, with extra dice remaining counted instead of adding these together to determine effect (e.g. number of wounds). Elaborations considered later included mixing dice types for more variability, or using the highest dice to hit the target number first vs. using them left-to-right.

Final Notes
Overall, multi-die addition systems are good at providing simple linear return (e.g. 1d6 damage per caster level) directly, or less than linear growth if slowed down first by e.g. escalating improvement point costs or the like. This is perhaps more likely to be desirable in rolls for 'how much' (effect) rather than 'do I succeed' (the question a core mechanic has to address primarily). The mechanic does combine well with extra match- or success-counting gimmicks as noted above, but in its basic form doesn't really have much to recommend it mechanically (...unless you want to roll lots of dice) since its non-transparent, requires a moderate amount of addition, scales badly and doesn't give any additional features beyond what most other options do. Multidie tends to happen fairly often in some of the oldest systems, from before polyhedral dice were as generally available.

In these games, a die roll is made under a character's statistic for them to succeed. This is mathematically almost equivalent to using addition (except on opposed checks where either side may fail their roll completely, making a margin of success comparison unnecessary; see post #117). It may be arguably less intuitive (lower numbers are better).
Roll-under may be slightly easier on the players mathematically than an additive system (the player is comparing numbers rather than adding them), particular where rolling multiple checks at once, although any benefit is lost as soon as margin of successes have to be calculated - something players may start to do automatically just in case. Opposed rolls tend to be particularly awkward in roll-under systems; the default mechanism being that both opponents have to calculate how far they rolled under their success number (e.g. GURPS), but this gets annoying for some players, particularly where d100s get involved.
Calculating margin of success with roll-under is the same as taking the stat and subtracting the die roll.
 
Roll-under systems are excellent for applying proportional modifications to chances of success - creating tasks with 1/2 normal chance of success, for instance (though low range roll under, like Lamentations of the Flame Princess' roll under X-in-6 with d6 skill system, or even Cadillacs & Dinosaurs 1-10 stats, make this awkward due to rounding). This works more poorly in additive systems because the opposing target number generally varies; for instance in a d20+modifier system, halving the bonus only decreases chance of success by half if the opposing target number is exactly 21.
 
In other games, opposed rolls may be handled by cross-referencing scores and the attacker rolling under the result (e.g. RuneQuest's "Resistance Table"), or by using an additive mechanic just for opposed rolls. LegendQuest and Synnibarr both use skill rating + an extra modifier (+d10 or +d20); For LQ this is done instead of the normal d100 roll (in some cases); Synnibarr makes the additive comparison only if both opponents first roll under their skill.
 
Initiative rules are particularly problematic in roll-under, since these involve a comparison between whatever number of characters (or groups) are involved in the conflict, rather than just seeing who wins out of two opponents. Attack rules are interesting; some games will handle 'defense' as an adjustment to the attacker's roll (adding more calculations to the roll, obviously, and perhaps losing some of the advantage of roll-under), while other systems give defenders a block percentage to roll against; which however means a characters' % to hit is basically the maximum possible chance to hit irrespective of how bad an opponent may be at combat.
 
Variants include
*Roll under using a number of dice varying by difficulty i.e. in The Fantasy Trip (precursor to GURPS) used a variable number of d6s (e.g. from 3d6 up to 7d6 for very hard rolls) under stat. (TFT can also handle multiple-stat rolls with more dice, e.g. unhorsing an opponent is 6d6 under [STR+DEX]. Another system for this was proposed here (http://cyclopeatron.blogspot.com.au/2010/07/simple-multi-ability-checks-in-classic.html?showComment=1308775704568#c8666153115333447209) for D&D, where a roll against 2 stats together is made with 3d12 instead of 6d6 - this has the benefit of having a very similar distribution to 3d6).
More recently 'Summerland' used the same mechanic (with 2d6 for easy tasks, 3d6 for average, or 4d6 for difficult; a check is made against a score of 2-9 + up to two 'tags' which start with values equal to 1/2 stat).
Examples in Summerland show an issue of double counting of bonuses' where the vagueness of the rules can lead to a high or low value also giving a character a higher or lower difficulty e.g. a strong , character [high body value] getting a lowered difficulty of routine/2 dice as well as having a higher score to begin with.
A number of game systems use this for some subsystems e.g.HarnMaster combat results (# dice determined by cross-referencing attacker and defender results), as does Monsters & Slayers for some rolls (reviewed in Dragon magazine #195, Monsters & Slayers is remarkable for having different mechanics for different tasks, while still using only d6s). Original red box (BECMI) D&D suggests using this for ability checks and varies both number and type of dice i.e. either d20 or whatever the GM feels like be it 3d6 or 3d8 or 5d6 to resolve unusual situations (DM book, pg 20); Dragon Warriors also does this regularly.
This concept doesn't combine at all well with blackjack success (see next point), as higher difficulty will also increase average success result.
*Blackjack Success (e.g.  Pendragon, QAGS, 2E AD&D psionics, and 1E AD&D surprise). In games using this, higher rolls are better as long as they don't go over the skill; this lets these handle opposed rolls fairly well since the raw numbers only are compared (if A rolls 12 on the dice and succeeds, and B rolls 15 on the dice and succeeds, B wins). This is normally used with single (linear) dice rolls - in which case the blackjack method gives results mathematically the same as comparing margins of success - but that breaks down with curved rolls like 3d6.
Note that tiny modifiers on the dice can occasionally convert a best-possible ('Power Score') success into a failure, or vice versa.
Like all roll-under systems, they scale poorly beyond the point where [stat = maximum roll on the dice]. Pendragon patches this by giving characters with skills of 21+ a bonus to their d20 die roll.
Pendragon does use the same mechanic for initiative as for everything else - only one side, the highest roller, wins the combat round.
Blackjack systems are also interesting in that they tend to have 3 unusual results, rather than the usual 2. For instance in a d20 blackjack system as well as critical success ("Power Score"/rolling whatever number your skill is) and critical failure (a roll of "20"), there is a "marginal success" i.e. "it worked, but badly" result (a roll of "1"). In a normal higher-is-better system, this would be analogous to giving a special, "half-success" result on a roll which exactly equals the required number to perform a task, as well as fumble/critical, which most additive systems don't bother with.

Other Elaborations
*Runequest has ‘special successes’ and ‘critical successes’ as a proportion of total % chance, as these are relatively easy to calculate.
 
*Alternity uses a d20 roll under stat/skill, plus or minus another dice which has a size determined by task difficulty i.e. , +0, +d4, +d6,+8 up to +d20; or -d4,-d6,-d8...up to -3d20; the theory being that an almost impossible task could still succeed occasionally, or a very easy task fail, due to characters rolling a low number on the extra dice. Special successes occurred at ½ and ¼ of base success chance, making specials and criticals equally likely unless a difficulty dice came into play. (this might be less bad if there was a following 'roll' step that generated partly overlapping results e.g. if Good and Amazing rolled d6 and d8 respectively for damage, as an idea. Alternity doesn't do that).
Alternity did use the same core mechanic for initiative, with characters acting in either Amazing phase (d20 roll less than 1/4 action score), Good phase (less than 1/2 action score), Ordinary phase (less than action score) or Marginal phase (failed roll), and all actions in the same phase considered simultanous. For other opposed rolls, it assigned the defender "resistance modifiers" which applied to an attacker's difficulty i.e. a 13 Dexterity (+2 steps) might increase an opponents ranged attack difficulty from (say), a -d4 penalty to a -d8 penalty. Historical note: In the introduction to Cortex Lester Smith claims the credit for the idea in Alternity, originally proposed as a skill check variant for a possible 3E D&D, which evolved into Sovereign Stone and later Cortex
 
*TriStat dX rolls under stat with 2 dice, with the campaign determining what sort of dice these are - from d4 (normal human) to d20 (godlike). A character can buy attributes up to [2x maximum size of the campaign dice]; a 4 represents human average in an attribute, and a normal task for the campaign requires a roll of 2 dice below the attribute.
 
*Dragon Warriors is usually roll-under on d20, with defence statistics (e.g. Defense, Evasion, Magical Defense) which subtract from the attacker's stat before they roll. In the case of physical defense, this lets defense be split among multiple attackers fairly easily; the system is fairly quick since the attacker (having already subtracted once ) basically never needs to calculate how much they've rolled under by, and will knows many rolls are misses (over their to-hit score) without having to calculate.
 
*Roll Middle: beejazz proposed an alternate method for handling task difficulty, which I hadn't seen in any games in the wild. The roll must be under the trait being tested, and also over the task difficulty. The aim of this is to cut down on math. For example if a character normally needs a 13 or less to succeed (say on d20) they succeed on a 1-13. On a difficulty 3 task they fail on a 1-3 task, succeed on a 4-13, and fail on a 14-20. That trades a subtraction for a (slightly easier) second comparison, while keeping the same odds. It could be thought of as related to the blackjack method- a blackjack system often does that on opposed rolls, or if a minimum amount of success is required. It is (like a number of roll-under common elaborations) perhaps slightly unintuitive, treating numbers as individual things with separate properties rather than their being quantitative.

*a weird rule from (poster) Talysman for arrow traps for 0D&D: for an arrow trap the trap makes an attack roll, with characters who have a DEX higher than the attack roll being able to make a saving throw to dodge (folding in a 'lower is better' DEX check and a 'higher is better' attack roll using the same dice roll ?).

*In Nomine -roll-under, [generally stat+skill] with 2d6, plus a third d6 (the 'check digit') is rolled for degree of success. A 1,1,1 results in divine intervention and a 6,6,6 infernal intervention: angelic players critically succeed on triple-1 and critically fail on triple-6, with the reverse for infernal players.

*Flipping between Roll under/Roll over: from rpg.net here (http://forum.rpg.net/showthread.php?695577-What-OSR-games-don-t-use-the-standard-d20-roll-over-system/page2):  Attack rolls in Searchers of the Unknown succeed if you roll under your opponent's AC plus your own level, on a d20. Cleverly, this is inverted for sneaking around — roll 1d20 under your AC plus your level. Since AC is descending, a good AC makes it harder to get hit, but also harder to sneak around. "So in battle, wear big thick plates of metal; when stealing the king's jewels, take only your oiled-up body."

Roll-under games sometimes handle additional difficulty through extra rolls (something that can happen in any system, but is perhaps more likely in roll-under since in e.g. additive or dice-pool its easy to adjust the target number). For instance, Fighting Fantasy in one adventure (Island of the Lizard King, IIRC) lets a character 'Test for Luck' twice in order to catch a water elemental in a Pouch of Unlimited Contents)(alluded to also in monster book Out of the Pit). In this case, two rolls also double the resource cost to do this (each Test for Luck costs a point of current Luck).

These are games where dice shift types e.g. from d4 to d6 to d8 as characters get better. There's a slight problem above d12 since Zocchi dice often aren't that common; multiple dice are sometimes used instead.
D&D uses this for damage rolls; it is seen as a core mechanic in for example Earthdawn, Savage Worlds, and Cortex.
 
Simple changing-dice-type
A simple example of this would be the miniatures game Great Rail Wars (Savage World's predecessor) which is closely related to SW, but simpler; notably there's no "wild die", and no skills i.e. it just uses attribute checks to resolve tasks (stats include Strength, Smarts, Vigour, Shooting, Fighting and Guts; there's no generic 'agility'). Normal 'Gunmen' for instance might just having Shooting d6, and hence roll d6 when they're shooting something.

Savage Worlds uses a single dice for characters, plus “Wild Cards” roll an additional d6 at the same time and take the highest result, with maximum results adding and rolling again. Having only a few steps means stats are fairly granular; roll-ups make results unpredictable. It has skills rated like stats at d4 through d12 (d4-2 untrained), with raising skills above stat being double cost. Otherwise, stats don't modify skill rolls directly.

Mathematically some tasks are easier with a smaller dice (using a d4 vs. TN 5 is around 2% more favourable than using a d6), but it allows rolling for large numbers of non-wild-card opponents at once quite easily (though OTOH,  it also tends to require mass combats since single 'boss' fights will end too quickly from damage rolls blowing out). The 'wild die' both adds more of a 'curve' to results and further softens the granularity of the steps, although it does mean that for a normal check (d6, d6) the odds of having to re-roll one or more dice is pretty high - 11/36 or nearing a third of the time.
In SW, odds of a ‘fumble’ decrease as character skill increases (instead of being a fixed 5% for a d20 system lacking a ‘fumble confirmation roll’) but odds of ‘exploding’ dice (rolling up on maximum) decreases as skill goes up. Difficulty modifiers normally apply as a + or - to the final roll - Dice type is not modified for external reasons  - which can be very significant/harsh (modifiers apply to the Wild Die as well, so are more significant that step changes).
SW is particularly hit by the cap at d12; SW attempts to deliberately always be single-die so mass combats can be rolled at once, and also handling multiple dice (additive) as well as a Wild Die would be messy, so it goes to d12+1, d12+2, etc. at the highest steps.
An interesting method for fixing the exploding dice problem using FUDGE dice can be found here (http://www.peginc.com/forum/viewtopic.php?t=41300).
Compared to additive systems the amount of mental effort is probably less. There is an extra step of choosing the correct die, although, this is typically minimized (in combat at least) by using the same die most of the time e.g. fighting die is always the same. In SW, damage is slightly confusing in that dice are added together for this in most versions, instead of taking highest.
The Wild dice can rarely be modified e.g. Suzerain (epic SW expansion) ups these to d8s, while a Legendary edge exist that ups the wild die for a single (d12 rated) trait to d10. The CoC SW system (Realms of Cthulhu) also allows for partial wild cards, which have a d4 wild die. (Pondering as a house rule having 'untrained' checks for PCs default to just the wild die, instead of d4 with -2 to both rolls)

Other Notes
*In my own homebrewing I'd experimented with a system where stat is rated 4-12, with even numbers giving an increase in step for raw attribute checks (4 = d4, 6 = d6, 8 = d8, etc), while odd numbers instead add a +1 modifier to all the skill ratings based on the attribute (i.e. 5=-1, 7=+1, 8=+2, 9=+3) - with skills on the same 4-12 scale i.e. base 4 for an untrained skill. This involves a bit of finangling of modifiers but reduces the granularity problem a bit, while still having one-roll resolution.

*The Battleball boardgame (mentioned here (http://forum.rpg.net/showthread.php?771379-High-and-Low-rolls-being-equally-valuable-How-can-I-do-this)) has movement rated d4 to d20, with lower being better about half the time (used to resist tackles).

*on SW's probability issue, another fix to prevent the TN problem could be to remove TNs - with opposed rolls for instance, there's no "set" TN beforehand, that would give an incentive to use d4 over d6. (That could change if a reroll is made e.g. from a 'bennie' though).

One friend's homebrew game, "Last Order" uses a single dice varying by skill (and potentially 'stepped up' by attribute bonus), with the dice size setting a 'variable raise number'; instead of each 4+ being a 'raise', raise numbers vary from 4 minimum up to about 7, with the margin being set based on an attempt to slow down the rate of several-raise results and worked out mathematically. For a normal TN 4 task e.g. a character rolling an 8 would get one 'raise' if they had skill of d4, but would have needed a roll of 11 if their skill was actually d20.
 In a sense, this gives result sort of similar to how a 'roll under' system can have higher success levels be a proportion of total success chance (e.g. like how Alternity has 'good' results under 1/2 success chance and 'excellent' results for rolling under 1/4). The system is slightly cumbersome in that of course a character has lots of different skills, and a player therefore has to record and use a different raise number for each. It also has problems should a task ever needto go back to counting success margin exactly instead of 'raises', since raises are worth more points for higher skill characters.

Combination Stat die + Skill die
Cortex uses the sum of two dice; one for attribute and one for skill. Final results follow a V-curve or truncated bell curve distribution. Unlike Savage Worlds it can incorporate d2s (since maximum rolls don't explode); it normally handles difficulty as a step up/down to the dice type.
Compared to SW, multiple rolls are slower since dice must be paired up. As a possible elaboration, one homebrew game of my design uses a similar stat die + skill die system, but also kept combat to single-die resolution like Savage Worlds by having players have to split their dice between attack and defense, taking average roll for defense. Saves and initiative are likewise kept to one die by using having them be a raw attribute check, not [attribute+skill].
A minor quirk of this setup in general [stat die+skill die] is that raw attribute checks using only 1 die- contests of strength for instance? - may be more variable than skill rolls, rather than less variable (as might be expected realistically)(the same quirk applies to dice pool games where dice pool is stat+skill, such as Storyteller). (Cortex does however often use [Attribute+Attribute rolls instead, however, e.g. Burst of Strength (Serenity pg 142) = Str+Str).
Games like this make it easy for the GM to notice and describe how much of someone's success is due to skill and how much to raw talent, if desired.

Dice Rolled determined by 'step' [dice chain]
Earthdawn uses multiple dice of various kinds additively (what is rolled being set by a ‘step number’), with individual dice able to ‘explode’ (roll up maximums). It uses multiple dice for higher steps (above d12).
Another (obscure) step die system, the 'HDL' (half dice level) system, used step numbers but with step based off [2xattribute] i.e. 2 = d4, 6 = d12, etc. and then skill as a separate (flat number) bonus; a stat bought at 1-10 set the step/dice rolled with skill score (also 1-10) then added to die roll, or raw stat rolls would roll the step and then add the 'step number' again.
 
Ad Hoc Dice Pool (dice of various sizes gathered individually).
The 2012  'Marvel Heroic Roleplaying' Game (MHR) is a changing-die dice pool where several dice of various sizes are rolled together (from different traits); 2 are chosen and added together to determine if the character succeeds, and another die used as an "effect" die to determine how well the task succeeds. A complaint on this system may be that extensively fiddly rules are needed to arrive at dice pools that feel the same in the end (with very nontransparent probabilities, to boot). Another odd feature is that the way pools are built requires several factors to be combined; something like a raw 'Strength check' isn't exactly possible because STR provides only one die. In general rolls are more likely to operate at a scene level with exactly how something has occurred requiring some interpretation. Its interesting to compare this with, say, One Roll Engine, which requires [stat+skill] pairings. Its also exactly the opposite of the original Marvel FASERIP which could apply a maximum of one attribute per check (apart from Karma effects). All MHR rolls are opposed (so both sides can roll 1s (http://forum.rpg.net/showthread.php?720729-Sell-me-on-an-Opposed-Roll-system/page4))
 
Other systems:
*Ironclaw (see discussion here (http://www.skotos.net/articles/BSTG_50.shtml)) uses a take-highest dice pool, but with dice of mixed sizes. Adding a small die has little effect on chances of succeeding a high difficulty task (e.g. making a difficulty 12 task isn't helped with another d4), but increases the chances for a low-difficulty task (and decreases chance of a fumble when all dice are 1s).

*The Agora system alpha playtest (a story-game-ish freerpg by Joshua BishopRoby) was step-die, often with multiple dice but with lower rolls being better (but with the extra complication that a die rolling a '1' is discarded). (note to self- check suballocation correct)

Changing-Die/Dice Pools - # Dice and Die Type determined separately
Ork! - The RPG uses additive step dice/dice pool, with attributes rated at d4 to d12. Skills start with default rating 1 but can go up to 5 dice (using the controlling attribute die type). Dice are added directly.
Fantasy Dice (which has free version Turbo Dice available from here (http://www.radicalapproach.co.uk/)) is the opposite, with skill giving the base die (d4 for untrained, up to d12) and attribute giving # dice, with highest result used. Characters can reduce their pool by 1 to increase the dice one step, or vice versa. In combat characters can sacrifice dice to increase damage, or gain dice by spending their second action of the round. Characters who rolled all maximum on their dice get +1 per extra maximum rolled (something less likely as skill dice/pool increases, though as its purely numeric the shift here is probably hidden by the normal increase from pool or step gain).
(drawbacks with this sort of combined system: usually half of the game numbers are effectively on a different scale making them difficult to convert between, though perhaps its not unusual to have skill/stat on a different scale.)

Deadlands also uses a combination of changing-die and dice pool: like Ork a character's attribute determines their base die (d4,d6,d8, etc) while skill determines how many dice are rolled. It takes highest die however, with any maximum rolls (i.e. 4 on d4) rolling again and adding to that die result (exception: damage dice are added together instead of take-highest).
Unlike Ork attributes don't default to just 1d but are actually described as a full pool i.e. a stat could be 3d4 or 2d12 or 4d6 or whatever. The # dice is irrelevant to skill checks, however. Stat rolls are therefore sort-of on the same scale as skill rolls, although with the issue the extra # dice for stats is usually a wasted number - its only not-unbalanced because chargen is random anyway, as described under card-based systems).

(Another hypothetically possible variation to this might be to have have basically binary skills - perhaps just stepping up attribute dice a size - but then have multiple skills applicable to a task all be rolled simultaneously. e.g. you could imagine a 5E type system where having both a skill and a 'specialty' on that skill means rolling with 'advantage' effectively).This could work with either a count-successes or take-highest setup).

Other Systems:
*TSR's CardMaster adventure design deck, theoretically for 2E AD&D, had a stripped down mini-system of its own, where creatures rolled dice equal to level: warriors rolled e.g. d10 to hit at 7+ while monsters hit on a 6-8 on d8. This is interesting in that as well as the step-die varying, the target number is also being adjusted in parallel with it to get the results desired (thanks to Omega for mentioning elsewhere).

*Another interesting way to combine step-die/dice pool (not seen in any extant system I know of) might be to use it to represent skill 'width'. A character might buy a number of dice, with that number being say d4 if the skill is extremely general, d6 for a more specific skill, and d8 or d10 for a highly focussed specialty skill. This would balance buying skills of varying width without complex point accounting, and enables easy 'stacking' of general and specialized skills (just roll a dice pool of mixed type).

Changing Die Type - by Difficulty
Tales of the Floating Vagabond uses a roll-under step die system where higher difficulty = larger dice rolled against a stat value (pitifully easy d4, easy d6, normal d10...through to nigh-impossible d100)(it instead uses comparison of d10+stat for opposed rolls). Similarly, Greg Stolze here http://forum.rpg.net/showthread.php?603858-Games-that-use-penalty-dice/page4 (http://forum.rpg.net/showthread.php?603858-Games-that-use-penalty-dice/page4) comes up with a similar inverted step-die system, where larger penalty dice are bad (subtracting from the base skill+stat value).

Dungeon Crawl Classics uses an OGL-derived d20+modifiers system at base, but with Zocchi dice, and significant penalties (or extra attacks gained from level, TWF, etc) can use smaller dice such as d16 or d14, while bonuses can shift rolls to d24 or d30. Effects such as criticals are handled somewhat awkwardly due to this i.e. a combat penalty can increase chances of a critical by requiring a 16 on d16, instead of 20 on d20 (although as critical effects are generated by rolling on a separate table, which has 'no extra effect' as an option, they could have patched this by handing out a separate penalty to the crit roll). DCC is in some ways the opposite of Savage Worlds - it has dice type shifts for penalties and plusses for character skill/stat advancement, instead of different dice from the fundamental skill/stat and flat bonuses/penalties for circumstances.


General Notes: Changing die systems give a great deal of variation in ability, but regardless of rating, a high result is not guaranteed. These systems are generally fairly granular unless multiple dice are used. Unlike most single-die systems, the main way to keep opponent abilities secret is to roll behind a screen, since otherwise the dice being rolled gives away what the check is for (the same problem occurs for DMs trying to make secret rolls in AD&D, where different subsystems use different dice, but its not quite as bad). If a player gets their dice wrong, its awkward to rework the result, unlike in an additive system. Describing attributes as die codes generates some awkwardness with mathematical operations e.g. addition, halving, etc. (in part because they usually starts at d4, in part because odd-numbered dice have poor availability).
 
Varying Dice Type as a supplemental mechanism:
Shifts in dice type are sometimes used with other dice mechanics in exceptional circumstances or edge cases e.g.
*Talislanta is normally d20+modifiers on a table, but untrained rolls are d10+modifiers.
 
*SenZar uses a roll of d20 equal or over a target number of [21-attribute], but scores of 20 higher instead let a character roll a d100 vs. target 05% , giving much larger margins of success for opposed rolls (and making difficulty adjustments less of an inconvenience to these characters).
 
*Cadillacs & Dinosaurs replaces its general d10 roll under character stat with [roll of d6+damage taken] vs. stat for determining some wound effects; interesting in that they've reduced the base amount of randomness in the check to allow for extra randomness coming from elsewhere (overflowing off other rolls). This feature is probably due to that subsystem being inherited separately from Twilight 2000 (pre- the core mechanic?), rather than being a conscious design decision.
 
*The Soothsayer RPG gives stats roll-over target numbers that are usually on d10 (a stat of 3 is 10 on d10 to succeed, 4 is 9+, 5 is 8+ etc); however a score of 2 instead requires a 12 on d12, while a 1 succeeds only on 20 on d20.
 
*IIRC, 1E AD&D shifted from rolling d6 for open doors to d8 at giant-level Strength, which was a continuation of higher than the table initially went. This was replaced with a consistent d20-based subsystem in 2nd ed.

*2E AD&D's Creative Campaigning supplement has guidelines for replacing d20 roll-under ability score checks with various other dice to control amounts of variability, e.g. with Strength rolls often being low variability [d4+8], Constitution [d6+7] and Dexterity/Intelligence/Charisma d10+5 or d12+4, as well as multiple dice (Con rolls of 3d4+3).

*Basic D&D [BECMI] GM book suggests ability checks rolling under the normal 3-18 D&D stat with various dice like 3d6 or 5d4, depending on difficulty. (later skill checks for general skills in Rules Cyclopaedia are usually d20) The Immortals rules let stats go up to 100, and change from d20 to d100 roll-under for herculean, Immortal-level tasks.

*The French-language RPG Mournblade reportedly uses d10+modifiers; characters have the option of rolling d20 instead but if so, odd numbers are not added (i.e. are treated as a roll of 0).

*Fairly granular rolls such as 2d6 can be replaced with e.g. d100 tables of results to produce results changed more subtly than is possible with just modifiers to the roll (as every +1 is a significant shift here). That can be used e.g. for 2-12 attribute generation with specific races etc.

*Class Warfare for Dungeon World has a 'Herculean Appetites' special ability that replaces the usual 2d6 roll with a d6+d8 roll; if the d6 is the higher of the pair, the GM introduces an extra 'complication or danger'.

Other Notes
Hypothetically changing-die-type seems like it could be interleaved with a dice pool system fairly easily for some rolls e.g. a 'd4' could be replaced with 4 dice, count successes, or d6 with 6 dice, count successes. Perhaps this could be used where more average results are required, or where more detailed readouts of numbers are required like trying to do ORE hit locations or count 1s on a successful check, or it could be converted back the other way to simplify a dice-pool game to a single roll. Adjusting the TN here would be roughly parallel to rolling the dice multiple times, take highest or lowest.
It would also be possible to throw in a x2, e.g. 2d = d4 up to 10d =d20, given some Zocchi dice at the upper end.

With varying dice sizes: occasionally an extra bonus might be a +1 regardless of die size, or there might be a +1 that applies only to a particular die size; these can generate problems since they're bonuses that function in a 'meta game' fashion.  Complete Viking's "Lucky" gift for example (AD&D 2nd edition which isn't mostly a step-die system, but go with me here for example purposes) let a character choose a +1 on a sort of die (d4,d6,d8, etc) - this gave some reliable effects like on hit points for levelling and damage, but beyond that has benefits that varied a lot depending on which subsystems were used or on how GMs adjudicate odd situations (e.g. whether an arm wrestle is d20-under-Str or both sides rolling d4+Str score as in Creative Campaigning matters, at a wholly metagame level, to someone who gets +1 on d4s, or a +1 to d10s for hit points might vanish if a fighter was upgraded to Skills and Powers rules and goes to d12s for HPs), or (IIRC) a + on d6 or d8 might be important if using optional crit rules from Combat & Tactics.

EDIT NOTE: I have revised the terminology for this post. Where I used to call 'changing die type' systems 'step die' systems, I'm now using 'step dice' more specifically to refer to e.g. cases like Earthdawn, where a dice chain or 'step' is what determines die size.

This category includes Marvel Super Heroes and a number of old TSR games (Gamma World 3rd ed., the Conan game And ZeFYRS), plus Indiana Jones, Top Secret, and DC Heroes.
There is some interesting analysis of the MSH table at darkshire here (http://darkshire.net/jhkim/rpg/systemdesign/dice-msh.html)
Tables let large ranges of values be assigned a chance of success (as in MSH, where scores range from a feeble 2 to cosmic ratings of up to 5000), and/or let a designer add various result levels with exact control over likelihood of them occurring (in MSH, likelihood of “Yellow”, “Green” or “Red” results, for instance). As such this gives ideal control over both success chance and achievement level, though the game may slow down while checking a table. A table may cross-reference either difficulty and statistic, or statistic and result level; doing both requires a series of tables (e.g. ‘slices’ of a table that actually extends into three dimensions).
Tables can be used to create more 'granular' increases in ability (i.e. preventing lots of point-counting), by controlling the number of rows.
 
James Bond's system was similar to MSH (though preceding it), with a score out of 30 assigned and multiplied by a difficulty factor to get a target % . A roll determines a quality number (1-4) which then modified effect e.g. damage.
 
A table system can have bonuses that work in multiple ways. A bonus can:
-increase the statistic being used to make the check
-increase the dice roll
-directly increase the result level (often called a "column shift" or similar).
Depending on table construction, increasing roll and directly altering result level can give very different results; this is a fairly unique feature of these games. (one effect of this is that, if desired, an 'opposed roll' might be between the rolls, ignoring the 'result level', so that e.g. effects of high skills are minimized; advantages might boost roll while skill boosts result lookup, or vice versa).
Perhaps comparable to with how in dice-pool games, shifting # successes required, # dice and target number all do different things.

Column shifts can sometimes be used to gear down or reduce modifiers, as an alternative to a flat + to a roll. For instance in 0D&D having a dwarf 'save as 2 levels higher' gives a boost probably less than a +2 bonus (which could also potentially scale differently between different classes).

Historical note: in a sense I think the 'universal table' games can be thought of as descending from the early 'matrix' approach used in D&D and the like, where various situations require different lookups of results (often attacker value vs. defender value e.g. to-hit charts in D&D); the universal table is basically an attempt to compile all the matrixes into one super-matrix, with enough caveats to cover most or all potential situations. Matrixes themselves presumably derive from Combat Results Tables (CRTs) like those seen in SPI wargames. This evolution itself may be most evident in 3E gamma world, migrating from lots of individual mini-tables into one.

Tables as a supplementary mechanism: the games above use tables to set the basic probability of an action succeeding itself. As an example of a table used as an accessory only, Chill starts with a basic d100 roll-up system. If the roll success (under the %) but a level of achievement is also required the player calculates the margin of success [skill percentage minus actual roll] and looks that up on a table to get a result.

EDIT NOTE: J Arcane later on here (http://www.therpgsite.com/showthread.php?p=729072#post729072) mentions Alternate Realities' DRF system - ' an actual trigonometric function you plugged your stat value into to get the target number on d100'.

Previous edits: added James Bond mention (thanks Jibba Jibba): tables as a supplementary system

DC Heroes 2E, which came in boxed format, apparently had a 'result wheel', a physical wheel that could be turned to line up acting and opposing numbers instead of cross-referencing - so equivalent to the table but more cool.

Not to discourage, in fact I hope this would encourage and help structure your efforts, but you could do worse than to look at John Kirk's collection of RPG Design Patterns from http://legendaryquest.netfirms.com/ (Note: there's a wiki and a PDF download. I'm only familiar with the latter.)

It's somewhat influenced by and reverential towards Forge theory and games, but fortunately not in a way that impedes clarity.

Quote from: Elliot Wilen;496084Not to discourage, in fact I hope this would encourage and help structure your efforts, but you could do worse than to look at John Kirk's collection of RPG Design Patterns from http://legendaryquest.netfirms.com/ (Note: there's a wiki and a PDF download. I'm only familiar with the latter.)
 
It's somewhat influenced by and reverential towards Forge theory and games, but fortunately not in a way that impedes clarity.

Hi Elliot. I've read it, actually (probably why I described Star Wars as using a "safety value" mechanic ;) )though I am unfamiliar with a number of the systems he references, and leery of his conclusions in places (like his discussion on how to "simplify" damage on pdf page 47, by applying to-hit overflow onto damage - since IMHO this adds a subtraction step to every hit roll). I do like the idea of design anti-patterns in an RPG context - pity that wasn't explored in more depth.
 
I'm planning on a different focus - looking more at the specific innovations of "fantasy heartbreakers"; hopefully by working through subsystem-by-subsystem I'll get a better view of context than if I were working it through pattern by pattern (divorced of context) even though some patterns may repeat themselves across different systems.  Thanks though, and I will promise to keep it in mind where relevant.

Interesting idea,  I look forward to following this thread.

Cheers : )

This section refers primarily to games which roll a number of dice and then count "successes" by finding rolls over a given target number (There are also 'die pool' systems which either take the highest roll out of a set of dice, or which are additive i.e. which just add together all the dice rolled; see below for more on these).

Shadowrun (1989) and Prince Valiant (1989; actually coin based, using total of stat+skill to determine pool) were two of the first of these, although Space 1889 also used dice pools for certain tasks (combat used target numbers, though the pool of d6s was typically used additively). EDIT : Chainmail used alot of d6s too, although its arguable if its really a dice pool, as each d6 rolled represented a separate attack. Shadowrun 1E used either attribute or skill to give number of dice (for untrained skill use or use of the wrong skill, penalties were determined using a relationship flowchart), while Prince Valiant and Storyteller use [stat+skill], giving slightly larger pools.
Systems can also have # dice determined by stat, with skill determining a base target number, or vice versa e.g.- Arrowflight 1E (2E differs) uses D6s equal to stat while skill sets the base target number to roll under.

Die pool systems are particularly good for determining how well a character succeeds, but less good at determining if a character succeeds – probabilities are less transparent and in practice designers tend to allocate # successes required for tasks in a fairly ad hoc fashion. ‘botch’ chances using 1s tend to do odd things.
Some systems independently vary both target number and # dice (oWoD – particularly Werewolf- and Shadowrun 1e/2e). This unpredictably/erratically increases the number of dice needed to get a given # successes and is an approach that should probably be used rarely. Shadowrun uses d6s and allows target numbers (TNs) over 6 (6s add and roll over).
This had a slight irregularity in that TN 7 was no more difficult than TN 6 (since there was a minimum of +1 when the d6 rerolls); shift from TN 7 to TN 8 also had much lower effect on probability of success than (say) 4 to 5, or 5 to 6. The hillbilly mecha game "Junk" was similar but rather than roll-and-add, instead required a minimum score on the reroll dice, based on the final TN e.g. TN 7 = needs a 3+ on the reroll success; equivalent to rerolling and adding using [d6-1].

oWod/Shadowrun dice pools also have some mathematical issues - e.g. see tgdmb post by sabs here (http://www.tgdmb.com/viewtopic.php?t=54721) on the problem that the descriptions given to skills in oWoD (3 dice = expert, 5 dice = top of field) don't match increases in dice pools, which usually are minor (or obscured by variation in attributes).

Dice roll systems integrate particularly well, with even damage etc. following the same universal system. Attack roll successes may add to Damage successes giving DEX a percentage flow-through into damage (less than Strength since successes are normally converted into extra dice, and have to be rolled again), without the math being excessively clunky.
Dice pool games are virtually never level-based: dice pools are fairly granular due to maximum pool size rapidly becoming unwieldy, making it difficult to have a reasonable number of levels. Dice pools also make "soak" rolls easy to implement, so such games are less likely to have open-ended hit point totals. Storyteller does give each of the character types a sort of 'key attribute' which is core to them and somewhat like 'level' - Generation in Vampire, Arete in Mage, Rank in Werewolf - but only somewhat.

Player errors in how many dice they should be rolling here can be fixed easily if they err on the low side (roll more dice), but tricky if they've rolled too many. This makes modifiers that subtract from # dice rolled potentially more tricky (its being easier to forget a modifier applies, than to just make a mistake in adding up skill+attribute or whatnot).

Applying Modifiers: Dice pool games may have target number shifts, bonus dice, bonus successes, conditional bonus successes (10 counts as 2 successes, 10s give a bonus dice, etc) or a total reroll which all do quite different things, and which synergize with each other to a varying extent and in different ways. "Reroll 1 die" may have little effect on success chance at TN 10 in Storyteller, but can massively decrease chance of a "botch" (excess 1s), while +1 success might guarantee success regardless of difficulty in some systems. A TN shift might have little effect or even no effect, or significantly change successes - TN 6 to TN 7 in 1E Shadowrun has no effect on successes, since 6s always rolled up by +1d6, while a shift from TN 5 to TN 6 halves expected final number of successes).
Dice pool penalties might cancel automatic successes instead (making these easier to lose) or just apply to the pool.

Critical fumble rules vary in dice pool games - generally '1s' rolled give some sort of negative, and a problem could occur if the whole pool is 1s, a majority of dice are 1s, or 1s may subtract from successes with a negative overall result being bad.

Other dice pool elaborations or examples:

*nWoD uses a fixed target number generally, however a character who would drop to a negative die pool can roll a single die (at difficulty 10 instead of the usual 8) to succeed, known as a 'hail mary'. In a sense then, this is similar to rolling 1/3 of a die.

*Shadowrun 5E has, for reasons, rules for "limits (http://shadowrun-5th-srd.wikia.com/wiki/Tests_and_Limits)" where a character has a maximum # of successes [hits] that can be generated regardless of the dice pool (excess successes are lost]. To be fair this lets them balance out some of the less valuable stats (Essence modifying social limit?). It does however seem to me problematic in that it is removing some of the purpose of rolling dice - it would be better to have a mechanic that only rarely generates outliers, but where those are at least possible.

*Shadowrun 4E has rules for 'glitches' - if a character succeeds but more than half their dice pool consists of 1s, they still succeed but with some drawback. This result might be comparable to 'marginal success' (roll exactly what you need and no higher) in a d20+mods, or d20 roll under system, except that chance of a glitch occurring decreases with greater skill in SR4.
Comparatively in Deadlands [though...this is a take highest step-die/dice-pool, see step dice] a character rolling a 'majority' of 1s in their dice pool 'goes bust' (Fumbles), and this overrides the normal success result.
(Characters in Deadlands can also have a fatal illness flaw [Ailin'] forcing them to roll a Vigour roll anytime they 'go bust' or die).

*Dice pools can also deliberately give negative complications e.g. from each extra '1' rolled, to discourage the maximum number of dice being rolled (e.g. area attacks in Marvel Heroic leading to collateral damage).

*The Ubiquity system (Hollow Earth Expedition) has a dice pool system where results are 0 or 1 (unlike say storyteller, 1s or 10s aren't ever specifically counted - only successes or failures). 'Ubiquity dice' let large dice pools be compressed into fewer dice e.g. a d8 labelled 0,1,1,1,1,2,2,3 (IIRC) duplicates the roll of 3 normal dice.

*Humandyne XdX (http://forum.rpg.net/showthread.php?492604-Humanydyne/page1) (unpublished?) lets players choose # dice (1-10) and dice type (usually d6), with evens = +1, odds = -1, 1s = -2 and max roll = +2. A trait rating cancels that number of "-1s". High number of dice gives more potential variation, though is less risky for characters with a high trait.

*The Spartacus boardgame (though its a boardgame) has a sort of interesting system for opposed rolls. A character has an 'attack' or 'defense' as a number of dice e.g. 2d or 3d; rolls are opposed, with both sides pools arranged highest to lowest, and the individual dice compared to each other. For example an attack of 4-4 might be compared to a defense of 5-3; the first defense roll is higher (5 vs. 4 and so is blocked, while for the second die attack is higher and so a success (wound) is inflicted (causing loss of one die from one of the target's stats). To prevent a larger attack pool being overwhelming, an 'unopposed' dice needs to be 3+ or is ignored (e.g. an attack of 6-5-2 vs. a defense of 6-5 would deal no damage; the last attack die is too low). Characters could also have special abilities triggered by e.g. doubles or triples, or rerolls. (Compare also resource-based dice pools - Dogs in the Vineyard being similar but more complex).

*Mutant Chronicles 3 (as I understand it) uses a '2d20 roll under system where attribute + skill = TN, and a roll under skill only counts as 2 successes. Characters can sometimes get double successes for a roll ("Focus") or an extra die; some tasks can therefore require >2 successes. Failure can also be penalized separately (if any dice fails).Because two dice are rolled, attributes normally range only from 6 to 12. The other interesting thing is that 'Chronicle Points' when spent give a bonus 'roll' set to 1; hence this counts as one extra success normally or two if a character has skill.  (Post here (http://www.therpgsite.com/showthread.php?p=857446#post857446) by JoeNuttall suggests a 3-die system that's similar, useful to give steeper differential in success rates between skill levels). A similar but simpler system is also used in Ron Edwards' "Elfs" game: this uses 3d10 rolling under [attribute or sum of two attributes], giving a range of 0 to 3 successes on any roll.

*Atomic Highway uses a success-counting system where attribute = number of d6s rolled, 6s are successes, and skill adds extra points which can be spent raising rolls to 6s. Natural 6s give a bonus d6 roll (which can't be adjusted). Raw attribute checks use stat as extra points as well as dice. Opposed rolls tie on # successes, broken by highest stat, then highest skill.

*Hypothetically, I could imagine a system that would use say stat 1-10, with a pool of dice by skill and an extra single 'die result' set as equal to the stat score (i.e. Dex 7, archery 3 dice...if you rolled 4,2,6 you would get a result of 4,2,6,7). This would only work with both variable TNs and tasks requiring different #s of successes (or an opposed roll) however - it would be essentially combining 'diceless' and 'dice pool' and so could be too deterministic if 1 success is all that was needed for most tasks. It would combine well with special abilities like '+1 to a single specific dice roll' (making the 'stat die' extra success less of purely yes/no) although these could be too fiddly. Potentially this could work as a houserule for Shadowrun 1E, since it by default has no attribute bonus to skills.

*Twilight 2013 reportedly uses a d20-dice-pool (unusual, though that's in principle no different from other pools).

*games rolling stat+skill, such as Storyteller, would make it possible to work out how much of a given success is due to skill and how much to raw ability, if desired.

Combining dice pool / count successes: hypothetically these could be combined, i.e. roll a 'pool' of dice vs. target number X, rolls of X+ are added together. e.g. 3d6, TN 4+ ---a roll of 4,6,2 would give a result of 10. Generally would work much like a 'count successes' system probability-wise, but slower for players due to addition; would allow for more fine detail e.g. a character could have a rating of [3dice+2]. Rerolls could be useful even where a roll is a 'success'. A character could also have an ability to 'keep unsuccessful roll' (adding it toward their total) which would be unique to this.
Adding exact rolls could also be an optional resolution system, e.g. for damage, or for replacing a multiplier of base successes (such as x2 successes = jump distance) with just success-counts used to see if something works.


Custom Dice Dice-Pool (=essentially success-counting)
A couple of FFG games (Warhammer 3E and Star Wars: Edge of the Empire) use pools of custom dice, with varying symbols. Dice can be replaced with more awesomer dice, or negative dice (difficulty dice) can be added. Edge of the Empire apparently adds more complications/interpretable complex results rather than success/failure. Probabilities are difficult to understand by players without knowing all the dice; pools are somewhat metagameable by players (difficulty modifiers can't be easily hidden - without the GM rolling them, anyway). EotE requires more meta-game interpretation of dice results into flavour text, rather than success/failure complications appearing emergently.
More simply, Tech Noir just has dice pools which (I believe) include specifically positive dice and specifically negative dice (e.g. a negative complication adds more negative dice to the pool).

One Roll Engine: Another sub-variety of dice pool system is the “match counting” system as used in the One Roll Engine (REIGN, Godlike, etc). To succeed in ORE a character needs 2 or more dice to face up the same number. This provides two readouts a “width” (how many successes) and a “height” (what the number is); The system is particularly good for doing Hit Location (i.e. a character a rolls 3,3,4,4,4,7 might opt to target a character in their “4” location for 3 successes of damage, or in their “3” location for 2 successes of damage. The system handles differing task difficulty only with some trouble - success or failure primarily depends on character talent rather than task difficulty - cannot have “fumbles” in combat (since 1s are “left foot” shots); and at least in Godlike, the additional data available is in practice rarely used for most non-combat rolls. In combat it has the slight problem that base damage and initiative are both based off roll "width" (i.e. shots that will kill someone automatically go first).
Rolls are fairly prone to failure, although the game suggests characters only need roll for tricky situations and it is hard to adjust for difficulty (one mechanism is to also require rolls be a minimum size e.g. difficulty 4 = matched 1s, 2s or 3s couldn't be counted - which doesn't work in combat as well, except for cover, since it puts some hit locations off limits). Roll 'height' is also used in opposed rolls; opposing sets become 'gobble dice' which cancel opposing sets only as long as the value of the dice in the set is equal or less.
One ORE dice pool can potentially resolve two or more actions (the default rule being that the pool is at -1, and separate counts of matches can be made for each action) although this can't give the two actions different base chances of success / dice pool sizes.
Match-counting success systems have fairly tight constraints on dice pool size: ORE limits rolls at 10 dice for instance as a double will always occur with 11 dice. This becomes tighter again with d6s (cf. Enchanted Tales, below; it gives out rerolls sometimes rather than extra dice, increasing the odds without guaranteeing a match).
(An interesting idea for ORE might be to include 'wild dice' to randomize outputs. For instance, your pool of 8d10 could have a red die and a blue die. This could give 'sets' of matches of a different colour - like 'slashing damage' vs. 'fire damage' for a flaming sword. An ORE-type hit location system might also be added to a damage dice pool without using the full ORE mechanic - see Hybridization (http://www.therpgsite.com/showthread.php?p=627226#post627226) for ideas. ORE is also referenced in the 'constrained design spaces (http://www.therpgsite.com/showthread.php?p=513841#post513841)' post.)
ORE struggles a bit with applying 'difficulty'. Another idea for adjusting difficulty with a match-counting game might be varying die-type - increasing die size decreases # matches - although this is mathematically messy, doesn't sync with ORE hit location, and has the feature (or bug) that the threshold for 'automatic success' drifts up and down ([dice size+1] die pool means a guaranteed match, i.e. 7 dice for d6s).

"Weapons of the Gods" is similar but breaks ties based off the number showing on the dice i.e. 3 rolls of 7 is treated as a '37', two 4s is a '24', two 6s is a '26', etc.
24-hr challenge rpg "Enchanted Tales (https://web.archive.org/web/20060301103400/http://www.1km1kt.net/rpg/Enchanted_Tales.pdf)" uses a d6 dice pool with a Poker-/ Yahtzee style ranking system rather than simply counting matches. By difficulty tasks may be Easy (one pair), Simple (Two pairs), Average (Three of a Kind), Tough (Full House i.e. triple / double of a different number), Hard (4 of a kind), or Impossible (5 of a kind). Damage eschews this to just add together some d6s. Without fully analyzing this, I think most likely unlike with cards where a limited number in the deck makes higher multiples significantly rarer, the mixed-pairing results are relatively rare and increase chance only slightly.
Here (http://forum.rpg.net/showthread.php?542800-HELP!-Dice-Mechanic-Choices!-AHHHHH!) someone combined 'count success' and 'count matches' with the idea that as well as a 'pair' counting as a success, so would a roll of 6.

recent edits: 3/10/2015 Spartacus note; Mutant Chronicles note; Enchanted Tales. 25/10/2015 - added ORE links
26/10 - mixed dice pool/synthetic dice, minor edits

Take-Highest Dice Pools:
...and I've completely missed systems where characters roll a number of dice, and take the highest (instead of counting them or adding them together! Thanks RobMaudib for pointing this out.
Known examples include:
Silhouette (Dream pod 9): as described by RobM here, skill level determines # dice, with highest roll taken and +1 added for each additional "6" rolled; attribute then adds to this.
Last Unicorn Games Icon system (e.g. Star Trek RPG) did the opposite, where attribute determines # of dice and skill gave a flat add; it also included a "drama die" which fumbles on a 1 or on a 6 let a character add the second-highest die, as well as the first (which would be 6).
Blue Planet also gave characters "Aptitudes" (rated from 1 die to 3 dice), with stat & skill both adding to the highest roll.
As can be seen, this sort of system is good for giving different effects to attributes and skills.
They are good for modelling situations where any character should have a chance of success, and where modelling extra benefit for higher scores isn't necessary (e.g. effect isn't a consideration). They also provide some inherent 'bonus control'.

Soothsayer (an obscure Australian RPG) uses take-highest dice pool for armour absorption, where highest value is used, with +1 for each additional roll of the same number. This was interesting in that a roll of say 4,3,3,3 (=6)gives a higher result than 5,3,3,3 (=5). (It was also interesting in that the armour roll operates differently to the damage roll).

Sorcerer (from what I hear) operates by having both sides of a conflict roll dice, with highest results on both sides cancelling out until an uncancelled roll remains.
(Altus sees to do this as well, with # dice and dice type generated from a table, based on relevant skill level).

Japanese supers RPG Double Cross uses a d10 take-highest dice pool system where any 10s rolled are re-rolled with the result added to 10 (if any are gotten in the second batch, those then are re-rolled and added to 20, etc). Some powers allow the 'critical threshold' to be lowered below 10.

Costume Fairy Adventures uses a dice pool where a pool of dice is rolled, and highest under trait score is used (i.e. a 'blackjack' system where more dice means scoring closer to the trait value).

The "Tribute (http://www.therpgsite.com/showthread.php?t=27990)" system in development has a complex setup which combines counting and take-highest.

There is also some discussion here (http://www.therpgsite.com/showthread.php?t=28085) of a combination percentile/take-highest dice pool system (perhaps similar to CoC 7E).

"Take highest" systems are fairly constrained in how many dice they can roll - chance of success rapidly approaches 100% and extra dice give little benefit (although kludges like "each maximized die rolled adds 1 to total" help). If there is no additional modifier to the dice result, chances of ties increase between opponents with large dice pools (the highest number is the most common "roll", if pool is 2+ dice). This can be moderated somewhat by taking the second highest roll, instead of the highest. The average result with 'take highest' is somewhat hard to determine - this makes it difficult to convert an opponent's roll into a fixed target number to cut down dice rolling (e.g. the way a D20 + bonuses game could just declare that a villain with +7 grapple has a 17 grapple defense). Note that unlike with 'success counting' systems, splitting a dice pool doesn't reduce chance of success (the highest result will be in either the first subpool or the second) so pool splitting can't be used for multiple attacks without additional penalties or kludges (extra 6s in a d6 pool each giving a +1, etc.).

Fantasy Dice (described under 'changing die type' games) uses a take-highest dice pool, with ties sometimes broken by second-highest dice. This has the added complication in that some cases an unopposed roll (attack) is made against fixed difficulty (i.e. no dice rolled - so no second roll). A default is used in this case.

Capes, Cowls and Villains Foul uses a mix of d12 dice pool and additive - traits have a number and an irregular (?) track which with use reduces the # d12s rolled. Penalties/overuse can drop dice pool below 1, in which case the worst die is used, much like Over The Edge (cf. multidie additive).

While its a co-op boardgame not an RPG, Legends of Andor shows an interesting way to implement a penalty here. Combat is a roll of 2-4 dice (take highest) for most characters; the Archer instead rolls one-at-a-time and can reroll until they run out of dice, meaning that a moderately high roll can get blown rerolling trying to score a 6. Some monsters / PCs with the helm can also add together doubles, while the Archer can't.

Another possible variation for a take-highest dice pool system is where dice are distinguished, for instance by colour or by position. One idea I'd had for instance, is to roll a set of attack rolls (4 dice) with the distance these land away from the player determining the hit location e.g. furthest away the head, then arms, torso, and finally legs. Simply choosing the highest result would give effectively random hit location, while higher skill lets a character perhaps still hit with a worse roll.

Yggdrasil (Cubicle7 translated) apparently uses a d10 dice pool where the best two dice are added (so not unlike Cortex+ except only d10s are used). A stat of 1 is obviously going to be disadvantaged, whereas each increase beyond 2 is less significant.

Resource-based Dice Pools
Some games also use dice pools as a resource of potential dice. Examples include Dying Earth and Dogs In the Vineyard; both handle checks as extended, opposed affairs; a conflict is continuing with the opponent putting out dice from their pool until they pool is exhausted or they cede the conflict. Dying Earth burns rolls usually one at a time, while DiTV lets characters use more than one and has multiple options (e.g. "raise", "see", and "reversing the blow" depending on how many dice are burned).
Note these are slightly different in that dogs (DiTV) uses up the whole pool in one 'conflict', while in Dying Earth a characters' dice pool is tracked in an ongoing fashion (over multiple scenes), and has varying refresh conditions. DiTV has been criticized for the way its dice pools work: d4s are described as 'complications', representing negative features, but actually do increase the chance of a character succeeding on checks.
 
Final (mathematical) note on probabilities: success-counting die pool systems have 'diminishing returns' in the increase in base odds as the dice pool increases, for 1-2 successes or so. e.g. if rolling d6s TN 4, going from 1 dice to 2 increases odds of getting 1 success by 25% (50% to 75%), from 2 to 3 by 12.5%, and from 3 to 4 by 6.25%. Hence each added dice has less effect on the final probability, despite the total number of expected successes increasing linearly. For minimum 2 or 3 successes etc. the same effect occurs beyond a certain point only - at the lower end chance of success with a small dice pool will be very low.
By contrast in a single-dice-roll game, an increase in skill level will generates a proportional increase in success chance.

Dice pools as a supplementary mechanism
Extra dice are often added via rerolls. Variants include:
*spending points of some kind to get a reroll. See 'Safety Valves'.
*D&D 5E uses a system of 'advantage/disadvantage' which lets a character roll twice and take best or worst if the task should be easier or harder than normal, according to Mearls reducing the number of possible fiddly modifiers (though potentially adding large numbers of extra rolls if you're surprised by something with lots of attacks). Barbarians of Lemuria (BoL) had this earlier with 'bonus dice' and 'penalty dice' (changing from 2d6 to 3d6). Another variation is where there are positive/negative dice and possibly multiple for either (as noted next post for Nexus).
While generally this just increases amount a roll succeeds by, a couple of experimental feats 'count successes' i.e. the 'fell handed' feat [Unearthed Arcana] lets a character with Advantage knock a target prone if both attacks would have hit.
*A system could have checks with dice rolls lower than e.g. [attribute score] being re-rolled, either just once [freerpg Incandescent example] or until a higher number or equal to than the attribute is rolled.
*Savage Worlds PCs ('wild cards') get an extra d6 to roll at the same time as their skill or stat die, but don't always get to roll this e.g. with full auto multiple shots only one wild die is rolled.
*Skills & Powers for AD&D 2E has a subsystem where high stats give extra rolls on stat checks, with some tasks potentially requiring multiple successes.
*one homebrew game I knew of, 'Brightblade', had at one stage a dice pool for determining fumbles on top of a d10 additive system. IIRC, in the event of a failed roll a '1' was a fumble, and rerolled to see if you got another 1, but tasks which the GM deemed likely to be problematic also caused extra fumble dice to be rolled and any extra 1s counted to determine fumble severity.

Lots of dice can also be rolled in extended checks such as Alternity or 4E D&D 'skill challenges'; sometimes multiple checks/dice pools could be used in less formal ways for specific subsystems - Palladium's has a rule for 'roll 2 out 3 successful coma/death rolls to recover', the GDW House System (Twilight 2000 2nd Ed, Cadillacs & Dinosaurs) uses a multiple D6 count successes dice pool for automatic weapons fire to determine number of hits, instead of a skill check (normally roll under with d10).

EDIT Notes: thanks Rob for notes here. Recent notes: 'fell handed'[5E]. Added note on Yggdrasil (*).

Kudos on starting this thread. It's a good read.

For attributes, what about fixed arrays like 3.5s standard and elite arrays?

Quote from: beejazz;496177Kudos on starting this thread. It's a good read.

For attributes, what about fixed arrays like 3.5s standard and elite arrays?

Cool, thanks.

Yes good. I'd consider these a way to speed up 'point spend' purchase systems; though it is possibly to generate a set of arrays and randomly roll which array you get, to randomly generate attributes that are still balanced by total points.

(edit note - sorry beejazz, deleted my reply to your post above to fix the page breaks between dice rolling and combat sections).

Some other exotic varieties or variants...
 
"Roll your modifier" systems - these are additive systems where the normal dice result is typically 0, so that a character can roll above or below their default rating. The interesting aspect of these is that a total die roll is theoretically on the same scale as an attribute score. 'attacking' and 'defending' values follow the same scales and can be used in unusual circumstances readily.
 
One downside here is that again, multiple rolls are difficult to make individually since dice must be paired/grouped; most of these generally assumes a group of mooks use a single die roll. Another is that with a tight range, rolling the dice may feel like a waste of time (why roll at all?).
Examples include:
*Fudge (uses 4 'Fudge dice' labelled 0,1,-1 twice) - later variants such as Fate typically use [d6-d6],
*Feng Shui (which uses d6-d6 with 6s exploding - meaning a 1 or 2 point modifier has a hugely significant effect on the probability of a task succeeding, but with explosions still occurring quite frequently that result in massive dice rolls).
*Two Fisted Tales (d10-d10)
*ShatterZone/Masterbook: this uses a roll of 2d10 and table lookup to determine the modifier, rather than a positive and negative die.
*Jasyn Jones' TORG variant (Storm Knights) (in development) apparently uses a 'hot' and 'cold' die - instead of subtracting one die from the other, the smallest of the two rolls is used with the 'hot' being positive and 'cold' negative (an identical distribution to subtracting). Babylon 5 also had the hot/cold concept, but (judging from rpgnet review) apparently used the higher of both rolls instead.
*Qin it is said uses a black (yang) d10 and a white (yin) d10. One adds and one subtracts; if both are equal and non zero a task automatically passes due to "yin and yang being in harmony" while if both are 0 the task fails due to the character being "out of touch with their chi". Which is higher may have other effects depending on the task.
 
In some of these e.g. FUDGE which is normally 4 Fudge Dice, it is possibly to easily modify the variation of a roll without changing the average result e.g. by adjusting how many dice are rolled - e.g. Mutant Bikers of the Atomic Wastelands (http://ukrpdc.files.wordpress.com/2013/08/fudge-mbaw.pdf)' NPCs. Another implementation might be to replace a standard [d6-d6] with a [d8-d8] or [d4-d4], depending on the situation; also, potentially the positive and negative dice could have their sizes adjusted separately by different conditions to give a range of d4-d6, d8-d4, etc.
Feng Shui's predecessor Nexus reportedly (here (http://forum.rpg.net/showthread.php?726039-Luck-Mechanics-That-Don-t-Actually-Work-As-Advertised)) used d6-d6, with a Luck/Unluck trait that gave additional positive or negative dice respectively with the highest die in the positive or negative pool counted -an interesting variation on 5E's "advantage/disadvantage" idea, though predating 5E of course.
There could potentially be abilities or rules giving more complex manipulation of either or both the positive and negative dice pools - storing rolls for either pool, moving a roll from one side to the other, rolling-up, ignore highest result if pool is 2+, getting a more average results by adding a die to both sides, etc.
One game in development mentioned here (http://www.therpgsite.com/showthread.php?p=853421#post853421) has circumstances where a roll is made but  + treated as 0, or minus as 0.
 
Note that rolling [d6-d6] against a difficulty of opponent target number, for example, does not basically differ from rolling 2d6 against a difficulty number of [opponent target number +7] unless other elaborations appear- the distribution is identical. "Roll up" or "roll down" mechanics usually do differ though, as do operations applying to a positive or negative die specifically; Feng Shui's "6 on either die rolls up" (i.e. 1 in 6 chance for each of this occurring) is very different to rolling down on 2 and up on 12 (each of which occur on a 1-in-36 chance).
 
A positive die/negative die system is actually pretty similar to what an opposed roll looks like in a normal additive system, except "within" one character.
Potentially in a dice-dice system, one of the paired dice could be considered to be the opponent's dice and one the active characters, with operations applied to just one dice in the pair as a consequence - for instance no negative die if a roll is wholly unresisted, or with opponents able to reroll the 'negative' die only with luck points etc.
 
OTHER WEIRD SYSTEMS:
 
 
Resource Pool Systems: (Gumshoe, Dying Earth); these systems give characters a number of rolls to perform a task based on their skill/attribute - in Dying Earth a task requires a d6 roll on the resolution table, with the result applying unless the opponent likewise spends a point from their pool to resist.
 
Full Light, Full Steam; an odd system which relies on rolling 4d6 and ordering them in a stack (figuratively speaking) of lowest-to-highest. Attribute and Skill are each rated 1-4, and let the character pick the appropriate die out of the stack i.e. 1 means take lowest dice, 2 is take the second-lowest, 3 is the second-highest, 4 is the highest; the two dice are then added together. As well as being slow, the system has a built in maximum for skills/attributes (4) and is quite granular. Stat and skill the same means the same dice will be counted twice e.g. rolls of 1,2,5,6 with stat 3, skill 3 would pick the second-highest twice for 5+5 = 10.
A similar, but simpler, system is Jeff Moore's interesting free rpg Hi/Lo Heroes. It rolls 2d6, with a stat being rated as either High (take highest) or Low (take lowest). It frequently uses the same pair of rolls for multiple things, with different attributes applying - a character with High to hit and Low damage might roll [5,2] using the 5 to hit and the 2 for base damage; this same setup was mirrored for Dodge/Soak. (See also the later post on system constraints for more on Hi/Lo Heroes). As it always uses two dice there is a 'doubles' mechanic where on a double both dice add together "as both dice are High or Low".
 
Four Colours Al Fresco (http://www.google.com.au/url?q=http://webpages.charter.net/woodelph/Gaming/Astrology/&sa=U&ved=0CBcQFjABahUKEwiQl6-35vDHAhWF5aYKHQfXCXU&sig2=8wkPjYVuRA68bzCkxite0g&usg=AFQjCNFODoM6r1MXqowDmt3pw1MYU42wEA): this (historical superhero) system (that I first saw mentioned here (http://www.therpgsite.com/showthread.php?p=91104#post91104)) uses an ordinal changing-die-type comparison system where a characters' ratings are compared to determine success. The games' conceit is that reality is governed by five forces (Dynamic, Static, Known, Lost, and Passion). A character rates each of these with a dice (relatively lower is better). On a given task these are rolled and are either Dominant (lowest number), major (second lowest), minor (2nd highest) or weak (highest), with ties eliminating extremes. A given task will Favour or Oppose a given aspect - a character wins if the dominant Aspect is the Favoured aspect (e.g. a character with Dynamic d4, Static d6, Known d8, Passion d10 attempts to push a boulder which is a task that's Favoured-Dynamic, Opposed-Static. They roll 3,4,5,5 for the aspects in order so Dynamic is dominant and they pass. (This is a summary only - the rules are also complicated by characters being usually un-rated ('Omega'd")in one attribute i.e. partly beyond the laws of physics, and rules for extra difficulty dice.). Because the ranking on a roll is internal to the character, scores have only relative importance (d20/d20/d20/d20 is about as good as d4/d4/d4/d4; wider spreads generate an advantage on some rolls but with equal handicap to others; it can also use zocchi dice e.g. d5s or d7s, up to about d34). Difficulty of a roll affects the number of Favoured or Opposed factors; conversely the GM may pick factors which logically affect a roll and that then sets the difficulty.

Diceless systems: use straight comparison to see who wins, plus either a fair degree of either GM arbitration (Amber) or use of specific details and modifiers needed. In some systems resource pools may be used to "buy" results, but with fixed results rather than dice being added. Amber has characters taking pools of 'Bad Stuff' or 'Good Stuff' to influence GM interpretation of how much a given PC should be interfered with.
A list of several diceless systems (not comprehensive) is here:  http://forum.rpg.net/showthread.php?747321-your-opinion-history-of-diceless-RPGs (http://forum.rpg.net/showthread.php?747321-your-opinion-history-of-diceless-RPGs)

Using Weird Dice: 'Sicherman dice' - a pair of differently labelled 6-sided dice giving the same results as 2 normal d6s are discussed here:
http://www.therpgsite.com/showthread.php?t=27498. This could have some sort of application where one roll is reused for something else (with a different range). A bonus smaller die would also have less effect than a normal +d6.
(Averaging dice are mentioned in post 4.)

"D10-X" - a roll-under variant seen in Cyborg Commando; two d10s are rolled and multiplied together. This has a slight failure chance even at very high attribute scores; an 'average' roll is 25 or less, but even a character with a 99 will fail occasionally). Probability distribution of the dice roll will be weird, but this system potentially allows unusual attribute scales (i.e. average 25; max. 100).
Another game using something similar is Jeff Moore's freerpg "5x5". This uses 2d6 multiplied together; however 6s are "trumps" and automatically succeed, instead of being the worst roll possible. It has the perverse additional elaboration that characters with no skill have a -5 rating, and have to try to roll 6 to win; they however only get one d6. Rolling only one die would in theory be good for most characters, but obviously won't help roll under a negative score.
Similarly, the Zero RPG rolls (d6 x d6); a character has a 'focus' score that has to be rolled over for 'focus' (class) abilities, or less than for general or background tasks. Difficulty modifiers add +1 to +3 to the lower die rolled before multiplying. Focus rolls give 1 success level, +1 per 10 over minimum, while other tasks always get only 1 success level.
 
Multiplicative rolling (BASH, Maid); a dice roll is multiplied by an attribute score. The upside of this, is that it gives a success chance based on a consistent ratio of any two scores. For example, a giant with a Strength of 200 wrestling a giant with a Strength of 220, has the same odds in a arm-wrestle as would a human of Strength 10 wrestling a human with Strength 11.
Note that another way to get this effect, is just to have an exponential strength scale (DC Heroes for example has Strength doubling each point, so that Str 4 is twice as strong as Strength 3; D&D 3.x, +10 Strength usually quadruples lifting capacity) and use an additive system.
 
'Floating' changing-dice-type (Conflicts in Sorcery & Super Science): see http://www.therpgsite.com/showthread.php?t=19822  (http://www.therpgsite.com/showthread.php?t=19822)
In this changing-dice-type variant, a character's actual dice rolled is based off the total of [their stat+opponent's stat], with their score adding to the roll. A roll greater than or over the dice maximum is a success. Again this system generates proportional success based on a ratio between opponents in a conflict.
 
Grid Rolling: a table variant sometimes used to generate treasure - not seen as a core mechanic AFAIK- a grid is made with one dice reading "across" and the other reading "down" to select a table entry.
EDIT: Old TSR wild west game Boot Hill uses this mechanic for wound rolling: ond d100 generates location, and a second d100 roll reading across gives severity e.g. head shots are more likely to be major/fatal. It is also used sometimes in Tunnels and Trolls for random treasure or monster generation - in this case usually using d6 and d6, it allows for tables with numerous, equally likely results without the user needing any polyhedral dice.
e.g. in the solo adventure Deathtrap Equalizer for T&T (Corgi Edition):

QuoteRoll 2 dice and cross-reference the result on the chart below. If you picked up more coins than the number on the chart, then you picked up a magically poisoned coin (which works even through gloves or armour). Take the difference between your total and the chart's total as hits from your totalled attributes. Divide the remaining attributes points evenly among your Prime Attributes, placing remainders where you will. You may keep as many coins as your new Strength will allow you to carry. If you die (less than 6 attribute points remain for distribution), go to 2. If you survive, go to 3.

___1_____2____3____4_____5____6____
1__1000__32____47____145___366___225___
2__82____800___333___579___1_____1515__
3__99____71____600___9_____13____111___
4__127___26____818___400___271___604___
5__8_____144___1066__1903__300___53____
6__56____4_____666___1492__446___500___

The table here could essentially be replaced with a 'd36'; it becomes more interesting if either the top/side roll are replaced with a variable like a skill roll or other modifiable roll, although that then requires the table to be logically constructed such that movement in one direction is better (cf. Harnmaster combat tables in Effect post).
The same sort of system is used in Atomic Highway random mutation and flaw rolling; this has the extra elaboration that a player can switch the two rolls. Potentially this lets the table be designed so that all the pairs of options give interesting choices, and can set up inescapable rolls (doubles like 1-1 or 4-4) to be either especially soft or especially awful.


The grid-roll table above in the Corgi edition (a 2-in-1 combined with Naked Doom) replaced a different method in the original Deathtrap Equalizer ; in the earlier Flying Buffalo edition instead had the player choose a number of coins 1-100 and triggered the same effect of stat loss for choosing either 69,77, or 100 coins). That would be one of few cases where a random number is just chosen by the player instead of being rolled. This didn't quite make sense in real-world terms (a magically poisoned coin is always the 77th coin you pick up?) but is interesting.
Player's choose naturally leads to just picking the highest number unless there's either a clear risk (e.g. spending a resource is 'player choice'), or a potential risk (in this case, that the GM might screw then over). The Kevin J. Anderson book 'Gamearth' also features a game being played by characters trying to pick the specific number(s) the GM is thinking of (awkward for complex odds which require the GM to pick multiple numbers). Guessing a number is more often used to factor into tactical decision-making (should I use power attack?) rather than being the whole resolution system. Picking numbers in chargen can also work (cf. 'Character Modelling' under generating attributes)


"Beat the Difference" - seen in the old "Time Lord" RPG. In this game, attribute was subtracted from difficulty to get a number. Then 2d6 are rolled and the difference between them is determined i.e. 1 & 2 gives a difference of 1, or 6 & 1 would give a difference of 5. If the difference on the dice is greater than the other difference, the tasks succeeds.

Roll Over: a few games use a roll over a target number, instead of roll under. This is a bit like additive except that bonuses subtract from the target number instead of adding to the die roll. Examples here include 2nd Edition AD&D THAC0, SenZar attribute checks (d20 vs. TN of [21-stat]), and MechWarrior 2nd Ed. MechWarrior uses 2d6 vs. TN of [characteristic - skill]; characteristics are derived scores where lower is better, calculated as (18 - sum of two 1-6 attributes) - build & reflexes for Athletic characteristic, reflexes & intuition for Physical, intuition & learn for Mental, intuition & charisma for Social. Attribute saves are (18 - double attribute).

Recent edits: roll over. Added 'grid rolling' example - thanks to rpg.net poster 'Cobb Webb' for Corgi Deathtrap Equalizer text. Added 'players choose a number' as a mechanic

Aside from dice, cards are a possibility. These are ideal really for generating non-numerical info (without needing a table), and may also hold some supporting rules text as a reference.
Examples:
-Savage Worlds uses ordinary playing cards for initiative determination (face cards going first, then 10s, 9s and so on). This may be intentional to reduce modifiers - unlike using opposed agility rolls, PCs don't get an edge on initiative with NPCs, despite their Wild Dice. Some Edges give a redraw, and Jokers give additional combat bonuses.
Deadlands uses playing cards as well; unlike SW the GM has his own deck so simultaneous initiatives are possible (if unlikely).

-Deadlands also uses playing cards to determine stats, which are rated for both die type and number of dice rolled (i.e. a character could have a stat of 1d12, or 4d8)
Card  Stat die
2                d4
3-8             d6
9-Jack         d8
Queen-King  d10
Ace             d12
Suit determines the # dice (Clubs=1, Diamonds=2,Hearts=3, Spades=4).
Jokers count as d12 and 'also mean that your character has a mysterious past'; they need a redraw to get a 'suit' and so # dice.

-In Everway, cards are read for GM inspiration (somewhat like fortune telling), though actual resolution is diceless - e.g. drawing the "Drowning in Armour" card means that protective measures turning against the user may be a factor influencing the outcome (however the GM wishes to interpret that).
 
-TORG and MasterBook uses a "Drama Deck" giving special results. see e.g.
http://torg.pbworks.com/w/page/22371954/Drama%20Deck (http://torg.pbworks.com/w/page/22371954/Drama%20Deck)
Players may use cards to gain advantages in combat such as bonuses to certain actions, second chance or removal of damage; a number of cards also allow for creation of "subplots" such as Nemesis (acquire enemy), Romance, or Mistaken Identity. Cards can be lost via enemy tricks/taunts results or gained by performing "approved actions" in combat.
 
-Castle Falkenstein uses cards directly for action resolution.
http://www.rpg.net/news+reviews/reviews/rev_1610.html (http://www.rpg.net/news+reviews/reviews/rev_1610.html)
Card values vary from 2-10, with different suites mapping to different action types and the right suit needed to get the full bonus.
(I haven't seen this one, so thanks Rob for this note)
 
-TSR's old SAGA system (used in Dragonlance: the 5th Age and the Marvel Super Heroes Adventure Game) used cards 1-10 (IIRC); a player held a "hand" of these and played them periodically - effectively making them like a pool of pre-rolled dice the player could allocate as desired. (something like this this could potentially be an interesting gimmick combined with a match-counting system like Weapons of the Gods, using the cards to represent "the river" of stored dice rolls). In Saga, Hand size increased with experience and also represented the character's health, with damage forcing a character to discard cards.. Suit on the card matching action type (i.e. swords for Str-related actions) it "trumps", allowing the player to immediately draw a second card from the deck and add it.
 
-FUDGE while in development was card-based. link: http://www.panix.com/~sos/rpg/fud-des.html (http://www.panix.com/~sos/rpg/fud-des.html)

Quote from: Steffan O'SullivanFudge was originally proposed with a card-based action resolution system, and I tried to make that work for a few months before scrapping it. The deciding factor, oddly enough, was shuffling. I playtested so many variants of card-based mechanisms that I came to realize that frequent shuffling was a pain compared to rolling dice over and over, and so finally scrapped the idea of using cards.

(Perhaps decks would be handy for something like Fudge; it might be possible to e.g. have a deck with cards labelled Good, Great, etc. and avoid numbers entirely).

-Other Decks are sometimes seen for specific applications (criticals, fumbles, etc); this is little different to using a table if the cards must be played immediately. 7th Ed. gamma world has tech and mutation decks - these are somewhat different from just using a table in that a player can have their own deck. Hucksters in Deadlands reportedly have a magic system based off drawing poker hands.
Compared to a table, all results with cards are equally probable (unless multiple cards are available), and the same card can't be drawn twice (or at least odds will decrease, if there are multiple copies in the deck) unless the deck is reshuffled. A card system is also customizable by adding/subtracting cards as appropriate i.e. if a card draw is used for hit determination, the GM can add more Leg cards to the location deck when the PCs are fighting a multi-legged monster.
With a large enough deck, a set of cards can have any distribution desired with a single draw, rather than a linear distribution of results. For example, Pyramid 3-34 suggests using a 216 card deck to replace GURPS' normal 3d6 roll with a card draw- possibly handy for combats with lots of rolls, though it actually also suggests sorting cards into piles to encourage card-counting of what rolls are left (!) - adding a metagame tactical level to the game and certainly slowing things down.
 
Cards will often provide results that are more difficult to modify than a die roll. If the card generates a number or [number+suite] then a bonus can be added to the final number, but it is more common for an ability to be "pick two cards" or similar. Its fairly easy to give 'pick best' of two cards (by player discretion), while choosing the worst of two cards may require adding a number or rank to all the cards, or GM arbitration.
'best of N cards' has results similar to a take-highest dice pool, although with cards with special effects rather than numbers, there may be rare massive spike results hidden in the deck (the odds of which increase slowly).
Deck-building games (non-rpg card games mainly) can include zero-value or low-value cards, which can be detrimental via pushing up deck size and making it harder to get a higher value or useful card. Cards can have rules dealing with looking ahead in a deck (see next N cards in deck, or view and rearrange before the next draw) that are distinct from what's possible with dice. Card games can also include a 'discard pile', although most manipulations of this will probably be too 'meta' for an RPG.
Once drawn, a card can also be used physically as a 'counter' of sorts, i.e. laid down with other cards with the spatial relationship meaning something. Again this is seen more in card games, e.g. the Space Crusade card game uses cards for space marines in a line showing who's close to the genestealers, exit door, or whatever (in this specific game, character cards aren't randomly generated, but it would be possible).
 
If each player has their own deck, cards can provide 'balanced randomness' since if you've drawn the 1, the 10 is still in the deck and now more likely.

Dominoes are another possibility (I believe at least one freerpg uses these; I don't remember the name.).
 
The Fastlane RPG uses a roulette wheel for randomization.

Fate of the Norns (3E onward, "Ragnarok" edition) uses viking runes for resolution.
Description here of how this handles damage by 'Raleel' on rpg.net here (http://forum.rpg.net/showthread.php?758779-Most-Interesting-Handling-of-Damage):

Quoteyou pull runes from a bag for powers. Each power is bound to a rune. Defenses and attacks do as well. Skill "rolls" come out of this bag. Damage ALSO comes out of the bag, so you can get hit and lose the ability to do a power or be debilitated and unable to succeed at a skill.
Runes assigned to damage move down a wound track (stun-wounds-death-drain(aka slow healing)) and the length of the track can be varied by the GM (normally, wounds is increased in length). Mental damage is handled by targeting your runes that you've drawn or played this round first, then moves into regular damage. Spiritual damage works just like physical damage, but can move things into drain (requires magical healing, or very slow). Additionally, some powers/abilities/resistances require a sacrifice to operate - that is, you move a number of wounds into various parts of the wound track on purpose to activate things. This gives the whole power management/damage management system similar to some resource management games.

The Sherpa RPG, designed to be played while hiking, assumes the GM uses a digital stopwatch, with the GM pressing the button without looking and checking the hundredths-of-a-second to get a random digit 0-9. Tokens representing luck points can be spent to give a bonus or cancel the need for a roll.
 
Coin-resolution systems are also occasionally seen (for instance, the Skyfall! series of gamebooks; Prince Valiant; Underworld).
Coins can be used as a simple "dice pool" (i.e. Prince Valiant where coins flipped =stat+skill; Gareth Michael Skarka's "Underworld"), or just used additively (i.e. base stat + number of heads rolled).
For the most part flipping a coin isn't particularly different to rolling a d2, though the joke game Combat Monster (http://www.hoboes.com/pub/Role-Playing/Humor/Combat%20Monster/) uses coin denomination as well (the players roll change with a total value equal to their attribute, counting the cash value of coins that come up heads; this lets it have a "dice pool" type system using arbitrarily large attribute scores - although the exact change chosen by the player would theoretically alter their chance of success at a given task difficulty). Skyfall adds heads and subtracts tails for some rolls (others are just e.g. +heads) making some rolls similar to FATE or Feng Shui's centered-on-zero approach (what I called a "roll your modifier" system above).
(thanks again to RobMaudib for Prince Valiant/Underworld/CF notes).
 
Player-skill-based random checks:
The game "Dread: The Impossible Dream" reputedly uses a Jenga tower, with difficult tasks requiring a pull from the tower.
Paper-Scissors-Rock (Janken) was (I think it is said) sometimes used in LARP as a convenient tie-breaker/resolver (requiring no dice, but is basically 50/50 and has no appreciable advantage over a coin flip).
Shooting hoops to win an 18 attribute (as noted in attribute generation) or having Ork miniatures that fall off the ork truck be considered killed are similar cases.

Randomization based on irrelevant details: T&T solo adventure "Hela's House of Dark Delights" features a race-change effect where a player references the monster table in the main rulebook, counting down an entry for each letter in the character's name.

Random numbers equivalent to dice rolls can also be generated without dice e.g. the Lone Wolf series of gamebooks has a table where a player can touch randomly to generate a 1-10 number, or a book may be printed with numbers at the tops of pages so opening to a random page generates a 'die roll'.

Edit history: recent 26/2/14- Fate of the Norns note. Older - added FUDGE notes; thanks to John Morrow; Fastlane note. 3/11/15-numbers equivalent to die rolls.

One of the quirks of OD&D which I've always loved is the proliferation of mini-systems within the basic rules. In modern game design parlance this is a thing of horror, much like the walking dead and upside-down crosses. Mini-systems?!? Lock the doors and get the shotgun, somebody's gotta die!! But personally I love it: it's the "spirit of adventure" in a rules system, where the creators are trying out new things, playing with options, and picking the right rules for a situation rather than maintaining consistency with a "system" at all costs. With that preface, I want to keep the class dice as a fun mini-system that makes certain classes distinct. The concept really works well with fighters, and works pretty well with thieves. I don't want to force it onto other classes where it doesn't naturally fit. And I'd rather have a distinctive feel (and a distinctive mechanic) for each class. - Joseph Goodman [Dungeon Crawl Classics designer] on subsystems , from the DCC messageboard (http://www.goodman-games.com/forums/viewtopic.php?f=60&t=15164&hilit=weapon+agility&start=25).

(I wish I had a balancing quote from someone that loved unified systems...:( After thinking about it though, actually, I didn't like the fighter's extra 'deed die' in DCC that much, and thief is just the standard d20+mods for most checks. But its an interesting POV, regardless)

Many older RPGs use a variety of die rolling systems – starting with D&D – even though the idea of having more or less one, central core game mechanic dates back at least as far as RuneQuest (1978). Even the second RPG published, Tunnels and Trolls (1975), uses only about three different die rolling methods (for melee combat, missile fire, and saving rolls respectively; missile combat would later integrate into the saving roll system).    A majority of systems took their lead from D&D however, and used different mechanics for different tasks -sometimes even different mechanics for what's virtually the same thing at a different degree of difficulty e.g. Open Doors vs. Bend Bars/Lift Gates. These systems vary between the somewhat baroque (where skill checks, ability checks, and hit rolls for example may use different mechanics) to the completely disjointed; for example a number of games split off from D&D even before ideas such as "ability checks" were in vogue, meaning a variety of very specific percentages and game functions had to be evolved.  In such games values (STR, HP, etc.) are under less pressure from conflicting reuses of mechanics, with each value having a scale designed in keep with its specific assigned function, sometimes with later kludges to add on effects such as skill adjustments or the like.
They perhaps show a design trend of having an attribute range decided first, before the mechanics were decided upon, whereas in a unified system the range is decided after the core mechanic is.

Examples of games with diverse methods of dice rolling:
 
  *Palladium has situational mechanics including percentages e.g." % to charm/impress", while other actions are purely GM fiat or use different systems e.g. Arm Wrestling [Mystic China] uses a d20 with a special Strength modifier (+1 per 3 PS above 16), while escaping a Crush/Squeeze (Ninjas & Superspies, Revised) requires an opposed roll of [d20+full PS score).  Lacking an ability check system removed a constraint on the scale of attributes, letting them range from 3-24 (higher for physical stats) - possibly helping it to later function as a supers game (?).
Much like older D&D, having even modifiers calculated differently for different stats makes it harder to handle e.g. situations where an unusual attribute would apply to a task.
Having very-specific situations having their own mechanics means often things will fall through the gaps, with none of them exactly applicable.

  *Synnibarr likewise has various ability derived percentages (for shock, finding traps, determining psionics, etc) and actually evolved different maxima for each ability score; while all are initially rolled with d20 (with initial values contributing equally to the 'skill points' used to buy skills, mutations and bionics), additional bonuses can get characters up to Con 20, Wis 25, Int 30, Dexterity or Agility 35, or Strength 1000. An emergent effect of this is that a high class minimum for Strength -which uses the initial score- balances/punishes a class noticeably, as the points could have made a much larger difference on another stat.
Synnibarr displays a breathtaking disarray even within the combat subsystem. It uses an additive d100 roll for shot rolls (roll d100 + 'shot bonus' based off Dex and level), while Dodge is a normal roll-under percentage (agility x 2%) instead of being directly opposed. While weird, playing it we found this does speed up the additive attack roll slightly; usually it is enough to know that you rolled "a lot" without actually calculating an exact number. For skill rolls it also switches between roll-under-d100 for normal skill checks and rolling [skill % + d20] for opposed rolls.

  *D&Ds 3-18 ability scale turned out to be coincidentally well adapted to d20 roll under; 2nd edition AD&D frequently uses this, but in conjunction with legacy mechanics from 1E such as "% to learn spell", "% system shock" and "wisdom % spell failure" despite these being mathematically almost identical to roll under with d20. A number of core mechanics (attack rolls, saves) instead use level-based matrices; the ability check mechanic suffered from not scaling up as these did, while also defaulting to a much higher chance of success than a save or attack roll - problematic in instances where it could be unclear if a stat check or save should apply (i.e. Dex check or save to dodge a trap? Or Con check or poison save to resist getting drunk?). This can also make opposed rolls awkward, if different sides are using different mechanics. (Note: the same issues with scaling and default success chances can also apply with pure d100 systems like RQ or HarnMaster with regard to ability checks vs. skill checks).
 3.0 D&D instead transitioned to [d20+modifiers] as a system, enabling a much higher range in ability scores (e.g. Titans went from Strength 25 to Strength 37) and making it more functional for superheroic characters, but also increasing the ability scores' importance to characters by making modifiers apply to many previously unmodified checks, ranging from Listen checks to breath weapon save DCs. It also renders odd-numbered ability scores pointless except as feat prerequisites, in spite of which the point-buy system generally charges more for each of those ability points than for the (actually useful) next point. A modifiers system consistent between attributes led to increases in cases where unusual attribute modifiers applied, such as Weapon Finesse.
Modularity: Older D&Ds in particular are fairly 'modular', with it being possible to replace the roll used by a subsystem with a different roll fairly readily (e.g. Dragon magazine has any number of skill-system variants for 2E or earlier). In part this is also due to most subsystems not requiring character-design decisions. In 3E by contrast, a characters' ability at something usually requires a skill-rank (or feat) expenditure, and changing a mechanic risks invalidating a players' "investment" in some skill.

*Warhammer Fantasy 1st ed (whose mechanics were derived from the skirmish game) has stats which sometimes rated up to 10 (Strength, Toughness) and sometimes  up to 100 (Weapon Skill, Ballistic Skill), and so while it does have ability checks, it uses a d10 for some checks and d100 for others. The 2nd edition streamlines this quite deftly by having all scores range to 100 and using the 10s place as a modifier when needed (e.g. for damage).

*Dragon Warriors, while its clearly D&D inspired (possibly Holmes, given its initiative system), shows extensive divergence from it, where the miscellany of rolls and checks are replaced individually, one-by-one, with different but no more unified systems. It is good in that individual systems are quite simple - actually, working with a simplicity that could be difficult in a unified system. For instance, a Weaken spell adds a -2 attack, -1 damage penalty but doesn't note the effects on other applications of Strength. The ability doesn't require notes on a beasts' existing Strength scores or table recalculation (indeed its inconsistent with any Strength score, as no Strength score gives a damage penalty) but the downside is that its effect on the fiction and on lifting, carrying, etc. is also unclear. Most other spells are likewise simply worded but may require considerable GM extrapolation from the listed effects, or at the very least searching for prior cases and general rules that might be applied.

*Satirical quasi-system SLUG (http://www.panix.com/~sos/rpg/slug.html) allows the GM to determine which dice are used and the target number, mainly for the purpose of slotting in characters from any system, making it wholly ruling-driven. It lets the GM use any sort of mechanic for whatever purpose.

*Hero manages to have somewhat different mechanics despite using only D6s, with separate mechanics for ability rolls (8+1/5 stat points, roll under 3d6), combat rolls (3d6 under something+OCV-opponent DCV), and damage rolls/presence attacks/opposed Str type checks (multiple dice additive). The combat subsystem being distinct causes some extra mucking around with skills, which generally run off ability checks but occasionally for combat skills, e.g. autofire, are applied to combat values.

Potentially miscellaneous mechanics might end up requiring a roll for both things (such as an attack roll + a skill roll) and so lower overall chance of success, compared to a single check working off unusual values.

Unified Systems

More recent systems strongly favour unified, cohesive core mechanics. A unified mechanic does offer a quite a few benefits i.e.
*easy for new gamers to learn
*easy for the GM to fit new situations into the framework; i.e. for 3E D&D the system is always roll d20, higher is better so the GM only has to determine which modifiers apply, and set a DC. This is particularly useful where a game is broad in scope, making it difficult to consider all situations. A notable example of this benefit would be Marvel Super Heroes: its descriptive 'Rank' system where things ranging from object Material Strengths to Resources to radiation intensity can be categorized as  "Typical" or "Good" or "Unearthly", plus a super powers system that gives examples of a wide variety of effects, let the GM fairly simply define more or less anything within the system.  (although: letting all powers scale up/down freely due to random roll, with damage etc. determined by rating rather than fluff, does you can have situations like rolling a character who does less damage with micro-missiles than they would with their fists - something that likely wouldn't happen if powers were ad hoc defined instead).

*similar resolution means a general ability can be written that affects a number of related circumstances.  For example, a -2/-2 multitasking penalty can be applied as easily to a character standing watch & also repairing repairing their armour, as it can to a character trying to fight with two weapons (since all these tasks use the same dice roll). Or a wound penalty can be applied to a variety of tasks consistently. However, the generalization can also be a potential drawback in that modifiers can unintentional affect strange things ("action at a distance", I think, in programming parlance); e.g. clerics in Castles and Crusades having better perception rolls than thieves due to having Wisdom as a "prime" stats.

Nonetheless, largely unified systems still quite often contain exceptions in how they operate since not all situations are identical, and some core mechanics struggle to cope in certain circumstances e.g.
-Storyteller at some stage used [d10+modifiers] for initiative to reduce simultaneous actions.
-D&Ds primary "effect" system uses a step-die system with d4 thru d12  (compare to True20's more integrated - if not necessarily better - "Toughness Saves" which spread around knockout/kill effects with considerable randomness).
-HarnMaster uses d100 for most checks, but with some attribute checks are done on 3d6 to skip the usual multiplication step (fumble tests) or on multiple d6s (combat results such as Stumble or Kill rolls which have a variable intensity, and where a highly random outcome is undesirable).
-MSH, despite its overall flexibility, uses a d10 roll with special modifiers for initiative.
-HERO generally uses 3d6 roll under [8+stat/5], but has a damage roll mechanic (d6 per 5 points) which is also used for grappling and Presence Attacks.
-roll-under games sometimes switch to an additive mechanic for opposed rolls - Fighting Fantasy /Advanced Fighting Fantasy used 2d6 under stat for stat checks (including ranged combat), but opposed rolls of 2d6+skill for fighting. LegendQuest used d100 under for most checks, but additive instead (d100+skill %) for opposed rolls.
-Savage Worlds uses a card draw system for initiative 'rolls', removing PCs Wild Die advantage and reducing the importance of Agility compared to the usual 'Dex check' initiative system.
Note: Attempting to use a 'universal mechanic' to cover movement as well has complications in some cases, as detailed in the 'movement' post.

Other games have a single system but have attempted to code in multiple options as a core mechanic (Interesting to me since I've noticed how specific many ideas/innovations are to only one or or a couple of the possible systems; cramming lots of them into a single RPG would probably need some method of combining mechanisms...).
-StarCluster 3E and related games uses a simple system which lets the GM/players drop in a huge variety of resolution system of their choice - whether percentile, die pool, d20, or diceless for example.
-FUDGE/FATE uses various systems to generate modifiers; as a centred-on-zero system, this generally works as it changes the range of the dice roll without changing the average (=appropriate attribute). An extreme variant here (https://web.archive.org/web/20060203094541/http://www.fudgefactor.org/2005/12/polyhedral-fudge.html) for 'polyhedral FUDGE' instead generates a wildly different result from 1 [Terrible] to [current rank + a bit], but still uses the base Fudge descriptor system.
-Tri-Stat  (I think ?) lets the group pick a resolution roll from +d4 to +d20 based on the "heroicness" of the particular universe.
-FUZION attempts to allow either a +d10 roll (from one of its precursors, the Interlok [Cyberpunk/Mekton] system) or +3d6 (related to its other precursor, HERO); the latter however works poorly since there can be a 20-point difference in possible values (cf. FrankTrollman's analysis here (http://www.tgdmb.com/viewtopic.php?t=50724)).          
-Space:1889 has a 1-6 stat scale, with two possible methods of rolling - a "quick roll" system (under stat on d6) for simple tasks, or by setting a difficulty (from 4 to 20) and rolling the stat or skill number in D6 to get the total.
-I've seen references to DramaScape using two separate core mechanics, but am unclear on the details.
-Stars Without Number (reportedly) handles combat and saves via d20 and skills via 2d6, but using the same bonuses for both.

Some core mechanics are slightly more intrinsically versatile than others; for instance if a designer wants Initiative to use a d10 roll and spellcasting to use a d6 roll, a "step die" system like Earthdawn's could let them do within the bounds of the system by declaring that Initiative defaults to "Step 5" for most or all characters and Spellcasting to "Step 3", or by creating new attributes specifically for those tasks. (Versions of Savage Worlds later than the "core rules revised" also declare its wild dice on/off in certain cases, such as damage rolls and running rolls; damage rolls add multiple dice instead of taking-highest)
Talislanta uses d10+modifiers for unskilled rolls and d20+modifiers for trained rolls; a system could build off this to have all raw attribute checks use d10s rather than d20s (as no skill applies) in order to weight upward the influence of attribute checks on rolls.

Even where only a particular dice is used, it may be ideal to change details of the rules connected with a roll to control uncertainty around a roll, level-scalingness, etc. For example in simple additive systems, heavier controls against gaining modifiers on tasks which are supposed to be more uncertain in outcome are reasonable; a word of warning here however is that if opposed rolls are possible between scores, a "fair" comparison between opponents requires similar scales of modifiers.
Adoption of "+level" to all dice rolls (such as in 4E D&D) lead to a "level treadmill" within the gameworld; leaving certain abilities unscaling (such as ability checks to break down doors, influence NPCs, or not fall over) produces less pressure on the GM to retrofit all the doors in the dungeon to adamantine and grease up the floors for the high level PCs.

Mechanics used consistently across the board may need adjustments to consider that different tasks need different fundamental failure rates. Stealth checks rolled repeatedly will fail -necessitating a high base chance or a 'let it ride' type rule) - conversely reactive perception checks rolled by a large party will almost certainly succeed. Hit rolls may be fine at a 60:40 or 50:50 odds; desired spell success rates may vary even between spells. A d% mechanic will usually have a varying base % allocated for different actions but opposed [d20+stat+skill] often default to the same 50/50 odds for everything, with deviations generated accidentally by scaling issues like one side being more likely to have a higher casting stat/good save/proficiency bonus. These deviations might be exploited deliberately by designers (choosing to use a skill check to increase chance of success, or make a save use a rarely improved category to reduce chance of success).

Edit: note to self- rpg.net's discussion on d20's problems as universal mechanic due to high variance here (http://forum.rpg.net/showthread.php?765133-What-has-quot-bounded-accuracy-quot-meant-for-your-character-amp-campaign/page20)

So you succeed at forging a sword, casting a spell (if that needs a check), or whatever else you were doing. The next question beyond if a character succeeds, is how well they did (effect). How this is handled depends largely on what the core mechanic is (d20, dice pool, percentile, etc). Depending on system this might be largely a matter of GM fiat, or precisely detailed. For systems which do have defined effect, the final result might be a number (damage; distance jumped;spell duration) or be some sort of special, specific effect (Slam!; Stun!).
An "effect" might also be describable as a bonus on a second follow-up roll, or the equivalent; Fuzion "Complementary Skills" lets a character make a skill roll to modify a related skill, or 4E D&D has a "skill power" [Tumbling Dodge] that adds [roll/10] to all defenses, or there can be 'Aid Another' actions giving an ally a bonus, or a spell boosting someone's values might increase for a high spellcasting roll.


Systems for effect determination vary in how much coupling there is between dice roll for success and for effect - whether difficulty is the same as degree of success. Most d20 mechanics are tightly coupled, with high roll or skill giving a large margin of success, but damage roll is largely unrelated to how good the hit roll is (uncoupled). In between these, a system like oWoD is loosely coupled - an increase in difficulty may or may not mean less effect (a single high roll gives basic success on a difficult task, but rolling above the minimum on each die doesn't boost effect further, so some detail from the roll is lost).

A number of mechanisms for effect determination are below:
 
Non-Dice-Requiring:

No effect system (binary): a roll either succeeds or not, with no particular further detail.
(without an effect system there may be a particular emphasis on bonuses to rolls being kept small, partly as after reaching 100% there is then no further incentive to improve).
It might be argued that in some games (maybe 3E D&D attack rolls), a general absence of specific extra-effect rules built into the roll, encourages addition of lots of specific character add-ons that give 'front loaded' extra effects...instead of a particularly high roll letting you add a cool extra effect, it becomes a 'feat' that you buy. Partly so that these can be added without the rolls themselves getting complicated, partly for the opposite reason that once a high roll gives you some special effect, it can't then be 'sold separately', or at least becomes more complicated to implement (e.g. Power Attack).

GM-defined effect: the GM determines how well a task succeeds depending on whatever factor - dice roll, how the player described the attempt, etc. The GM might decide to make rolls for some specific of the situation on an ad hoc basis to see exactly how well a task succeeds. Basically will resemble some combination of below systems but via an improvised ruling. Examples: for failure  Fate Core has GM advice on letting failure become 'success at a cost', with varying complications (tough choices, foreshadowed perils, temporary aspects, plot wrinkles, new opposition, delays, damage). Assigning costs on a scale commensurate with the task being rolled for can be tricky, however (the cost should be less bad than failing the roll, so is easier the higher the stakes, and also has to make sense for the roll in question; depending on circumstances delays may not be significant, while systems with lots of PC healing including FATE make damage as a consequence less meaningful; permanent losses of equipment, etc. work for critical failures but can be too common/harsh as a consequence of fail forward).
Where the GM accepts considerable player input you can instead have 'negotiated resolution', as seen in some 'narrative' games, where stakes are set by agreement between the player and GM. Negotiated resolutions occasionally appear for normal systems in unusual circumstances, where rules are ambiguous or produce effects not desired by either players or GM - a player may then get some leeway to suggest a patch to a stupid rule.
(One homebrew game I play in (designed by someone else) deliberately runs "Partial success" results with some ambiguity - the idea being that a partial success is set up so that the GM describes it as something that could be resolved one way or the other by player skill or roleplaying, or in some cases perhaps additional rolls).

Fixed effect: whatever you rolled (assuming you passed) is irrelevant; you get a value based on the appropriate statistic or skill; being a 5th level thief gives you +3d6 sneak attack, being a 4th level wizard gives you a Rope Trick that lasts for 4 hours, or a telekinesis spell has Strength equal to the caster’s intelligence.  
Attribute-based effect can be a problem as e.g. a class ability in level-based games, since a character's ability in their class can't improve with level. The early 3.5 D&D marshal with its Cha-based 'auras' is one example.

Resource Driven Effect: e.g. in 4E D&D , the main thing determining how much damage an attack deals is what power (from a variety of one-shot power selections) is being spent. The complex 3.x variant FantasyCraft has a resource-driven setup throughout, where a high or low roll is potentially a 'critical' but must be 'activated' or 'triggered' by spending an Action Die. Likewise a fumble requires a low roll, and the GM or opponent to spend dice. Various character abilities interact with the mechanic; one thing of note is that NPCs can't score critical hits on PCs unless they burn the points to do so. In a resource driven system, characters can have modifiers to resource cost i.e. reduced cost if the character can have a particular ability, or a character might an ability that lets them recharge a power.  High results generally appear under the control of the player - making it less exciting and more metagame in nature, but also more tactical than most other options ('Going for Broke' is also somewhat player controlled, but not as predictably). Mathematically speaking, adding a resource cost can also be used to keep down the frequency of criticals which might otherwise become too common: requiring a character to spend a point to confirm a critical might be useful in e.g. a d10 system, as otherwise criticals on 10 would occur 10% of the time (a friend of mine has a homebrew simple step-wise system where a skill roll is usually just d4 to d12; it gives PCs 'catastrophe tokens' equal to 1/2 Combat Experience die which can negate 1s, among other things).
Note that although a 'safety valve' system where a player can spend points to add to their dice rolls also makes high rolls more controllable by players and so adds a resource dimension to another sort of effect determination, high rolls would still periodically occur on their own due to chance.
'Time' can also be a resource here in a way - effect may be reduced by attempting a task quickly (e.g. HERO 'casual STR', letting a character use 1/2 STR for a task but taking less time), or increased by taking longer. (It can work indirectly by giving a die roll bonus, hence better margin of success).
HERO also has a point-spend involved in effect, as Endurance can be spent to Push an ability (e.g.: Strength, Running, casting a 'spell', firing an 'energy blast') to be more powerful than normal.
Another wrinkle on this, from Marvel Heroic (MHR) is that it lets a character get 'effect' off reaction rolls by spending a plot point - so for a point a successful defense might become a riposte that deals damage.

Allocated multiple subeffects: A character using an ability gets X points to buy various sub-effects (e.g. for a spell might choose to allocate points into damage, area, or duration; LegendQuest does this with spell 'control levels'). When rolls are involved this can also be done but with the number of points varying, or even rolled after being allocated (see. HGT, below).
Note: I'm distinguishing this from 'resource' above where a character is burning an ongoing resource (powers or a point pool); here each ability use is a new 'resource pool'.

Dice-Requiring
Note that despite the below methods being classed as 'dice-requiring', occasionally a game will have diceless resolution using one of these by synthetically generating a 'die roll' number - e.g. a 3E character can 'take 10' and use that number to calculate a 'margin of success' result, or a Storyteller character can automatically pass a task with difficulty < dice pool, at one success.

Natural dice roll: particular numbers on the dice give more effect i.e. “pin on a natural 18-20” or “critical on a natural 20” (Palladium). The effect could be based off high roll (additive or 'blackjack' system), low roll (roll under), or occasionally occurs on doubles (on multiple dice or d100) e.g. IIRC 'Arms Law' for RM used to have weapon breakage on doubles, or having doubles produce 'yes, but..' partial successes for Barbarians of Lemuria (2d6+mods) is suggested in this thread (http://forum.rpg.net/showthread.php?762631-BOL-idea-adding-quot-but-quot-results). Whitehack typically rolls 1 die, but characters roll 2 dice (take best or take worst) if they have a relevant quality ('group') much like 5E D&D advantage/disadvantage, with GM-defined special success or failure on doubles. The "Metagene" RPG rolls 2d12 with a 'triumph' on doubles that succeed or a 'near triumph' if rolls are within 1 of each other (e.g. 6 and 7 rather than double-6 or double-7), giving three categories of success and making 'near' results just under twice as likely -a given result 1-12 has two adjacent numbers that are 'near' to it, aside from 1 and 12.
A natural-roll setup gives a named/specific effect, i.e. qualitative as opposed to a numerical [quantitative] output. This is similar to a table, but unlike a table, you get one or at most two specific results (e.g. for critical/fumble). In most games exceptional results are kept rare, regardless of a characters bonuses or total success chance - single die/fixed die type systems may add kludges that increase the range of critical numbers e.g. "Improved Critical" in 3.x D&D. GURPS expands its critical range based on total skill - from a natural 3-4 on 3d6 up to 3-5 at skill 15, and up to 3-6 for skill 16+.
The odds of a particular natural dice roll occurring may also vary intrinsically with character ability e.g. in a step die system, or for odds of doubles in a roll-under percentage system (1/10 of skill), or if rerolls are permitted. Some systems e.g. FantasyCraft, or D&D 3E critical hits, have more detailed subsystems for applying various modifiers to the ranges, independent of the modifier on the roll itself.

Natural dice rolls in dice pools can include e.g. 10s on d10s rerolling or counting as multiple successes (e.g. Aberrant mega-attributes), but this really works fairly similarly to a margin of success in these systems, unless a single 'wild die' is called out. Dice pools (whether count-success or multidie additive) generate numbers that are intrinsically quite 'open ended' and so it is difficult to separate off 'crits' in the same way as e.g. 20 on d20. This sometimes has the effect of requiring a separate dice roll for a special effect to be triggered (cf. 'attack rolls' in T&T, which uses lots of dice as the attack; having the entangle monster squeeze at a '1 on d6) chance rolled separately is fairer).

A natural dice roll to trigger a specific result could potentially be set to a number other than the top one or two dice values, which might be most useful if rolling multiple dice - for instance using 2d10, a critical roll of 20 would occur 1% of the time, while a roll of 16 exactly (no higher or lower) is 5% likely - I know of no systems that use that however.  

Natural dice roll has a quirk that an increase in chance of success lowers the average 'successful' roll, and vice versa (unless the roll is 'semi-independent' (see below) such as where using a wild die or 1's place die on d100. This can result in checks that automatically critical if they succeed (i.e. critical on a 20 but a 20 is needed to hit) or quirks like the 'Glass ninja' syndrome in TORG, where a target with high defense is hit only with an attack that (because of the high roll) also does a lot of damage. (Potentially this could be offset by giving a high defense a separate damage reduction also?).
Using rolling up + a margin of success mechanic can give results similar to using natural dice roll, but with more increase in success rate for characters with bonuses and possibly more useable numbers for defining effect-increase.

Margin of success: a fairly straightforward system, in the simplest version of this the character’s dice roll only determines how well they do i.e. how far they roll under the target number (roll under) or over the target number (additive). Rolling over the target number by 5 is half as good as rolling over by 10. This is fairly intuitive; it directly rewards large bonuses to checks. Minor subtraction is required. The amount of success is a number, and may be directly useful in calculating 'effect' (in damage, days of food, GP produced, or whatever). More rarely 'margin of failure' is considered rather than margin of success e.g. more damage is taken if a save is blown badly.
Effect increase under a margin of success setup has a linear return if the dice roll is linear (such as d20), while for bell curve rolls (e.g. 3d6 such as GURPS) diminishing returns is built into the margin of success - e.g. beating a TN by 6 is much less common than beating it by 4. 3d6 roll under  margins of success are generally more directly useful at a 1:1 ratio than in d20, which is more likely to use 3:1 or 5:1.
Rolling up can give blowouts in margin of success (frequently without modifying chance of success, if the max die roll would have succeeded anyway).
Systems may alter margins of success as well as bonuses; for example the Charlatan in the 2E AD&D "Complete Bard" has a Charlatanry skill whose 'margin of failure' widens as their Charisma increases; if a Pick Pockets roll fails by more than [Charisma] a critical failure occurs. Luchador: way of the mask notes that 'hasty actions' double margin of success on a failure or halve it on a success, as well as being +1 difficulty.
One friend's homebrew game, "Last Order", also has a "variable raise number" where the greater someone's skill is the larger the margin per 'raise' - needed math-wise because it uses larger dice for higher skill (...something like Savage Worlds). (see 'variable dice' post).
Complex margins of success can require a table lookup e.g. in Unisystem, the range of numbers generating success level 1 is smaller than the range of numbers generating success level 2 and it continues to widen each level to make the higher level progressively rarer. (an interesting house rule for Unisystem limits # success levels to no more than skill level despite roll).
SenZar has an odd group success system where multiple characters roll, and all separately determine margin of success and add this together to determine final margin; it also has some holes in the margin of success interpretation system in that a stat of '*' (i.e. unlimited or $TEXAS in the attribute) automatically wins opposed rolls with lower ratings without needing a roll but doesn't give a clear margin of success for system uses (such as a VoidSpawn's WILL roll to negate incoming damage, where margin of success determines maximum damage absorbed).
Dungeon World/Apocalypse World have an interesting twist on margin of success by adding player choice to what effects are generated - typically rolls are 2d6 and there's a list where 7-9 is "pick one", and 10+ gives 2 or 3 picks. So instead of a normal vanilla success and a high roll being super-success, a normal success actually comes in various "flavours". DW sometimes builds off the move structure by cross-matching lists, such as (in an early version) Sharpshooting letting a character choose 'pull a stunt' options as part of an Archery roll, or the mind-reading 'violation glaive' letting a character choose Discern Realities move options based off the targets' knowledge with a Hack and Slash move.
Teenagers From Outer Space has an 'Its Too Much' rule where a roll that's too high 'backfires' (e.g. the girl the PC asks to the movies starts stalking them) - the margin before backfire being randomly determined each session with D6. Margins of success can also just be capped e.g. in Buffy (Unisystem) a character with the 'talentless' disadvantage can't get more than level 1 on artistic rolls, as well as taking a penalty.
One other variation on the basic 'margin of success' is to replace a rounding of results with a second roll based on the remainder. The (slightly scary) Phoenix Command Amatorial Rules house rules included a roll where a result is divided by 3, with a final outcome of 4.33 then being resolved as 4 + a 33% chance of an extra success. This probably makes more sense with larger divisors and/or a linear die roll.

Base effect, plus a bonus determined by how much your total roll (dice + bonuses) exceeds the target number (for example hitting by 3 might add +3 to damage). Minor subtraction required. This is basically a hybrid of a ‘fixed’ system and the ‘margin of success’ system. It gives numerical results i.e. "damage points" or "result points". This system lets a character have an effect modifier that applies to tasks independently of the success roll e.g. a bonus to damage from Strength.
The most comprehensive and interesting system of this type is probably DC Heroes (perhaps particularly 2nd or 3rd editions). This sets separate Acting Value, Opposing Value, Effect Values and Resistance values for all rolls - e.g. to hit in combat uses a comparison of attacker DEX (acting) vs. opponent DEX (opposing), then damage would be found by comparing attacker STR (effect) and target BODY (resistance), plus column shifts from the hit roll. Parallel systems also existed for e.g. social interaction (which involves comparing Influence, Aura and Spirit) and all other tasks, though many used doubling up of the same attribute or power (for both the action roll and effect), or used points where they were likely to be unnecessary complication on rolls that should be simple pass/fail. Possibly an issue is that a 'mirror match' between characters tends to favour the defender, since equal effect stat/resistance stat gives usually only a couple of points of base effect, requiring an especially good die roll to then raise the effect more. Effect could sometimes be converted into exact distance, area, etc. via tables, or sometimes became ad hoc - e.g. 'Danger Sense' notes there's a sense of danger with 1+ effect, or exact source with 8+, after a messy process of comparing power rating as acting value/power rating as effect value vs. a table of opposing and resistance values based on danger seriousness-critical 2/2, major 4/4, minor 8/8 (though at least this is consistent for adjudicating how other powers can affect the numbers). DC Heroes also had the concept of ‘Pushing’, where an effect works at the base value automatically, but requires a dice roll to strain that limit e.g. lift more than usual. Another game using this would be FGU's Daredevils; margin of success on Athletics or Swimming rolls adds to Speed when running or Swimming, while Jumping margin of success adds to Strength for calculating distance jumped.
 
Attribute-scaled effect: in a 'roll your modifier' type system where the dice give a + or - to the base score, such as FUDGE, the final roll can give a result that's on the same scale as the stats i.e. a "Great" result. The results in this sort of game can be used to either check for success or as an effect value (although its perhaps dodgy to use one roll to give both). This is basically a variant of 'margin of success'. Note that FATE probably inflates this due to Aspects.
In some respects this is similar to what DC Heroes attempted, which also attempted to give an output in terms of 'attribute points', except that DC's output only theoretically is scaled as a stat (RAPs obtained vary from about 0 to 2x stat) and include input from multiple stats, four per check. (DC Heroes' relative Shatterzone is also an interesting development here in that it also uses an attribute-based scaling, with base attribute plus a 'bonus number' generated by a roll, but that number is used as difficulty mostly, with effect then calculated more indirectly or complexly with tables IIRC.)
It could be imagined this would combine interesting with a setup like ROAR (see advantages) where a low/high score for attributes automatically added the equivalent of flaws or merits; an effect result could then have various positive or negative traits working the same way, parallel to how attributes worked.

Independently rolled effect: the most common case of this is damage e.g. in games where hitting with your longsword deals d8 damage this is an effect largely separate to what your attack roll was, barring criticals (More on damage later). This system is readily shoe-hornable onto whatever other system is in place; it provides slightly less logical results (a huge skill check can earn minimal success) but does not excessively reward high bonuses i.e. it is ‘balanced’, and there is little extra math involved.
A separate roll is good in that its easy to vary average amount by varying what die is rolled. (If a game uses another mechanic (like pulling one die out of a dice pool for 'effect' - say damage) a separate roll could be used as an exceptional cases, e.g. for small or large weapons the roll might be separated so we could roll d4 or d8).

A roll can also be “semi independent” - for d100 systems that have special results based on the 1s die (see above), this is almost a form of built in separate roll –since the 1s place is often largely irrelevant (one-eleventh of the total dice roll on average). In a couple of systems dice are read additively but with one of the dice determining special effects e.g. in Valherjar (another Haiti disaster relief download RPG), a roll is [stat+3d6] but one of the dice is a special colour and determines effect. The Dragon Age RPG is similar - 2 dice + a wild die, with a critical occurring on any successful roll of doubles [44% chance] and giving 'stunt points' equal to the wild die which can be spend on various effects - this again gives a chance of 'critical' which is independent of character skill and can only improves only rarely/arbitrarily as a result of special abilities giving stunt cost discounts and the like. J Arcane's Drums of War uses 2d10, but also reads them as a d100 roll (as noted later in Criticals).
As another example, the "Envoy" class in Starfinder gets an 'expertise die' (+d6, etc) which normally adds to the skill result, but levels of failure can be modified by it - e.g. a Sense Motive check critical fail is reduced to a normal fail "unless the expertise die is a 1".

A simple 'semi independent' mechanism is just to count odds/evens as different results. For instance, the 5E playtest displacer beast (IIRC) incorporated a 50% miss chance into the attack roll by having odd numbered attack rolls miss, while in the solo adventure Red Circle in Tunnels and Trolls a missed save (falling into a pit) send characters to different pits depending on whether the roll is failed by an odd or even amount (using the margin here lets odds/even be used easily despite a roll using 2 dice).

The Marvel Heroic game (2012) uses a pool of dice, where 2 are selected and added to determine success, and a third selected as the "effect" die - a quirk being that the result is based on the raw die size, regardless of the actual roll. Characters may therefore sometimes lower their success roll to allocate a higher die to effect (a rules outcome similar to that of 'going for broke' -see below - though in MHR this is something that comes into play only on some die rolls in MHR since the effect die roll might not have been particularly good). A high dice could equally well contribute to 'hit' or 'damage', so there's no default distinction between effects that increase damage and that boost accuracy (reminiscent of Tunnels and Trolls). (a few SFX can step up the effect die/damage specifically e.g. Constructs, Dangerous but these are uncommon).
MHR also has a resource dimension in that 'plot points' can add an extra die, or allow a character to keep two 'effect dice' (such as dealing damage vs. two thugs).

Another more complex example of this was apparently proposed in Pyramid (noted here (http://forum.rpg.net/showthread.php?408412-Dicepoll-Systems-but-with-different-functions-for-each-dice) by Wil):

QuoteWhile not tied to any specific system, Justin Bacon wrote a very interesting article for Pyramid called "Dice of Destiny" that is usable with a dice pool system. Unfortunately you have to be a pyramid subscriber to view it (which I am not anymore). In essence, the article describes assigning attributes to each die rolled, such as time, quality, finesse, etc. When the dice are rolled, they are read normally but then the individual dice can be evaluated to unpack more information about the roll. So if, for example, you are using SilCore and roll 3 dice for results of 3,5,5 and the dice were assigned time, quality and finesse, the result would be 5 and the individual dice could be evaluated as the task taking an average amount of time, but with higher quality and finesse.

(Compare this to Heroic Golden Turbulence, below - somewhat similar outcome but without the issue of dice pool variability or needing huge dice pools ? However, it does differ in that dice are allocated after rolling, unlike HGT).

Multiple rolls: here after succeeding the initial check, the character has to make additional checks to determine exactly how well they do/or make further progress. This might appear naturally enough in play when a GM doesn’t have a system to handle effect readily. An example of this method might be running speed in 2nd ed. D&D; a character can roll a Strength check with a penalty to reach 5x normal speed, then if that fails Str checks with successively lower penalties to try for 4x speed, and finally 3x speed; 2x is automatic).
 
A rarely seen version of this that crossbreeds it with margin of success systems is to 'reroll remainder' - count the amount the roll is over the target, and then reroll against it. For example in a roll under system a character might need a 15 or less to succeed; rolling a 12 they get a reroll against 3 or less (as 15-12 = 3) for some extra benefit. (The translation of this to an additive system would be for the margin of success on a roll to be used as the bonus for a follow-up roll).
 
Going for broke: the character can get an effect bonus by taking a penalty on their dice roll (usually an add-on to another system). Examples include 3.x D&D Power Attack (i.e. take a -5 to hit, get a +5 or +10 to damage; Synchronicity (a free rpg) does the same with swashbuckling manuevers (swinging on ropes at -5 adds +5 to damage); DC Heroes has a an option called "Going for Broke" that applies to most actions.
This mechanic gives characters a chance to pull off something very risky, but very rewarding. This mechanic does help gameplay, by slowing down the rate at which dice rolls become irrelevant to characters with huge bonuses (characters are incentivized to take penalties and so continue to fail) however, some players may be deterred from doing anything cool by the chance of failure, and high rolls are less exciting if they don't provide any automatic increase in effect.
This sort of thing can in a sense occur in an informal way in many game systems/situations, often covered by GM adjudication; it can also occur on a case-by-case basis by situational rules e.g. a game might have called shots to limbs or vital locations, even if there's no general system whereby a character can trade success % for more power.
The main thing to watch is that if a character gets bonuses to effect already from the dice roll for rolling high, the effect bonus has to exceed the effect points they lose from taking the penalty. DC Heroes has a good setup for this (the effect bonus is precalculated to more than offset the penalty).
An example of what not to do is Fading Suns 1e; it uses a d20 roll under Blackjack system, where a character can voluntarily choose to add a bonus/penalty to their dice roll ("Accenting"). While this probably seemed like a good idea superficially, calculating this out shows that there is no increase in average effect - the maximum result is unchanged - just a loss in chance of success. That is a character with skill 12 generates results from 1-12 with a roll of 12, while at modifier +5 the character generates results of 6-12 at natural rolls of 1-7 but fails on a natural roll of 8+. Negative accenting in FS i.e. taking a penalty to the roll which increases success chance but decreases average victory points, fails to work for the opposite reason; it only adds to chance of success.
Feng Shui is interesting in that it has 'stunt' guidelines where extra effect has a difficulty increase based off game-level advantage, rather than real-world difficulty ('fluff') i.e. taking out 4 mooks with a trick boomerang shot is at a -4 penalty. This mirrors the sort of logic seen in super power construction in games like Hero/Champions ("effect based reasoning").
As well as a penalty to die roll, success chance can also be reduced by requiring a second die roll. One French RPG as noted elsewhere lets characters roll d20 instead of d10, increasing margin of success directly, but with autofails on odd numbers.
The 'going for broke' idea may also be applied in a margin of success system by changing dice rolled to give a greater 'spread' of results without changing the average; for instance replacing 3d6 with d20, or the mechanic seen in 'Combat Monster' (see Non-dice randomization) where a character could choose to roll either a dollar or 10 nickels, and counts the total values of heads.

Going for broke - type II: a mechanic described here (http://forum.rpg.net/showthread.php?561075-list-the-CORE-Mechanic) for the (unpublished?) 'triune' RPG let a character increase effect by also increasing failure effect if they fail; actual success chance doesn't change. After making the roll, the character opts to roll a separate pool of 1, 2 or 3 dice (their choice) with a success being boosted by more successes and a failure worsened by more failures.

Trading down effect (for a roll bonus): The opposite of 'going for broke. "Fragged Empire" uses a 3d6+modifiers system where a character gets one "Strong Hit" per 6 rolled on the dice, letting them choose various items. This would be a straight-up natural dice roll system (in a sense combining additive and dice pool), except that the default "Strong Hit" result, "Effort" lets a character re-roll one of the other dice (that didn't come up 6). Consequently, effect is being artificially lowered for low-bonus characters because they're probably spending effect to boost up the die roll, instead of choosing other effects. This works as the opposite of the 'going for broke' option, in that it has to be an option after the roll is made, instead of before.

Extra effect, from additional actions: e.g. a character might combine a 'gather more energy' roll with a 'spellcasting' roll, to cast a spell with more oomph. This may require 'multiple rolls' (similar to the above). If a game has rules where doing extra actions gives a multitasking penalty, it is also similar to 'Going for broke' although it possibly scales differently: instead of a flat +x to effect, -y to the roll, the extra effect is generated from a whole new roll, and so could be massive if the assist task dice pool is large.

Success counting: as seen in dice pool systems (e.g. perhaps the vampire attempting to pick up in a bar rolls Appearance +Seduction and get 3 successes, so he finds a target with an Appearance of 3). Success counting systems, as with margin of success type systems and indeed most of the systems, typically give simple, numeric outputs –with a couple of exceptions e.g. *Warhammer Fantasy, 3rd edition uses custom symbol-marked dice of various kinds – some good, some bad. Individual cards/rules help interpret these custom symbols to give a variety of specific effects.
* the game Heroic Golden Turbulence  (http://web.archive.org/web/20001020164051/http://www-personal.monash.edu.au/%7Esbeattie/HGT/hgtindex.htm) uses a standard d6 dice pool which is however colour coded; the player allocates their dice pool across various colours as they wish, with the count of successes earnt in a category giving the GM info on that aspect of the conflict – an incredibly detailed result output. For example:
 
 

QuoteLau Wang is sneaking into the temple of the blood god in order to find the scripture of the armour of ancients, using his Martial Arts of 6 and the specialty stunt: stealth. He may wish to get in as quickly as possible, while avoiding death traps. This is an important crisis, requiring 2 goals. He decides on 3 dice for caution (blue), 1 dice for speed (green) and 2 dice for offsetting the death traps (grey). He scores 3 goals, 2 in caution (he doesn't get caught) and one in offsetting (he avoids the scything trap but not the secret poison spray - damn!). Because the green dice did not score a goal, he did not get out especially quickly. Now he has to contend with the imperial guard.

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Somewhat similarly, Ouroboros Engine is a dice pool game where 'dangers' and 'opportunities' each represent individual successes. Players and GM work to set stakes for rolls i.e. a character rescuing children from a burning building might need 1 success to escape damage, 1 to save a child, 2 to save an extra child - the player would choose how to allocate successes after rolling (not dissimilar to how Apocalypse World/ Dungeon World works, but using a dice pool). The key difference between this and Heroic Golden Turbulence would be that because in it, rolls are divided across multiple 'colours' before rolling, a character doesn't reliably get the specific effects they're aiming for. HGTs dice pool mechanic also makes more complex results hard to achieve for characters with low dice pools (more deterministic).
Counting successes is good for calculating damage; Twisting Tunnels (see post 13) is interesting in that expected successes work well as a 'condition', with the # dice modifying follow-up rolls.
Success-counting off a success roll can be combined with a separate roll as well, e.g. how oWoD rolls damage with base damage dice for Strength & weapon getting bonus dice from extra successes on the preceding attack roll.
ORE type systems can potentially have interesting results here if multiple matches are used to grade different aspects of success. (Legends of the Wulin?).

Counting + and - dice: reportedly, Bliss Stage rolls a pool of Fudge Dice with the + and - assigned to various categories of outcomes. This seems similar to "success levels" generally, but with negative complications occurring rather than success dimensions all being counted upward from normal or 0.

Named result levels (off a table); as seen in various universal tables these are usually non-numeric i.e. a “Great success” (Lost Souls), or a “Green” result (MSH), or a “special success” (RQ). They require referencing more rules to work out exactly what a named result does, but for clearly defined situations give perhaps more interesting results (a result might be a Slam or a Kill, instead of a +3 on damage). The most advanced system for this may be Rolemaster, which uses incredibly detailed tables giving exact descriptions of what happens for more or less any situation/dice roll. Tables can of course also just be used to get a numerical value for success in some way.

A table can also be used to cross-reference two different dice rolls/results to get a final result. 'Grid rolling (http://www.therpgsite.com/showthread.php?p=496201&highlight=grid+rolling#post496201)' (above) is a simple case, or another example is HarnMaster combat (below) which compares two rolls' results - critical failure (CF), marginal failure (MF), marginal success (MS) or critical success (CS) for both attacker and defender - to get a result. Below; outcomes are BS (both stumble), DS (defender stumble), AS (attacker stumble), DTA (Defender Tactical Advantage i.e. free attack), nothing (dot), or a number of  impact dice for a attack that hits (A*2 = 2 dice, etc).
(http://i1239.photobucket.com/albums/ff507/BSJ17/harncombat_zpsu1mi2tl9.jpg)

Advanced Concerns
Systems sometimes can add a layer of differing interpretation of effect, in addition to the raw check modifier e.g. for Marvel Super Heroes' Intensity rules applies different interpretation of effect to widen the gap between characters of different attributes, who otherwise have very similar chances of success (+5% per ability level, e.g. from Remarkable to Incredible or Incredible to Amazing).

Quote from: Dragon #187Arachne’s spikes can deliver direct injections of poisonous venom into a victim’s body. Her venom injections are of Incredible (40) intensity and can kill anyone in three to six (1d4 +2) rounds who fails an Endurance FEAT roll. Those victims with Amazing or greater Endurance need a green Endurance FEAT roll; those with Endurance ranks of In-credible need a Yellow result; and those with Endurance ranks below Incredible need a Red result to take only 10 points of damage. Failure indicates death.

In this case while 1 rank gives only +5% chance of any non-failure, shifting from requiring Red to Yellow success at Incredible boosts success chance from about 10% to 40%.

Defensive Effect: not a separate method but a principle that applies in some systems. A game may let the defender generate an 'effect' which discounts the offensive effect generated, however usually as a new separate roll, rather than following on from an existing roll, since any defense roll must already have been failed. This can be seen for instance in DC Heroes where the defense attribute directly reduces base result points (without a roll), or oWoD Storyteller, where Stamina dice are rolled to 'soak' (balancing Str successes on damage, though its slightly one-sided in that the damage roll can get bonuses from a good attack roll whereas this can't, being a standalone effect roll). Luck point (safety valve) spending can also sometimes boost 'defensive' effect.

Varying effect systems by subsystem:
Game subsystems most likely to use a different subsystem to whatever the general effect mechanism is include:
*damage (most often rolled, even if most subsystems are margin-of-result)
*magic (often somewhat resource-based when most other checks aren't)
*extended actions/group checks (accumulating multiple 'successes' and therefore discarding individual margins of success).
Of these, most can still be handled consistently in a dice pool game. but otherwise will vary.

Thoughts in closing: most systems run OK without a detailed, consistent effect-determination system, given a GM with at least a modicum of imagination.
On the one hand, systems with no coherent single effect-determination system (most of them) have evolved various different approaches to handle this - a d10 roll here; a level-based damage progression there; yet elsewhere, a direct Jump-check-DC-to-distance-jumped conversion chart. On the other hand, a built-in system for effect can be a solution in search of a problem, with unnecessarily complex subsystems built off the basic system when really, simple pass/fail checks are all that is necessary.
In a wholly integrated system, be careful that unifying major systems doesn't break them. The most important form of "effect" is the damage aspect, and while its a bonus to have other subsystems run consistently with this, make sure that sub-rules intended to facilitate other actions like running or determining spell durations don't somehow mess up the damage system.
 
Conversely, the effect mechanism used does determine how information flows through the system, and a good effect system can cover a number of things that would otherwise require additional complicating rules. For example, if amount of attack over target defense affects damage, then a good attack roll includes 'critical' effects by default, and catching an opponent with their pants down and so zero defense automatically increases damage without need for 'sneak attack' rules.

Note: see also post 136 (http://www.therpgsite.com/showthread.php?p=567848&#post567848) for details on critical hit systems specifically, and magic (http://www.therpgsite.com/showthread.php?p=507599&#post507599) for more details on that.

[Note to edit] Different effect systems give different degrees of 'granularity' in results. Some of these options only provide a yes/no result (i.e. 'crits' or high natural-die-roll), while others give slightly different results depending on the die type combined with i.e. 'margin' on a d100 is much larger than 'margin' on a Savage Worlds style single d8 roll, or distribution is very different for 3d6 vs. d20. Dungeon World 'moves' gives a result of basically '1 or 2 successes', similar to counting 'raises' for Savage Worlds. Similar results can be coded in different ways depending on the granularities involved i.e. a Dungeon World 'move' spending one option (out of max. 2 for a 10+ roll) to get 'your spell is not expended' is a purely yes/no equivalent of a more discrete 'subtract your margin of success from the spell point cost to cast your spell'. A finer-grain system probably provides the option to have more complex or detailed manipulation of the effect system.

('Effect' systems can sometimes be called in as part of a high-level task resolution system, letting multiple factors be considered. Say a task might add together levels of achievement for one roll, and 1/2 level of achievement off another roll so as to actually resolve a yes/no question, but stepping up or down importance of various factors (e.g. you might add together Level of Achievement for a Persuade roll, and half Level of Achievement for a Physics roll, to successfully impersonate a famous physicist).

A dice roll on a table might include 'effect' variation that's a bit of random shift, as well as improvement. An example there is 'mutation rolls' in Mutant Crawl Classics, where on a roll for extra limbs higher is generally better (add +level) but might give more arms, more legs, or both. Adding [+level] to the roll could give you more legs when you wanted more arms, however. This would be avoided if it were split into two rolls - one for bonus where level is added, and one randomizing exactly what the mutation does - though that would also mean generating a lot more results since most of the variation is in specific entries rather than effectiveness.

Treasure determination as an example of an 'effect' system:
As well as simple hit/damage, generating treasure can be a sort of 'effect' - much more complex since it isn't a result of X 'hit points' but has to include any number of specific items.
A character's attributes also aren't important here or involved in a check, though an NPC's stats might be used somehow.

Depending on the system this might be wholly freeform, involve rolling on some random tables, or be GM-determined within a budget based on e.g. an NPCs level [X GPs for a level-x NPC] or wealth rating. Occasionally a player gets some choices in treasure determination [e.g. 4E] although this is rather meta since it involves what's primarily a world detail. In a sense a player gets some input into treasure determination also by deciding who they go after.
As an example that's eerily reminiscent of doing hit/damage, here's Dragon Warriors' treasure determination rules based on a monster's treasure code for how rich it is (see also 'Monsters' post) - with roll for if you hit the jackpot and then how much is in it - some monsters may have set treasure codes while others might have the code rolled first e.g. roll d6, 1-5 meagre, 6 = poor:

(http://i1239.photobucket.com/albums/ff507/BSJ17/treasuretype_zpsmmovpeys.jpg)

Edit notes: Last order notes, Fragged Empire notes (*); varying effect systems by subsystem(*), note that yes/no systems encourage 'front-loaded' effect bonuses.(*), note on granularities. Luchador note (*), more DC Heroes notes (*), treasure determination notes.

When designing a system, when to roll dice is an important question - as it is something frequently overused. Dice rolls take time and require additional invocation of rules to resolve, and additionally generate chances of PCs failing, that may not always be appropriate. Though some players just like rolling dice. While this is partly a matter of taste, IMHO a dice roll should be a moment of drama or tension.
Dice aren't the only possible source of tension and diceless systems do exist; Amber in particular accesses fear of the unknown in players by keeping difficulty of tasks, and even a player's own character capabilities, obscure to them, rather than having uncertain dice outcomes.
 
Burning Wheel uses rolls, but generally forbids re-rolling unless a situation significantly changes ('Let It Ride'); e.g. several connected acts of sneaking requires only one sneaking roll. The justification for this is again mathematically reasonable ; that repeated rolls will eventually be the undoing of a character.
 
Similarly, people who have played sneaky rogues in 3.x should know the value of Always Taking 10 on their Hide/Move Silently, for the same reasons - sooner or later the character sneaking through a house and rolling Move Silently all the time will roll a "1" and get caught). Dungeons and Dragons 3.x calls for checks reasonably frequently, but lets characters sidestep many rolls by 'taking 10'; when not threatened or distracted a character can act as if they rolled a 10 on their d20. The positive aspect of this is that what constitutes an 'automatic' task is definable within the DC system (if my bonus is +10, I can auto-succeed on tasks with a DC of 20 or lower) rather than being set by GM fiat, as in most other systems.
The downside is that this system eliminates a number of dangerous task to cut down on die rolls - jumping chasms, climbing walls or the like can also be "take-10'd", so to be effective a terrain hazard generated by the GM must have a success chance of less than 50/50, rather than just "don't roll a 1" risky.
(A possible alternative, which cuts down fiat but would not generate this effect, is to provide bonuses on the dice roll for easy tasks, and not call for a roll when failure chance drops to 0%).
Related to Take-10, the 'Take-20' mechanic lets characters under no time pressure act as if they rolled a 20 - reasonable given situations where there is no chance of failure or time limit and multiple retries are allowed, since it avoids players rolling endlessly until they get a 20 anyway. Another alternative to this is the 'fail until you fail forever' rule, where each failure increases the target number until the check can't be passed, often seen with Open Lock in particular (or alternatively the "keep trying until you critically fail and jam your lockpicks in the lock", etc).
5E replaces the 'take-10' with a 'passive skill check' of 10+modifier; the distinction being that usually when the passive score applies is at GM discretion rather than player discretion. It sometimes becomes overly deterministic by having an opposed roll reduce to passive score for both sides, giving a set result as to whether a trap is found for instance.
Some modifiers can apply only to synthetic die roll results e.g. 3.5 includes a couple of feats/options that let characters 'Take 12' ( Int checks w/ 'Focussed Mind', Races of the Wild) or 'Take 15' (expending Psionic Focus on Concentration). These may, however, discourage dice rolling too much, and generally seem to have little justification for how they work.

Similar to Take-10, 'D6 Space' (and possibly other d6 system sourcebooks) suggests instead of rolling several d6s for rolls (particularly unimportant rolls), the gamer should just multiply the # of dice by 3 or 4. It biases this (applying an ad hoc modifier which would never have applied were the dice actually rolled) by using x3 for rolls which 'ought to fail' ("cannon fodder damage resistance checks") and x4 for actions that ought to succeed ("something the player characters are doing").
Unisystem takes a mechanically similar approach but applies 'take average roll' to NPCs only - NPCs has scores for 'Muscle', 'Combat' and 'Brains' which are base stat +6 (average for d10). Muscle being prefigured still allows randomization via the player's roll. For Combat dice are still rolled, but the average combat number is used instead to determine 'success level' i.e. damage modifier for attacks, without table checking.
BESM 3E rolls 2d6 and has a d20-inspired "Take 6" rule; it  also separately gives lots of guidelines to the GM on 'when not to roll' that are maybe redundant with this.
Damage rolls with lots of dice can sometimes also be shortcut. The Epic Level Handbook suggests using average damage for serious damaging spells (20d6 fireballs etc); the Immortals boxed set for BECMI D&D suggests a similar system, but also proposed adding an arbitrary random variable i.e. to a base of 158 average damage for a 45 die fireball, the DM could add say (2d20-20) random variation.

Though not innovative in terms of cutting down dice rolls, Unknown Armies is interesting in how it runs with the implications of the 'die rolls as dramatic" idea in setting its percentages for success: it assumes rolls will only be required in difficult situations so percentage chance of say, fixing your car, is precalculated to minimize modifying by assuming you're under (for example) time pressure from zombie attack, rather than having (as it says) the default % be the expected rating for a 'lazy Sunday'. This is probably a good idea in the context of its roll-under d% system, as psychologically there is a tendency for GMs to use the unmodified rating in roll-under (cf. John Kim's essay at Darkshire on roll-under systems).
 
A review elsewhere on the site here mentions a 'Tatzelwurm' system [2d6]; it lets PCs overcome Simple difficulty tasks by 'just roleplaying, no roll required'.

A number of games also have rolling only for the players, not the GM: these include Legendary Lives (http://www.hauntedattic.org/legendarylives/LegendaryLives.pdf) (1990), Whispering Vault (1993), and more recently Icons, Apocalypse World, Numenera, and Soylent Green's freerpg Bounty Hunters of the Atomic Wastelands (http://www.therpgsite.com/showthread.php?t=28112) (Fate). (thanks RobM for some info). Dragonlance SAGA also had a system equivalent to 'player's roll' based on a player card deck - saving the GM from needing a separate deck and giving players more control (some genuine randomness is however provided with separate 'fate' cards).
See thread here (http://www.therpgsite.com/showthread.php?t=32929) for some discussion of 'players' only roll games (includes various contentions re. immersion, overcomplexification to compensate for removal of GM rolling, philosophy of player rolls vs. GM roll [epistemiological questions vs. in character], and different style of 'interpretations of results' required in player-only vs. both-sides-rolling i.e. the GM folding description of opponent actions into the roll as well.
 
Earthdawn has a strain mechanic where using certain Talents causes the user to take damage. 3E Earthdawn sometimes uses this to discourage some skill re-rolling i.e. Search checks actually cause the user damage. "As it is, an Adept and move silently indefinitely without problem, whereas it is totally possible for that same Adept to weary himself into unconsciousness by looking for something." (quote from here (http://forum.rpg.net/showthread.php?689042-Earthdawn-and-the-cost-of-Strain)).

Dragon Warriors (and the earliest versions of 5th Edition D&D) had a mechanic for automatic success on attribute checks, where no check was required if the difficulty was less than the attribute score. This gave slightly odd results in that giving an auto-success resulted in a higher success boost with lower attribute scores e.g. automatic success at a stat of 8 would boost chance of success from 40% to 100%, while for a 15 it would boost it from only 75% to 100%). 5E D&D as of the mid-2013 playtest retains the ability in a barbarian special class feature (a character can roll, substituting their Str for the result if they don't like it; which incidentally also means that the automatic success value increases twice as fast as the average value generated - 1:1 per stat point rather than 1:2 stat points. The ability also probably peaks in usefulness at a Str of 15 or 20, as these are default benchmark difficulties.)
Dragon Warriors also has a durational 'spell expiry' roll (probably to replace having to count duration of spells in combat rounds). This was normally a 2d6 roll each combat with a "12" being spell expiry, but was replaced with a 25% chance per minute of spell expiration out of combat (an equivalent percentage but with number of rolls cut down, though the need for the initial roll is maybe questionable).

Marvel Super Heroes has an 'automatic FEAT' rule, where a character succeeds automatically on a task whose Rank is 3 or more less than their attribute rank - for example, a character with Remarkable (30) Strength vs. a task of Typical (10) difficulty. This is not so much to cut down 'excessive' rolling as it is a patch on characters' relatively limited chance of success - 3 ranks increase success chance by only +15%, so without a rule such as this characters would frequently fail what should be easy tasks. Note that apart from this effect, and a rule where tasks of higher difficulty are impossible, task difficulty doesn't otherwise alter the chance of success. Conversely, a task may be 'impossible' if task difficulty is higher than the PCs rank in the ability (though it is suggested a PC be allowed to roll if an action being impossible would result in certain death).

Dice rolling is sometimes disallowed in a system because the result would be too random. D20 system for example would probably resolve an arm-wrestling contest as a 'highest wins' because opposed (d20+modifiers), its universal system, would give the higher score too little comparative advantage. In GURPS however, opposed 3d6 rolls give results that are much more predictable, so its likely to be acceptable, making GURPS paradoxically less deterministic than d20 in this instance.

The Ubiquity System (e.g. Hollow Earth Expedition) has a 'take 10' type step which instead of being optional, engages on every dice roll: if a character's average # successes from their dice pool beats the difficulty, they don't have to roll. As ubiquity dice are 50/50 likely to succeed, the average is calculated as 1/2 the full dice pool; in the case of an odd total (e.g. 5 = 2.5 average successes) the player rolls a single die as part of the 'Taking the Average' procedure, before moving on to a full dice roll if necessary (which isn't affected by this roll).

DC Heroes has 'automatic actions', generally relating to 'effect' attributes such as STR, where characters automatically get effect points equal to the attribute without having to roll on the usual success table (which could however potentially generate more action points, depending on the roll and the assigned resistance value).

One-off special situations generating 'synthetic' rolls: Apocalypse World generally just believes in not rolling unless necessary, but one interesting idea is here. "When you give 1-barter to someone but with strings attached, it counts as manipulating them and hitting the roll with a 10+ [i.e. on 2d6], no roll required" i.e. this specific circumstances is equivalent to an automatic roll of 10. Another example of the 'special situation synthetic roll' might be 3E's 'coup de grace', which gives an automatic critical (=mostly equivalent to a free '20') on a helpless foe. The same principle sometimes applies to damage (e.g. a monster taking 'minimum damage' from fire or guns or etc., instead of it being rolled). Some rolls can also be overriden by GM judgment i.e. the GM setting the result - 5E T&T has a rule where an unwounded character can lift twice 'weight possible' for 1-6 turns (which 'might' be set by roll of a die, or not). A circumstance might also generate a 'synthetic' result from a different die roll (e.g. the coup de grace 'critical' might in a sense result from a successful Move Silently roll; in a less unified system, different subsystems might need to be translated between, converting a number generated by a different die roll.

(another idea on 'synthetic' rolls: - see recently-added note under 'dice pools' for a dice pool system using a synthetic roll, added to the normally rolled pool)

It may also be worth looking at some particularly egregious instances of excessive dice rolling in games:
 
*active (defender-side) rather than passive (attacker-side) rolling for perception. A roll for a form of Perception - to search for traps, or spot opponents - can in a dungeon generate large numbers of rolls - potentially one per 10-ft square or one per room whether or not an opponent is there. The converse situation where a trap or attacker rolls to surprise a character vs. the character's relevant defense is made only when a trap or threat actually exists, cutting down potential rolling opportunities.
(Note that who rolls can be important if one side gets re-rolls for whatever reason. 5E D&D uses a rule where a character has 'advantage' gets +5 to their passive score as a fix for this).
 
*Randomized movement; some games way roll for random movement - which can be problem if taken to extremes.
(This is discussed further in the "Movement" section for combat).

*oWoD Mage can have lots of rolling since mages tend to use magic for virtually everything more complex than tying their shoelines, with the main balancing mechanic for magic really being the chance of a 'botch' that will cause paradox, making it tricky to skip over trivial rolls even when the outcome of the task itself isn't greatly important.
 
Excessive dice rolling in a system can occur for various reasons:
*when a situation originally dangerous/dramatic situation turns out, through rules drift across editions or just a misapprehension on the part of the designer as to how their game would actually be played, to be something routine and dull. For example, Cure Light Wounds in AD&D (heal d8+0 hit points, a rare effect healing a significant chunk of a targets HP) became 3E's Cure Light Wounds Wand, requiring the roll of dozens (or more) of dice between combats to determine charge depletion. Note a number of spell-point systems (T&T, SenZar) avoid similar situations by having simple 1:1 ratios of spell points-spent-to-HP-healed.
 
*when a system allows players to skip over rolls, but still gives them an incentive to roll in routine circumstances, to get higher results or extra bonuses. For example, oWoD Storyteller or Shadowrun 4E both allow "auto success" if a character has a sufficiently large dice pool (either where number of dice >difficulty rating, or at a rate of 1 success per 4 dice, respectively) but a player may frequently still wish to roll to get more successes - particularly in Storyteller, where chance of failure is probably quite low.
To address this, a designer may be able to readjust the cost/benefit ratio of this to deter extra rolling by ensuring such "voluntary rolls" retain significant failure chances, or even critical failure results (if they're a jerk).
 
*when additional rolls are call for just because a task takes a long time in-game to accomplish (extended checks in some systems). Often it may be more appropriate to roll to see how long it takes to perform a task, rather than rolling success checks over and over until a target # of successes is reached.
 
Additional Note: choosing when to roll, or not roll, can be important due to secondary rules that are invoked.
For example, if a flat roll is used for Defense, this will not be affected by other to-hit penalties. Systems where attack rolls are used to parry however, normally add an exception to applying off-hand penalties to shield parry rolls (e.g. GURPS, IIRC).
 
Extra Note: for events which have a low probability of occurring, rolls for these can sometimes be streamlined out of a system by having the roll only occur in specific circumstances (i.e. only critical hits require a hit location roll), or having something occur as a byproduct of critical success/critical failure on another roll (a 1 on your armour bypass roll results in a weapon breakage check [not from a published game; this is a Dragon Warriors house rule I've considered using]). When doing this the designer should be careful that doing so doesn't skew the likelihood of the result; e.g. in the above armour bypass example the designer would have to be careful that a larger armour bypass die for swords would result in them breaking less frequently than maces, unless the second roll to confirm the breakage was adjusted to compensate for this.
 
Similarly to this, 4E D&D streamlines out extra saving throws against effects by having one 'attack' cover both normal and 'rider' effects - e.g. an attack that hits might generate both damage and a stun. This avoids the extra dice roll, but requires a 'conflation' of defense factors - a [damage+move] effect is against the resistance score for being moved, so that defense against damage isn't considered. It also means a situation of "damage, but no move", isn't possible.
A similar case of 'conflation' of multiple rolls into one (questionable) one for simplification would be ranged attack powers in Savage Worlds i.e. Bolt. The arcane skill roll to activate the power is also the attack roll for the power: this generally works since both ranged attacks and spells have a fixed (4) target number. Complex cases can be weird e.g. " should a Bolt receive a casting roll bonus for attacking a Large monster, if yes would raises due to this still reduce the power point cost if the character has the wizard Edge?" - might lead to the same roll getting different sets of modifiers for one use for another use. The same rules quirk lets Weird Science characters just use Shooting to hit with devices and so avoid buying arcane skill in the first place if they largely intend just to Shoot things.

Occasionally an alternate system is used to shortcut what would otherwise require lots of normal rolls - for example, having a 'mass combat' subsystem instead of rolling attack rolls for a large number of participants.
Dragon...#113? has another approach; it has binomial probability tables set up using d100, which gives percentage chances of a given number of successes/failures for up to 20 d20 rolls at a given TN. That means that 20 d20 rolls can be replaced with a single d100 table check.
In other cases, rather than rolling lots of small individual probabilities for different things, its possible to have a single roll for a # of things, then a random allocation of which. For example, deadEarth rolls for ability/inability (2 or 12 on 2d6) for each of 100 individual skills in character generation - a roll of 200d6 than has to be done one at a time to pair up the dice. The end result of all this is, however, usually not much different to rolling a small variable number of abilities and inabilities (say d4 of each) and then rolling d100s on a table to determine which skills are affected.  

Another approach is prerolling, where the GM rolls lots of dice in advance then consults a list. Not something I'm terribly fond of, although its been argued that it avoids the interruption of the scene by the dice/break in immersion. Note this doesn't tend to work well with a step die system, since a different chart would need to be consulted for each die type (d6,d8, d20, etc), or for a dice pool system where number of dice varies each time.

A final note: some games are built up with lots of excessive dice rolling on the idea that its 'fun' to roll lots of dice. They can burn in hell - deliberately overengineering a complex system is insane. Situations will arise where even a simple system results in lots of rolling (like large combats), without going out of your way to add mess - and you should aim to use dice and mechanics where necessary to represent something rather than for the hell of it. Multiple dice on the same roll also give more predictable results and so can make doing checks more dull.

Rolling to determine TN.
Games also sometimes have extra unnecessary rolling, with a roll in order to set the odds of success. Because the final chance of an event occurring is the multiplication of the two probabilities, this has the same effect as just setting the final score appropriately to begin with - unless other modifiers apply at some stage, of course.
Examples here include:
World of Synnibarr luck rolls - where a d100 is rolled to find a % that is then rolled against to determine success/failure. 4d10s therefore replicating a coin flip.
In HarnMaster (3E?), the sample monster has a 1d4% chance of something (hatching?) i.e. a 2.5% chance.
In CoC, Azathoth has a roll to determine what his skill is (it might be 100%) and then a skill check against it - which could be replaced with just a single (average) attack %.
This sort of arrangement can arise naturally as a result of multiple rules interacting to simulate something; if the dice rolls together can be solved down to something similar this may be preferable, but that cause is at least some justification.

recent edits: rolls disallowed as too variable, special situations. 21/11 - Hollow Earth Expedition notes.

An interesting case of where an extra roll can't easily be streamlined out is Palladium defense numbers. Palladium gives armour a fixed AR, with a hit roll over the AR needed to damage the roll. The defender can also opt to roll a Parry or Dodge, which then is used as the target number instead of the AR (if its higher). A parry or dodge roll can't be replaced easily with a 'fixed' result since that will either be pointless, or make the AR pointless.

Extended actions

An 'extended action' can be a higher-level resolution system in a game; the hierarchy is perhaps basic action - opposed action - extended action, with extended actions being the basis of e.g. combat, and often Craft or similar tasks. The principal question is how to 'add' the results from individual dice rolls, which might be answered by the Effect subsystem- e.g. in many games beating an opponent to death requires adding together weapon damage (a sort of effect) until it exceeds the target's HP...other sorts of extended checks might simply count a 'successful' roll as 1 unit toward task completion, or a higher roll might contribute more success (SenZar). A roll might also be theoretically accomplishable in one action, with a high but not quite high enough result giving a bonus to the next check (some Rolemaster results).
# rolls permitted may be limited by time, or counts of failures may be tracked (note this discourages lower-skill involvement if multiple PCs are cooperating). Another variant is to track only critical failures.

Interesting subsystems relating to extended actions include:
*SpyCraft has an 'advisor' special ability letting them use an action die to let the advisor take-10 on that number of checks in an extended action, decreasing chances of failure.

*Dying Earth uses a table where an opponent's result (if high) forces an opponent to use more dice rolls from their resource pool.

*Rolemaster chart frequently list a % of completion, allowing continuing action across multiple rounds (barring a disastrous failure triggering a reset).

*3E D&D Craft uses the DC of the check to give GP of progress; a character can voluntarily increase the DC to work faster, but with more chance of failure.

*Dogs in the Vineyard's standard conflict resolution mechanic is extended; it has no system for simple checks however.

*DC Heroes may use cumulative result points (RAPs) for some things, but this is generally awkward in it due to the exponential nature of attributes.

*Fate Core has a contest system that looks relatively interesting - not just dice rolling since aspects/fate point costs/consequences can make the process more complicated. It does look unclear (or somewhat GM fiat) as to when a situation calls for an extended action vs. a single roll. Its abstract general systems can produce odd results when used directly - a chase for example gets a bonus to the athletics check for multiple participants, rather than considering that multiple targets won't be generally much faster, or that some may fall behind.

Some games may have specialized extended action systems of whatever kind. Palladium Arm Wrestling skill (in Mystic China) for example uses a series of rolls (d20+ 1 per 3 PS above 16) with 3 successes in a row required to succeed - first roll steadies the grip, second roll tilts their arm down, third roll slams their hand down into the table. One Marvel Super Heroes adventure, Secret Wars, represents an incredibly difficult action (persuading Galactus to help you) as needing a series of 3 Red Popularity checks, just one being not difficult enough! (perhaps fair enough considering that Karma could be spent on this).

Das Schwarze Auge (The Dark Eye) apparently uses extended rolls as the default procedure for skill checks - for instance a Climbing might be roll of d20 against STR/STR/DEX, with the difficulty of the climb giving the total margin of failure allowed. For the most part this is non-transparent, slow, and the extra rolls provide no information that couldn't have been gained from a single check, although proponents of this sort of system (such as 4E's Skill Challenge system) believe it adds more 'drama' to rolls. For games using 'safety valves', this sort of check can also require more resource burning to achieve. Requiring multiple rolls gives a more predictable outcome (despite less transparency!) but one akin to what would result from just a multidie system.
JAGS uses a very similar system to DSA for 'Drama' rolls, perhaps partly to give a more predictable outcome.

5E D&D has an interesting rule for group checks, where a group task like sneaking is successful if 50% of the party are successful. Therefore tasks aren't automatically becoming harder as number of people increase, and skill ratings for everyone involved remain relevant. Small numbers of PCs with this give wonky results - 2 characters will pass if either succeed (so its easier to sneak with 2 rogues than with one, meaning allowing a group check here is probably disallowed), and four characters have a better chance of success than three (50% of party means either three or four need 2 successes total, with four getting an extra roll to get there). 5E sneaking is thus slightly a problem in that you would expect moving an army to be more difficult than moving a single person - even if 3E dropped the odds too fast. A quick fixit would be for the GM to allow a group check, but increase the DC based on # characters.

"Stupid effing die. I haven't made a skill check yet tonight. Can I use my luck to retest?"
"No Tim, Tanya has "very lucky"; you have "strange luck". There is a difference. She gets the two free retests. You are about to get hosed."
-Midian Dark Fantasy (https://web.archive.org/web/20040610005110/http://lost-souls.servebeer.com/Midian.htm)
 
 
'Luck points' of whatever sort give a player control over the outcomes for their PC. Depending on the game these might be fluffed as 'luck points', 'willpower points' or 'action points' (the PC tries extra hard), represent an application of experience (Over the Edge) or be left as some sort of abstact 'story point'. The fluff mainly affects whether points are vaguely conceivable as being spent in character (i.e. are an 'associated' mechanic, to use Justin Alexander's term) or not; what they can be spent to do affects how believable this is. In terms of fiction, spending a luck point (defined as just 'good fortune') might be described as a near-miss than is recovered at the last minute, or the mechanics can be ignored to treat it like any other roll that was successful the first time.
Purpose-wise, as well as aiding character survival against the odds, a willpower-type interpretation of safety valve points (if not pure luck) can also give a way to factor a character's personality onto rolls, if a system doesn't have more detailed mechanisms that do that (Cortex+, Heart & Souls), since a player can opt to spend points on rolls important to the character (Whether that's desirable is another question, your answer to which depends on your desire for realism and/or difficulty).
Balance-wise, some characters may be given more 'luck points' as a way to compensate them for lower stats/less directly useful characters - e.g. Zander-type 'White Hats' in Buffy [Unisystem] get more Drama Points than 'slayers' and the like.

Depending on the game, points spend may be gone for good, or refresh can be based on certain conditions, or luck points can recover on a per-day, per-game-session, or per-adventure schedule. Points might also be bought with XP even if XP isn't directly used as the luck points (Unisystem, Mutazoids 2nd ed.), or recovered through some other factor. If points are spent permanently then the total is usually not directly connected to any attribute (except perhaps initially). They might be equal to leftover points from character design (SenZar, DC Heroes), rolled randomly (Warhammer 1E/2E), or be a set starting number.

A luck point might add an extra 'success' (common in dice pool systems where, otherwise, difficult tasks are impossible for weaker characters); an extra dice (in dice pool systems); a bonus to a roll (sometimes rolled); an automatically maximized dice roll; or a reroll which can be either mandatory ("the player must take the result regardless, as luck can be either good or bad"- 3E Luck domain) or 'choose the highest'; a reroll could also be against a different target number or with a different bonus. Luck can be measureable as just a number of rerolls, and can also have a bonus value itself in some games (+2 vs. +3, +d8 vs. +d6) or refer to another number as a bonus value (reroll with +Cha modifier).
Some sorts of luck point offer automatic success, while others give a reroll, or reroll with a bonus. Feel-wise, the balance here is between wanting use of a luck point to not be wasted (i.e. a reroll that's worse is anticlimactic), and having it be possible to avoid any risk/danger if a luck point is used (for instance, the argument the designers of Savage Worlds put forward re. 'soaking').
Full rerolls are probably more common in games where rolls are of single dice with very variable results (i.e. 1d20) to counteract the inherent chanciness of the core mechanic. A re-roll is a less powerful boost when more dice are used by default e.g. if rolls are normally 2d10 or a dice pool.
From a player point of view rerolls are particularly strategically valuable for minimizing critical failures and the like - since a critical failure is an uncommon event, a re-roll will almost certainly negate one easily (even if the new roll still isn't sufficient to get a success). Some systems take this into account and either ban rerolls of critical failures (an optional rule in Savage Worlds), or add extra cost to re-rolling particularly poor results (Dying Earth, as part of its core mechanic).
Rerolls (as opposed to a flat bonus) may feel more like a do-over (luck) as opposed to extra effort (willpower), and so be more metagame.
The full impact of spending 'luck points' can vary depending on effect-determination (if a high hit roll also increases damage) or other flow-throughs from rolls (if a higher attack roll also wins initiative, if a higher initiative roll gives more attacks).
Rerolls tend to be either/or, whereas a bonus can be variable - a character might spend several points boosting their roll. The latter has more opportunity for special abilities to modify (e.g. Jack Diamond in the Arkham Horror boardgame has a 'gain an extra bonus die when you spend clue tokens' ability). Rarely a reroll might also get a bonus as well (e.g. Savage Worlds' "elan" edge IIRC).

Luck may be an intrinsic attribute, or a special advantage possessed by only a few characters - more or less depending on whether the tone of a game setting is cinematic or realistic.
Dangerous games which do not use a luck point system are more likely to allow PC raise dead/resurrection (e.g. D&D). Or just encourage GM fudging outside the system :(
In systems that are more tightly integrated/highly evolved, the luck point metagame currency may be the same power points used in the spellcasting system as power/mana (Legends of Anglerre, I think). Conversely, supers games can have Luck as a super power, in which case its less common but using it may cost points off whatever point pool powers normally draw from. A couple of the weirder systems for calculating luck points would be Alternity (where 'last resort points' are based on the Charisma attribute, "Personality", for game balance reasons) or Fuzion (where Luck is a derived stat based on Int+Reflexes.
 
Luck may operate to reduce incoming damage and so increase character survival, allow rerolls of whatever checks the player may choose (whether life-threatening or not), or both. Sometimes there may be basic uses of luck points available to all characters but with specific abilities required to allow points to be spent to boost certain things (e.g. damage rolls or saves as well as skills, etc).
 
For some systems, luck points may be a necessary 'kludge' to getting the right results: Savage Worlds' bennies help mitigate what could otherwise be a quite deadly system due to frequent open-ended damage rolls, while in DC Heroes 1E Batman would automatically kill/knock out the Joker with one punch, unless the latter spent points to boost his defense. FATE or Marvel Heroic rely on application of aspects/assets (by point burning) to give mechanical weight to bits of the scene or character the players/GM deem relevant.  Some games deliberately mitigate lethality by removing 'save-or-die' effects [4E], instead having multiple rolls required before a death effect applies (such as beholder petrification in 4E requiring multiple saving throws over a couple of rounds) but giving characters spendable rerolls also works. IIRC, FATE Core often does both.
 
There are pros and cons to having luck points work both for absorbing damage (Savage Worlds, Mutants and Masterminds) and rerolling checks. If these are the same, then there may be an incentive for players to hoard points, not spending them outside of combat. On the other hand, if soaking and other rolling use the same resource, there is more synergy between attacks that cause damage, and attacks that force a saving throw - avoiding issues such as fighters and wizards not cooperating in combat (i.e. if the wizard repeatedly save-or-dies a monster for several rounds while the fighter does damage, they're both effectively attacking separate hit point tracks).

 Some systems also take 'luck points' further, allowing PCs to co-opt GMing or provide control over some aspect of game reality e.g. with GM approval a character can spend hero points to definitely find a beaker of acid nearby, while fighting in the mad scientists' laboratory). These include some Fate variants and DC Heroes.
Some interesting discussion here (http://www.therpgsite.com/showthread.php?35443-Bonus-Currencies-and-Avoiding-the-Narrative-Stance&p=926540#post926540) by Lunamancer on 'story' effects of luck points and how points tend to be spent to avoid some plot complications rather than survive them. (points tend to be spent early to block complications, so a merciful GM giving some way out of a tough situation may give different results than luck points. Also, perhaps powerful but gone-for-good points have a different incentive structure than just 'rerolls' which tend to be used early on).

Note also some RPGs have Luck attributes that are not spent and so aren't 'safety valves': in this group we could include Luck in Tunnels and Trolls (which is instead analogous to a 'saving throw') or Bad Stuff in Amber (which isn't rolled but helps influence GM narration). T&T Deluxe does however have a 'Better Lucky Than Good' spell that lets a character (for 4 Wiz) use LK instead of any other attribute for a saving throw.
 
General Notes
The thread here has some more discussion about 'hero points' that may be of interest: http://www.therpgsite.com/showthread.php?t=13530
Likewise this one brings up an idea that GM control of luck point flow is an issue, and that a resource giving a bonus reflects willpower (extra effort) better, while a reroll more resembles luck (metagame). http://www.therpgsite.com/showthread.php?t=26416
Non-Point-Based Resources: TORG/MasterBook's 'Drama Deck' gives cards that give some metagame effect on game results.

More or less every safety valve system (I know of) ignores the 'stakes' of a roll (how important that roll was) in determining its cost to reroll, apart from very basic limits on types of checks that a reroll can be applied to in some cases (e.g. rerolls not being useable for saves & only skill checks, or not on damage)

A situation in a game with safety valves sometimes calls for multiple rolls to resolve an event, which makes it harder to accomplish and - also - requires additional resources to pull off artificially, with resources burned to augment each roll. (as noted in roll-under) Island of the Lizard King for Fighting Fantasy has a difficult task that requires two Tests for Luck, and hence costs 2 Luck, while persuading Galactus in one TSR adventure needs three separate Red successes, and so forcing a success on the roll costs a significant chunk of Karma.

Generally a luck point is probably assumed to be spent at the moment in play it occurs, which would often limit their usage to checks which happen 'now'. For instance, if you're rolling a Wisdom check to see if you packed a whatsit in your bag earlier that would help in this situation, whether you should be able to spend a luck point is debateable since it relates to an action that occurred earlier. It might be OK if luck points are metagame anyway, or the GM might take a dim view of this as a sort of time travel.

Examples of Safety Valve Systems


Damage-mitigation-only systems
*Warhammer - has "Fate points" which let characters survive a lethal circumstance. Once used they're gone for good.
*Apocalypse World lets a character soak some incoming damage by taking a broken condition to one of their stats, reducing it by -1 permanently. (This also reminded me of Rage in Werewolf, where a Garou could not die by spending a Rage point and rolling on the 'battlescars' table).
*Fighting Fantasy gives PCs a Luck score with a successful roll giving 1/2 damage and a failed roll double damage (it is slightly more useful to characters with even Stamina scores. Each time it is used the score takes a point of temporary damage. It does have one function beyond just damage-mitigation: it can be used deliberately in combat to deal 2x damage with a successful check (but half damage on a failure) i.e. it adds variation to the normally-fixed damage result (usually 2 points).
*Mutants & Masterminds/True20 has 'conviction' points allowing reroll of any d20 roll. These do more than just altering damage, but that is a very common use, since Toughness saves are made with d20 (it uses these in place of hit points).

General Task Bonuses & Rerolls
*TORG (possibilities): while this give PCs ability to manipulate reality, they are interesting in that they are used in-character by PCs ("Storm Knights"), who have a limited ability to manipulate reality and understand that they have a limited supply of "possibility energy". (the Drama Deck card system is still quite metagame, however)
*HOL (Human Occupied Landfill) gives the players as a group a reserve of "Grace of God" points - how many is determined by rolling d6. A player who attempts to use a GOG point when the pool is exhausted gets the "Wrath of God" point instead.
*Weapons of the Gods lets characters store up a limited number of die rolls for later ("the river"). This is complicated slightly by it using a One-Roll-Engine-esque match-counting system; higher rolls are slightly better but various rolls in storage let a character bolster more rolls (improving a roll of 2-2 requires another 2, while 7-7-7 needs another 7). (This sort of mechanic works well for it since its not entirely 'all or nothing' as it would be in a system where only 1 die is rolled; die 'storage' also obviously would be a problem in a 'step die' system since replacing a d6 with a stored d10 would be fairly unfair, needing complex mapping or requiring a roll be a minimum height - giving synergy with other powers temporarily increasing step)
*The "2d20 system" (i.e. Mutant Chronicles, the Conan game in kickstarter) has a system of "Momentum" which lets characters store 'successes' for later, rather than specific die rolls.
*Dragonlance: the 5th Age (the SAGA system) uses cards instead of dice, with players choosing which number to play from their hand. Hence players are always using the 'roll' they think is useful and/or dramatically appropriate.
*Shadowrun 4E lets characters spend "Edge" either before or after a roll to get bonus dice (equal to their Edge score), and 6s give an extra roll. If a character declares their use of Edge before the first roll is made, the secondary benefit (6s give an extra die) applies to the entire dice pool, while if declared afterward it applies only to the bonus Edge dice.
Shadowrun 1e-3e (maybe 4e, not sure) is also notable for having an 'action pool' of dice in combat which can be spent in various ways (attack, dodge, soak; not initiative) and which refresh each round.
*Earthdawn 1E gives characters different "Karma action dice" based on race; a Obsidiman who spends a Karma gets only +d4 to their total; a human or ork gets +d8 while a tiny windling would get +d10; an additional game balancing mechanism (and a way to differentiate levels of luckiness that doesn't exist if luck only grants rerolls -at least if the new roll is by default at the original odds). Note that spending Karma here is unreliable due to the bonus being rolled. In 1E at least, Karma points seem to be limited to use on only a few possible actions; one of the major benefits of levelling up is the ability to spend Karma on particular class-related die rolls. Some magical rituals may also cost Karma. Each class has a described "karma ritual" for recharge, though the fluff is largely irrelevant (effectively its a daily recharging).
*Risus similarly has no "luck point" score, but the function of a safety valve is achieved by "pumping". Each character score can add a number of bonus dice for a turn, after which the score is reduced by that much. In Risus' quite abstract system, a character may then be able to carry on without a huge disadvantage by switching to another, vaguely related skill - The viking [4]/swashbuckler [3] who "berserks" for an extra 3 dice in combat drops to Viking [1], but can keep fighting on without much penalty using their Swashbuckler rating.
*Underground (a disturbing cousin of DC Heroes) is unusual for awarding luck points for high die rolls (any natural rolls of 24+ on 2d10/doubles roll up) as well as good play.
*HackMaster gives characters 'Honor points', initially based off stats and later awarded for defending their reputation or class-based behaviour; these can be burned for a reroll. Honor affects NPC reactions to the character and based on the characters level they can have 'too much honor' or 'dishonor'.
*4th edition D&D has "Action Points" which are somewhat different to the other varieties listed, granting an additional action when spent. This is perhaps about as good as a reroll in many cases - although if a character has used up a particular 'power' it isn't available for the second attempt, or on the plus side potentially having 2 successful actions in a round. A character can also use an action point to recover from (rather than prevent) damage by using a 'second wind' & spending a healing surge, and a number of effects can add a bonus to these actions (i.e. paragon abilities or the human 'Action Surge' feat). Action points are gained each second encounter and reset to 1 after resting, buffering characters against the '5 minute workday'. An early 2014/late 2013 dragon magazine reportedly adds other uses for action points, e.g. re-using encounter powers.
(An effect giving extra actions can also be gotten with rerolls in games where high initiative grants bonus attacks such as Midian Dark Fantasy, quoted)
*AIF, a freerpg allows characters to bring forward dice from the next round (sometimes giving similar results to how other games, e.g. HERO let characters perform a Dodge by 'aborting' next rounds' action). It also lets characters lower their pool this round to add dice to next round. Its perhaps also sort-of similar to the resource dice pools of games like Dogs In The Vineyard.
*Al-Qadim for AD&D 2E (the 'land of fate') let characters 'call upon fate' making a % roll to see if the situation improved. A bad roll instead worsened the situation.
*Casefile: Zodiac (freerpg I think) uses a 'blackjack' roll-under system where higher is better until you roll over the target number and 'go bust'. Bonus dice can increase score but pushing it over the target number causes bursting as usual.
*Old School Hack reportedly has a pool of bonus dice in the centre of the table which can be awarded by players to other players, rather than having awards be GM-controlled.
*Savage Worlds - has 'bennies' which can be spent to either reroll checks or 'soak' damage. Best use of 'bennies' can require some metagame calculation, in particular a large damage roll may be better off handled with Incapacitation Roll rerolls that direct 'soak' as novice players are likely to do. SW sometimes uses odd die mechanisms that prevent characters from rerolling such as a fixed 50% chance to rise as a vampire if killed by one, the card-based initiative, or slightly different damage rules (the 'No Mercy' edge is needed to reroll damage rolls; probably not terribly optimal). (this sort of way of siloing subsystems isn't really that uncommon - see bonus and penalty accumulation post later)
*FantasyCraft has action dice which add bonuses to rolls (e.g. +d6). Its interesting in having abilities that interact with this to define specific character capabilities, e.g. a human character can have a 'Talent' that lets them double-boost rolls related to their area of competency e.g. spend two bonus dice to boost Strength rolls, or a wizard can have a 'practiced spellcasting' which gives them a refund on a spend action die if the roll still fails (against all targets). Rune knights have a 'battle mage' ability which after an action die is spent on attack/spellcasting, applies again the next round to the other type, encouraging a mix of both (3E has a similar feat which applies a save DC/attack benefit without a resource cost).
In addition to action points it also has distinct 'fortune' and 'edge' subsystems (allowing building up & then using points in connection with more specific families of feats).
Spycraft (its predecessor) has untrained maximums on skill checks (>15 requires training) which can be bypassed by spending 3 action dice. (the rule would potentially be a bad idea without a bypass like this).
*Sovereign Stone (the precursor of the Cortex system) let characters "exert", taking Stun damage, to roll an extra dice along with the normal 2 dice, prior to the roll being made. Characters could also use "last ditch exertion" after the dice were rolling, with 1 point of damage adding +1 to the roll (more expensive, given that 1 pt would have bought a d4).
This method could potentially lead to alot of metagame tactical evaluation as to whether PCs will suffer more damage from failing the roll or exerting themselves, as well as making healing magic a free source of 'luck points'. As it ties together an abstraction (dice rolls) with something concrete (damage) it can also lead to bizarre results and justifications - e.g. characters taking damage from upping their dice rolls to find information at the library.
Cortex: Assets (advantages) in Cortex taken at D6 level or more often are specified to add a bonus (+2 step to the dice) to rolls, if plot points are spent before the roll, in addition to the assets' normal bonus i.e. the asset die code.
The 3.x fatespinner has a mechanism for representing luck which doesn't modify rolls directly: they can subtract points from a spell save DC, making it easier to save, which is saved as 'spin' in order to boost the save DCs of other spells later.
Legends of the Wulin has 'Joss' which is interesting in that the PC starts with 3 points of it, opting to divide it between Chivalrous (positive for them, an extra die for a round) and Malicious (reduces enemy dice pool by a die).
Barbarians of Lemuria gives characters 5 'hero points' initially which can be spent to either avoid death, increase damage, or raise a die roll. These are per-adventure, however, rather than automatic full replentishment the GM may award 'a point or two less' 'if the Saga went badly'.
*DC Adventures [M&M 3E] has an 'extra effort' rule where a character can become fatigued/exhausted to add a bonus to a dice roll, or other bonus (stat increase or special effect). A Hero Point can be spent to negate the fatigue. This is mainly used for the power stunts (its interesting to compare this with MSH where the stunting uses a roll, and points are spent to increase the stunt roll instead of directly spending points for an automatic special effect).
*An interesting "Doom" houserule for any system is described here: http://www.therpgsite.com/showthread.php?p=831281#post831281 (http://www.therpgsite.com/showthread.php?p=831281#post831281)
*FUDGE has 'FUDGE points' (allowing rerolls IIRC?). Not terribly useful in combat? While it has a damage system, the damage spiral is steep enough that a system was proposed (here (https://web.archive.org/web/20071008184646/http://www.fudgefactor.org/2005/08/cinematic-damage-alternatives.html)) to have extra 'hit points' as well which operate much like a safety valve -  suggesting these be used alongside and separate to Fudge points because 'most GMs keep tight rein on Fudge points' and to prevent abuse of points outside combat.
*fairly obscure freerpg World of Terath is d% roll-under, with each 'ki point' spent adding 100% to chance of success; a 'critical' is 1/10th of normal skill so ki is often spent in multiples to increase chance of a crit.
*an interesting non-RPG system example, the recent Warhammer Quest card game lets characters use aid actions on each other to get bonus auto-success tokens, with tokens however being assigned to specific actions only (each player having four: Aid, Attack, Rest, Explore).
*Low Fantasy Gaming has skills that only add +1 to the character's (3-18) stat for rolling under. However, if a character has a Skill they can spend a 'reroll' from a reroll pool equal to their level. This approach is slightly a problem due to its race system (where a given race gets 'advantage' on stat checks instead of a stat mod) - race gives much more of an improvement in ability than does skill.

Advancement Currencies
*DC Heroes ("hero points"); these are integrated with the advancement currency of the game i.e. they also work as 'xp'. The system here was intended to make sure heroes did not advance with experience (as genre emulation); the perhaps unfortunate effect of this is that a character in an 'unbalanced' party struggling to survive burns hero points, while the unbalanced party members can save resources to advance faster. Points here have various uses including: pumping attribute values (max. of double), building gadgets, resisting successful social attacks and powering certain metagame abilities such as Omni-Connection, as well as (with GM veto) minor reality editing. Points are spent frequently and there are opposed bidding rules. Characters usually can't spend points on rolls to avoid 'disadvantages', such as stopping a psychological complication from manifesting, presumably since a character could use points from taking the disadvantage to negate it even though that wouldn't be point-efficient in the long run.
While "hero points" act as a general use safety valve, 3E is interesting in having a "Lucky" advantage that lets a character get an OV/RV shift once per adventure (cost 15 to buy initially so expensive, but multiple use and more importantly, can be used in various situations where hero points can't be spent, like resisting disadvantages or on Danger Sense rolls. Compare to say Savage Worlds where there's a "lucky" advantage but it just gives an extra 'bennie'.
*Marvel Super Heroes (Karma) has a similar setup (see below); GURPS also has an optional rule whereby character points can be spent to boost rolls.
*Over The Edge represents experience as a pool of re-roll dice which can be spent each session; they can also be traded in for permanent increases. Unlike the two systems above the character never has to choose between using a resource temporarily or getting a permanent bonus, however.
*Savage Worlds - Older versions of this let a character make a roll for each unspent bennie at the end of a session to convert it to XP; this was dropped to encourage players to use all their bennies (it also has problems with Luck, which gave an extra bennie, giving extra points over the long-term).
*SenZar lets a character spend a character point permanently to act as if they rolled a perfect "20" on a d20 roll. (Character points are used to buy merits or raise stats, but were awarded separately to the XP used to gain levels). It also has a 'luckster' class which can burn a large number of magic points temporarily to achieve the same effect.

Unintended Interaction of Safety Valves with advancement: some games have randomized advancement, such as random-roll hit points or checks for attribute increases. It may be possible to spend luck to assist on these rolls and so get permanent enhancements from rerolls - this is usually an undesirable result however unless the safety valve points are spent permanently, in which case it may be OK. As well as rewarding system mastery around purely metagame factors, this sort of interaction can be undesirable since per-session or per-day luck recovery can give ambiguous or excessive numbers of rerolls in downtime or between sessions. Safety valves can likewise interfere with mechanics where character gains incur a risk (e.g. where PCs can gain a stat boost by drinking from a magic fountain or whatnot but then have to roll for death/side effects)

Roleplay-based Bonuses
*Storyteller (Willpower): willpower here is an attribute, recovered through acting in accordance with a characters' Nature. It provides a single automatic success, added to the dice pool - in original Vampire this made it particularly useful on high-difficulty rolls (e.g. difficulty 10, which was as likely to succeed as botch regardless of dice pool). Since 'willpower' is an attribute all characters (PC or NPC) have it, though most GMs neglects to spend Willpower for NPCs/enemy combatants all that often.
While its classified here as 'roleplay based' its actually just the recovery of Willpower governed by the characters' roleplaying - point expenditure isn't directly affected by personality.
(A dice pool system could also have luck give (less reliable) extra dice, of course [Arkham Horror - though technically a boardgame] lets characters spend 'clue tokens' to roll extra dice.)
One oWoD storyteller game, Mage, has a 'Destiny' background which plugs into the willpower by letting a character roll dice = background (diff. 8) to recover Willpower when appropriate to their destiny, in most cases including to avoid dying. There is also a separate 'Luck' merit, which just grants a total reroll (and a 'Charmed Existence' merit that just reduces chance of botching by taking away a single roll of '1').
In my experience large Willpower ratings seem to be not-especially useful, just because refreshing Willpower is so difficult - though this is subject to GM whim, and with guidelines fuzzy enough that the GM could fix if they noticed. Basically, if you can only get back a couple of Willpower, you can only spend a couple of Willpower - so there isn't much difference between 6 and a 10 here, apart from the odd roll of the rating itself
*Exalted has a series of 'virtues'; as well as spending Willpower similarly to Storyteller, a character can spend a Willpower to roll their virtue rating as bonus dice. However, virtues can also limit conflicting behaviour.
*Deathwatch, a Warhammer 40K rpg about space warriors, has Fate points, as well as 'demeanors' like 'scornful' or 'calculating' which give the character an equivalent bonus 1/session on a task related to the demeanor (Interesting in that its a more direct link between playing personality and dice bonus than in Storyteller, though it needs to be in addition to Fate points, as there's no guarantee a 'demeanor' is relevant enough to save a character's bacon).
*FATE (Fate points) gives characters points for having a negative complication of a character's Aspect come into play (Aspects working as both advantages and disadvantages). Scaling up from this, 'Capes, Cowls and Villains Foul' has one Complication per character including things like Kryptonite susceptibility, klutziness, or a loved one that gets in the way frequenntly) that the player can invoke to disable the PC for 3 rounds but grant a point of 'editorial control' (good for a reroll).
*Marvel Super Heroes lets the PC/NPC completely 'call' the result of a die roll in advance by spending Karma. They declare the final result before rolling, which might be only a success ("Green Result") or might be a higher Yellow or Red result. The dice are then rolled and the difference between the roll and the minimum necessary is the Karma cost, with a minimum cost of 10 if the character would've made it without the attempt (e.g. with an Incredible score, a character would need 91+ on d100 to get a Red result; if they actually rolled only a 67, the cost is [91-67], or 24 Karma points.
Specific rules on how Karma can be used sometimes reflect genre conventions, but as with Vampire, I've largely grouped this in the 'narrative' category because they way points are saved up is RP driven.
*Icons (essentially a FATE rebuild of MSH) has similar rules around use of 'Determination' points. It adds the extra complication that it can only be spent if a roll is one-try only, or has been tried and failed previously, preventing characters from 'alpha striking' (as noted by Soylent Green). Both MSH and Icons allow parties to form group pools of Karma or determination which all members of a hero team can draw off; Icons also suggests using or burning team determination to generate physical resources (team vehicles, HQs, needed devices).
*HarnMaster has 'piety points' which are randomly rolled (at a penalty if a character chooses a deity at odds with their own morality). These are earned for pious acts and, apparently, expended for divine intervention (I never got whichever supplement fully explained this). Atheist characters get nada.
*The Dying Earth (and relatedly, Gumshoe) systems have no single "luck point" score, but all of a characters skills individually function as pools of rerolls or bonuses, with some odd effects. Recharge conditions are assigned for each score.
*5E D&D: characters may gain 'inspiration' (allowing advantage on a roll after it is made i.e. a reroll) as a result of playing bonds, ideals, personality traits or flaws at GM discretion. A character with inspiration may also transfer it to another character (if they play well). As well as a numerical bonus, advantage can trigger extra abilities e.g. sneak attack can apply to damage when a character has advantage in combat (weirdly, some bonuses hence allow sneak attack while others, such as fighter precision manuever, boost the to-hit by as much but just don't).
*Invulnerable lets characters earn Determination based on things related to their characters' Motivation. The interesting thing here though IMHO is that uses of Determination include letting characters with 'hyper-attributes' (powers boosting an attribute directly) automatically win contests against characters who aren't hyper; in spite of hyper-attributes normally being rated as extra dice so that normals always have a chance.
*characters may get a GM-assigned 'role playing bonus' to a check - for instance, in My Life With Master the GM may give out a bonus "sincerity" or "desperation" die at his option [cf. use of player skill, non-resource-based mechanics section].
 
Narrative Control systems
Narrative control usage: sometimes games allow reality adjustments for using 'safety valve' points. Note that's at odds with the reserve having an in-world representation (e.g. a character shouldn't be able to "Willpower"  a contact into existence), but can be a fairly common ad-on to a basic system. FantasyCraft can allow it, as does Thrilling Tales supplement for Savage Worlds. Other examples around this feature:
*Superbabes lets PCs take "Bimbo Points" to succeed on rolls or break the rules. At the start of the adventure, a roll less than a PCs current Bimbo Point total entitles the GM to a roll on the "Bimbo Events" table, which includes such entries as "cult wishes to sacrifice the character", "character gains 10 pounds" and "costume destroyed in battle". The roll of a bimbo event resets their points back to zero.
*FATE -many versions may enter into this with negotiation over some sorts of compels and the like.

GM-side resource systems:
 On the other side of the screen, luck points for NPCs may be controlled by a parallel system to what PCs have, or a different system (e.g. the GM may have a single reserve of points for all NPCs, or no points). Both PCs and NPCs are going to be tied into using the same system if "luck points" are based off a basic character attribute.
Where GMs have large supplies of 'luck points', GM fudging of dice rolls is effectively built into the system legally; it also may be problematic that PCs use the same reserve for the whole adventure, while fresh NPCs may appear in each encounter.
*DC Heroes (see above for basics) gives the GM a potentially unlimited supply of hero points; NPCs follow the same rules as the heroes and can have whatever number of points the GM deems appropriate (sample NPCs can have up to 200). Bidding wars are possible between PCs and bad guys. As noted in the old Dragon #165 review (http://www.allenvarney.com/rev_02.html): "there's always a heavy Hero Point flow during play. Sometimes so many get blown in a single phase, maybe on a single punch, that it's like the Weimar Republic, where townspeople hauled hyper-inflated Deutschmarks in wheelbarrows to buy a loaf of bread."
*Savage Worlds gives the GM a limited supply of 'bennies'; 2 plus 2 for each 'wild card' NPC (archvillains and the like).
*SenZar lets the GM give exceptional NPCs only 'Fate Points'; if the players win, they get the bad guy's Fate Points.
*MSH gives bad guys a fixed karma supply equal to the sum of a character's mental attributes when they enter play; however bad guys have different spending rules (and refresh rules) to good guys, limiting their use except in dramatic escapes or story-furthering events.
*Cortex+ Marvel Heroic (MHR) gives the GM a 'doom pool' starting at 2d6, more for important scenes, which resets each scene and can increase e.g. if PCs perform certain actions or roll 1s on their dice. Another twist to this is that the Doom Pool is used as an opposing roll when no opponent with scores is available.
*Fighting Fantasy gives PCs a Luck score. NPCs were not usually given a Luck, making it unclear how they interact with effects that require a test on it (AFF 2E eventually clarifies they use Skill, for involuntary checks only).

Non-Resource-Based "Safety Valves"
Systems can also allow for characters to reduce their chances of failure by metagame means not involving point spending, or in-game means. For example:
*some games (or GMs) may allow a bonus to a roll if a player can describe well how their character is performing the action. For instance, jumping a chasm might be easier if a character throws their heavy items across first, or climbing may be easier if a character throws up a rope using a grappling hook and takes off their armour.
*Take-10 in 3E D&D lets a character pass a mundane skill or ability check by forsaking any chance of rolling higher.
*Call of Cthulhu 7E lets a character re-roll a skill check, but with the stakes increasing (such as a failed attempt to open a door alerting monsters on the other side).
*Gumshoe eliminates failed investigation rolls entirely - characters always find clues.
*Level-based (D20/D&D derived) games rarely have point spending on dice rolls. This may be partly just tradition, but its also possible to consider Levels as a sort of 'safety valve' mechanism, in and of themselves. An experienced character becomes a protagonist and gets higher numbers across the board giving them more success/survivability. Some D&D editions claim that 'luck' is a factor accounting for a portion of the character's HP total. In a sense having Han Solo be a high-level Smuggler in D20 Star Wars gives some results similar to giving him CPs to spend in WEG D6 Star Wars.

Edit history: Extra notes on Willpower (*); FF (*), rerolls and special abilities (*), invulnerable (*), story twists being avoided by luck points (*).

Moving along into combat...which probably means I've skipped a few things, but its an easy few topics and I'm lazy...
 
Normally a round is only a few seconds, from 3 seconds (Cyberpunk) to 6 seconds (3.x D&D) to 15 seconds (Palladium). AD&D uses minute-long rounds but with most sword swings abstracted away as being blocked, except during surprise rounds where a character can instead perform a full round worth of attacks each segment. Tunnels and Trolls has 2-minute-long combat rounds, which are quite abstract. I think – but not quite sure – that Amber runs combat largely through GM fiat or has subjectively defined rounds which could potentially be much longer. EABA v2 reportedly includes the idea of 'Turn Mod', where the real-world length of a round increases each round, allowing more shots etc. (to fast-forward through stalemate situations ?). Full Light, Full Steam uses a single opposed roll to resolve a whole combat - much like how most games handle e.g. routine skill checks - and so doesn't have 'rounds' per se.
Length of rounds does affect design choices as regards fatigue (which becomes more of a concern where rounds are longer) and movement (longer rounds tend to allow more movement and so requires less rules controlling this). Longer rounds usually permit more actions in each.
 
Usually an initiative system tells a character what they can do during a round. A couple of games (Fighting Fantasy, Tunnels and Trolls) have rounds where everything is simultaneous – both sides roll an attack total and the loser takes damage (though in T&T spells and then missile attacks are resolved before all melee; timing for other events in the round is not normally defined, and need only be calculated in special cases - the solo adventures using various procedures).
In One-Roll-Engine games such as Godlike, initiative is determined as part of the combat roll so while all players roll individually at the same time, combat rolls do take effect in a sequence. Pendragon is similar - highest successful skill roll goes first. (These sort of games generally need additional rules to determine where 'automatic' actions, those not requiring a roll, go in the action sequence - I could however imagine a system where everyone gets an automatic action + a dice action and automatic actions resolving first was a feature not a bug, or last such that volunteering to roll the skill check makes it go faster but risks botching it).

Most other games have characters acting in sequence, which may be determined every round (most older games, Savage Worlds), or just once per combat (3E D&D and many recent games); Palladium compromises with one initiative roll per combat but with a round being several turns of 'attacks'. Cortex keeps the same initiative for the whole combat, but a character can spend a 'plot point' to reroll (taking higher only) in a later round. Hazard Studios' Supers! normally keeps initiative to later rounds, except loss of the initiative stat [Reaction] can force a re-roll. Round-by-round initiative can have tactical effects e.g. a penalty that lasts for one round (e.g. from Taunt in Savage Worlds) may be irrelevant if the target wins initiative the next round and recovers.

Determining order can be handled in various ways, handled by either counting up or counting down:
 
*Round Robin – more a boardgame feature, but it is possible for players to resolve actions clockwise or counter-clockwise around the table, based on where the players are sitting. Doesn’t work for virtual environments,and may be unfair. Treating the GM as a player here means all the monsters go at once. Might be combined with Dex Countdown if the players are willing to be seated in order of Dexterity. Doesn't work in online environments like Roll20.
 
*Dexterity Countdown (Highest goes first): Holmes D&D, Dragon Warriors, Arduin and SenZar use a Dexterity Countdown system where characters go from highest to lowest Dex (SenZar's system is also complicated by using 'phases' however- see below). This method requires all monsters have a defined Dexterity score (they don't get one in Holmes, or for Dragon Warriors either...presumably this is meant to be rolled on 3d6). While fast, it is predictable and IMHO somewhat unsatisfying.
Unlike randomized initiative systems, a countdown system usually can't have penalties for going later (e.g. 'flatfootedness' in 3E, or being unable to perform interrupt actions as in JAGS) since the determinacy of the fixed order makes this somewhat unfair.
0D&D has a Dex-based initiative system in Eldritch Wizardry, I believe predating Holmes; this actually does include some randomness via an effective Dex adjustment for being surprised or completely surprised (-4), as well as armour and action adjustments; there is also a table for 'phase' derived from the adjusted Dex which might be necessary if Dex scores are similar or for very high scores (which could allow 2 actions). As noted under multiple actions, Arduin also gives higher DEX to give multiple actions (if double the opponent).
Fate Core uses countdown based off Notice skill rating. Trail of Cthulhu reportedly uses countdown based on the (current?) skill pool for the characters' actions (more complicated in that the initiative resulting can be a factor when choosing actions).
Highest-goes-first is fairly often used as a secondary, tie-breaking system in a conventional die-roll-based initiative system.


*a simple die roll (Initiative Roll) –usually an additive roll, more or less regardless of what the games’ core mechanic is. Initiative rolls need to handle opposed rolls (ordering several opponents usually - unless wholly side-based), and it also needs to be reasonably fast to resolve (e.g. no tables).
Interesting elaborations here:
-Rolemaster lets characters get a bonus to initiative by getting a penalty to their action.
-3E/4E D&D uses the same initiative roll every round, meaning that durations measured in rounds can be tracked as expiring on the character’s next turn.
-Savage Worlds uses standard playing cards to determine initiative, with some draws (Jokers) granting a character additional bonuses. Doing this denies "wild card" PCs their normal bonuses against NPCs - they don't receive the extra Wild Die - as well as making initiative non-stat-based (certain Edges only give a character extra draws or redraws, making them more likely to go first and increasing their chance of getting a Joker).
Usually only the card number is really important, though 'suit' breaks ties - there is a 'Monologuer' hindrance that makes a character stop and rant if their card is a 'club' however.
-Warhammer 3E encourages teamwork by allowing PCs to exchange initiative rolls.
-A couple of games including Marvel Super Heroes, AD&D-2 (unless using optional rules), and TORG have side-based initiative rather than individual initiative, with players generally free to determine their precise order amongst themselves; similar to the ‘exchanging rolls’ option except that monsters can’t spoil their plans. The Torg roleplaying game (and successors, Shatterzone and Masterbook) used a "per side" initiative, splitting the combat into Heroes and Villains. Which side had initiative was determined by a card drawn from the Drama Deck. The Initiative line listed which side would go first, and sometimes detailed a special effect that applied to one side or the other. The game distinguished between Standard scenes, in which there was a 50/50 split between Heroes and Villains, and Dramatic scenes, in which Villains won initiative about 2/3rds of the time.
-the 'Advantage system' (actually just a houserule by Raven McCracken for whatever system), rolls one initiative die for each attack a character has, with each attack acting on the appropriate initiative. Not too dissimilarly, LegendQuest lets two-weapon fighting characters roll Initiative for each weapon separately. 'Dark Fantasy' also does this; however, it also notes a TWF character can only attack with the primary weapon unless at least one initiative roll beats the opponents'.
-Shadowrun 4E a character can fumble initiative, which results in them going last against someone with the same total initiative (on a 'glitch')(might actually be relevant since total initiative is Initiative score + the successes on the initiative roll), and take a penalty at GM discretion. They also lose an extra action on a 'critical glitch' (only if they have multiple actions).  
-in Hackmaster (revised 5th ed?) a character hit by a weapon can act 2 seconds/initiative points later, probably increasing their initial initiative roll.
-Hackmaster (http://www.kenzerco.com/hackmaster/downloads/HMPHB_illustrated_example.pdf) also has a 'mitigating surprise' rule, whereby a character can assist another character in noticing ambush, in which case their initiative rolls are averaged e.g. a PC with '5' helping a PC with '11' would reset both to initiative 8.

Rolled initiative can interact weirdly with surprise unless the GM is careful. Often someone initiating trouble will get a 'free go' first; if they also then roll initiative normally, the GM might be inclined to have a 'low' roll stand as-is, while a 'high' roll might be interpreted as being the next turn, i.e. actually later. A fix would be to have a surprise attack be set to a good initiative, instead of an extra turn (Hackmaster also does this; e.g. lower is better and an ambush goes off on "1").

*Phases – a more elaborate version of Countdown allowing for multiple actions, seen in e.g. HERO. Here the round has 12 (1 second long) segments; a character with SPD 1 acts in segment 7, a character with SPD 2 in segments 6 and 12, a character with SPD 3 in 4, 8 and 12, and so on. In HERO, Initiative rolls still order actions within a phase; phases likely require some additional method for handling exact timing.
Another example would be SenZar; this has phases 1-10, with characters acting in Speed order ("Dex Countdown" method) within each Phase. Unlike HERO a character with multiple actions in SenZar has actions in the first phases of the round; e.g. a character with 3 attacks goes in Phase1, Phase2 and Phase3. This can also be seen to be quite similar to Palladium's system (where all 1st attacks go, then all 2nd attacks, and so on) except without an initiative roll). While it uses the DEX to countdown within each phase, characters never gain extra actions for high DEX (SPD) in SenZar as they do in some other systems like Arduin, or OD&D w/ eldritch wizardry; this is solely determined by combat skill level.
 
*Strike ranks – older Runequest typically determined who went first based on reach, with weapons able to act again after a certain number of “strike ranks”. Rounds may still be kept, however; see next pattern.
 
*Continuous Initiative- a few systems (e.g. Exalted) do not divide combat into rounds. Instead actions continuously count up. In this system any action will take a certain number of 'ticks' or 'segments' - similar to strike ranks. This lets faster weapons/actions go more often; also there are no weird "metagame" effects from round structure - compare to how in a round system with initiative rolled each round, how a spell or effect with duration that lasts "until the end of the round" or "until your next turn" goes away sooner (or sooner on average) if triggered toward the end of the round. Time between actions might be fixed or might be rolled (e.g. in the Omnifray system when a character rolls d12+reaction time to see how many 0.1 second increments before they next act).
 
*If-Action systems- once seen in a friends homebrew system, every character rolls and only the one character with the best roll receives an action. Losers get a bonus each round they lose, until they finally get a turn. Painful, as this generates initiative rolls equal to the number of combatants per action, instead of one initiative roll per action (most systems), one per combatant (the 3E system) or no rolls at all (Dex countdown or round robin systems).
 
*Tagging- Marvel Heroic Roleplaying (MHR) selects one participant as having the initiative; they then select the next person (either ally or enemy) and so on until all participants have been activated. This is a strange mechanism unlike anything seen in nature; like much of MHR it generates complex metagame tactics whereby characters may try to breakup opponent tactics based on specific strike orders, or may activate the enemies before allies to prevent an enemy going last and seizing the advantage for next round.
 
*Bidding-potentially characters could bid some resource to decide who goes first (not sure if any RPG systems do this; happens in some boardgames, I think.).(edit: proposed for David Johansen's "World of Disney (http://www.therpgsite.com/showthread.php?t=28015)" system, with characters choosing a difficulty penalty ('risk') to see who goes first.
 
*player declaration (BASH ??) - the character declaring an aggressive action automatically goes first. Cortex also does this (e.g. Supernatural); the initiator can do one brief surprise action, then initiative is rolled.
 
*GM-determined initiative - e.g. Dungeon World uses GM arbitration to determine who goes when; combats are not strictly speaking in rounds, just turns for each character, so one character may get multiple turns (though more alternation is generally encouraged) making this an ad hoc version of 'if-action'. Monster results may occur 'within' a PCs turn as a result of bad rolling, making more actions not necessarily good.
Amber is also GM-arbitrated, although its core mechanic being an opposed comparison (and without a detailed 'move' structure forcing character-by-character resolution) it might be closer to an initiativeless system.

*Level-based initiative: 'Sharp Swords and Sinister Spells determines initiative based on the Level/Hit dice of opponents. If a player character ties in HD with an opponent they (the PC) make an Agility check to go first; if two PCs tie (probably very likely!) they go in order of Agility or test if they have the same score.

Rounds can be split up more elaborately, such as by having separate Move phases before or after regular combat rounds (Battletech ? ). AD&D 2nd Ed’s Combat and Tactics breaks combat into Very Fast, Fast, Average, Slow and Very Slow phases, with the phase a character goes on determined mostly by their Size; this is very granular and as implemented quite messily , but does let actions like movement delay characters without too much hassle. Rolemaster Standard System has Snap, Normal and Deliberate action phases, each resolved in initiative order.
Some games (Riddle of Steel, 2nd ed. D&D with some optional rules) may have different initiative/combat procedures for duelling as opposed to general melee.
 
Simultaneous Actions
Games vary in whether they permit simultaneous actions, or whether these are forbidden (with ties broken by reroll, reroll of another statistic, or stat comparison). Games may also have a tacit understanding of initiative as a convenient 'fiction' for player-resolution rather than having in-game parallels, so that there may be an initiative order for dice rolling but with (e.g.) all actions being completed before results such as damage are applied. Another example of this may be in 2E initiative - feysquare.com (now down?) at one point had an interesting quote from Steve Winter on how one PC casting a fireball could be thwarted by another PC charging, due to assumption that the spell would take time to cast in 'game reality' despite group-based initiatives making a whole groups actions theoretically simultaneous.
 
Action Type and Initiative
Some initiative systems may consider what a character is doing to be the primary factor determining order of actions (e.g. games with more phases/more complex round arrangements as noted above). e.g. T&T handles spells/then missile fire/then melee resolution system; the cubicle-7 Dr Who RPG has phases of Talking, Moving, Doing (e.g. fixing things or other skills) and then Fighting, giving social characters the opportunity to talk people out of being attacked first (as the Doctor often does); changing actions incurs a -2 (on 2d6) penalty and can cause things to happen out of the usual order.
Conversely in other systems characters may be able to do virtually any action, with no modifier for action type - D20 system for instance does this with the equalization meaning that the separate declaration of actions before rolling in 2E could be phased out (see Rich Baker's comments in the 3.5 Rules Compendium, pg 71). This is usually more likely to be the case with simple action systems; e.g. Dragon Warriors- in this a handful of actions take multiple rounds, and the Dexterity comparison determining who goes when is not usually modified (although there is a variety of mummy that goes last automatically when spellcasting, due to having to cast spells with a ritual dance). Many systems may be somewhere in the middle, with action modifying the initiative result in some way. Individual weapon choice can even modify initiative - 2nd edition D&D using individual initiative adds weapon 'speed factor' to initiative results making larger weapons slower, which is interestingly the exact opposite of what Runequest did i.e. giving a bonus to who goes first based on weapon reach.
Some games may have actions which count as multiple actions (e.g. "power punch, counts as two attacks"[Palladium]); these can potentially be delayed to a later initiative if multiple actions are staggered rather than being all at once, or may just resolve in normal order.
 
Advance Action Declaration
Some systems have action declaration rules which affect how combat plays out; a character might declare actions before initiative is rolled (meaning the wrong initiative can ruin their plan)(e.g. Unisystem, 2E AD&D, oWoD), rather than declaring on their turn. Where actions are declared before initiative is rolled, an order of declaration is sometimes also enforced – as in oWoD Storyteller where characters declare in reverse initiative order. This last method is a fairly exacting system perhaps suited to high PvP games.  A system might have action declaration for some actions but not others, such as a wizard needing to declare spells for next round before initiative while fighters are free to declare actions in response to the situation. 'Chill' lets characters with multiple attacks have to declare their first action only, with later attacks decided upon 'after the results of the prior attack is determined'. A system might also consider a whole 'family' of actions to be an allowable declaration, or can be very specific e.g. called shots might need to be declared ahead of time (Chill, AD&D - in this case perhaps because it carries a +1 initiative penalty) or just be a form of attack.
Games where actions are ordered primarily by action type essentially have to have a declaration phase in advance, whether or not there's an initiative roll - e.g. T&T a character has to choose [Magic, Ranged, Melee] so the latter two can happen first, then moves into simultaneous combat for melee. The solo 'Arena of Khazan' plays with this a little by asking first if the player wants magic, then asking if they want to do ranged, then moving into melee, via paragraph but essentially a series of Yes/No declaration choices where either side [player or NPC] can one-up the other and 'jump in' by choosing an appropriate faster option, instead of the declaration being handled in e.g. initiative order like Storyteller.

Initiative and Actions
Initiative and # action systems in RPGs are also closely intertwined. Normally the number of actions depends on the initiative system, but systems which go the other way do exist. The simplest would be the 'advantage system' above, but AD&D 1E (not 2E) is interesting in that it works out numbers of actions very precisely and then uses a potentially complex priority system to work out who goes when.
(summarized in the ADDICT file found here - http://www.dragonsfoot.org/fe/ )
 
Other Elaborations: an odd initiative idea where initiative is spent as 'fatigue' to absorb damage can be found here:
http://forum.rpg.net/showthread.php?676703-New-(possibly)-Initiative-Idea
 
Factors that have been used to modify Initiative include: Dexterity and/or Speed attribute, weapon size (bonus for reach or penalty for size), creature size, number of actions, armour (penalty), action type, environmental penalties (underwater, etc), spells (haste/slow), character level or weapon skill modifier, surprise or weapon draw penalty, fatigue and/or injury penalty. Mental actions may substitute Int or other modifier for Dex/Spd in some games. DC Heroes uses total of all 'action' attributes (Dexterity, Intelligence, Influence) plus d10 for initiative, instead of its usual 2d10 on a table roll of stat vs. stat.
Hackmaster apparently has a rule where a player who hesitates or screws around can suffer initiative penalties for 'indecision' for their character.

An old article for FUDGE here (https://web.archive.org/web/20051220142931/http://www.fudgefactor.org/2005/06/activereactive-conflict-description.html) deals with attempting to adjust Fudge simultaneous initiative to an action-based system where characters can take/lose initiative. Though I like its goals/criticism of normal systems more than the execution: "[for most initiative systems]..their effects appear random and unrelated to the events of the conflict."

Systems may drop the usual initiative system for a sub-system in unusual cases e.g. 3E D&D Oriental Adventures has samurai roll Iajutsu Focus skill in duels to determine who strikes first, with the winner gaining several bonus dice damage [to duplicate lethal samurai duels despite D&D's large HP pools]. The skill does not help in normal combats, however. Star Wars - Edge of the Empire reportedly has two separate skills for initiative, one used if a character initiates combat (Cool) and another if they are drawn into combat (Vigilance).
(It would be easy to imagine special cases where unusual rolls are made for initiative as well, e.g. if everyone is being psionically attacked, initiative might be slowed for those who failed their saves - the most basic way to do that being to have the save be the initiative roll).

Recent edits: rolling initiative and surprise (*), Monologuer (*)

How much a character can do in a round is another question, though one often tied to the Initiative system. This is something that requires particular caution for a designer, as it is very easy to design a system that is either too slow due to too many actions and action types, or where variation in the Speed attribute/number of attacks per round is very unbalanced.

(D&D Note - note that letting # attacks escalate with level (e.g. in D&D) to balance more powerful spells is more feasible with some setups - e.g. not with action points, games where everyone gets just one action, or most attribute-based # actions (apart maybe from Warhammer)).

 
Types of setups known include:
 
*one main action per round on a characters initiative. Movement may be an action, or limited movement may be allowed in addition, or movement can delay a character’s initiative. The simplest and most balanced system.
Here extra actions is a rare (and powerful) ability, sometimes needing extra checks and balances; a common one is that extra attacks don't also grant extra movement. Systems sometimes give out 'partial' attacks - AD&D weapon specialization gives 3/2 attacks per round (a second attack every second round), or multiple attacks can be made at a penalty (3rd edition D&D), while Dragon Warriors 'Master Bowman' gives a 50% chance of a character getting a second attack. 'Elven Grace' in 13th Age gives the elf an extra attack that round if they roll under the 'escalation die' with a d6, but the die size increases each time a roll is successful. Leonard Lakofka (Leomund) notes in Gygax Magazine #1 that he used to house-rule the 3/2 attacks per round into a % chance of an extra attack each round based on level, which would remove the level-based breakpoint and the metagaminess of every second round getting an extra attack (on the subject of extra attack systems, he also randomly rolled manticores # attacks randomly; d6+2 tail spikes/round instead of a fixed 6).
The roll for extra attacks could also be part of another roll; i.e. 2nd Ed. D&D has an optional critical system where a critical (natural 20) gives a second free attack, instead of double damage.

Another way of handing out a 'partial' action that was interesting was in D&D 5E (19 Sept playtest); rogues at 2nd level gained a 'cunning action' ability that gave them an extra action which could only be used for disengage, hide or hustle; one build option could expand on this with 'Fast Hands' letting the action be used for Sleight of Hand, disable a trap, or open a lock. (The extra action gives results essentially the same as making one of these actions a 'free action' for a rogue).
 
4E/5E boss monsters (4E D&D solos or 5E D&D legendary monsters) got extra actions in those systems (this sort of thing is more a feature of 'one action per round' games - in a game with lots of attacks per round the DM can just build boss creatures with higher SPD/more actions, and too many starts to get problematic for the GM to handle).

Tunnels and Trolls, because of its heavily abstracted combat system, has things generally equivalent to extra actions (or natural weapons) just add bonus dice to the combat dice pool (e.g. special abilities in M&M (http://wizardawn.and-mag.com/game_mm.php) supplement).
 
oWoD Vampire would be nominally a 'single action' system, but with the super-speed "Celerity" power sufficiently common that quite a few to most characters would have it.

D&D 4E gave an extra 'minor action' on top of the main action, somewhat similar to the 'bonus action' idea of 5E; for example, healer characters usually only spent minor actions to heal, fixing a problem that healing is often suboptimal in combat due to this not contributing to taking down the opponent and so resulting in taking more damage.

*a number of multiple actions based off combat skill (default 1). 3E for instance starts at one attack, with more accruing based on Base Attack Bonus. Lower attack bonuses for secondary attacks make these a way of handing out 'partial' attacks, with the problem that they against a worthy opponent they may just be 'fishing' for 20s (they're useful against multiple weaker opponents but that may be better implemented by giving a character the option of multiple attacks at a significant penalty).
Palladium gives extra attacks for Martial Arts and Boxing (which also apply when shooting guns or firing energy blasts). Savage Worlds gives out increases in attacks largely via specific Edges (Frenzy/Improved Frenzy, Double arrow shot, Two Weapon Fighting etc.), some of which have rank minimums IIRC, so more skilled characters still get more attacks but in a roundabout way. While still powerful, level minimums can keep extra attacks at 'level appropriate' point.
[in discussion offline, a friend discussed a system where a higher TN task inherently takes more actions to perform - this probably works best offset by a system like this, where more skill also gives more actions]
Extra actions based off combat skill usually can't be used for movement - fighters aren't meant to just run at the speed of light - e.g. Savage Rifts has a 'Split the Seconds' edge which can't be used for movement, while 3E D&D has separate 'move actions' regardless of number of attacks.
5E D&D is interesting just since it has extra attacks that vary between classes, seeming (I think) relatively balanced despite quite different structures. A fighter may have several attacks; a ranger might trades Extra Attack for a beast companion with its own set of actions; a rogue has extra damage while wizards generally cast one spell/round  that levels up in power.
SenZar had a system where # attacks per round is based off combat skill (1, +1 at 5th, 10th, 15th and 20th). Spellcasters instead gained actions at only 10th and 20th. Spells cost only 1 action, so multiclassed fighter/wizards could cast more per round, although spells also took one 'phase' per level to cast with only 10 phases in a round, so extra actions were likely to be limited to lower-level spells.
NOTE that systems where you gain extra attacks with level, tend to be more balanced in games where there's a lot of hit point inflation. If a game has basically fixed hit points despite level, everyone getting an extra attack = fights now last half as long (and possibly come down to who wins initiative). Single-action only (Dragon Warriors), or the 'you can take two actions, but at a penalty' (Talislanta 3E etc.) tends to work better if HPs are more static.

*One action by default, but with a high Initiative roll granting bonus attacks - as seen in 1st edition Shadowrun (where result - 10 gave timing of the next attack i.e. a 27 gives attacks on 27, 17, 7). Fairly elegant, but not necessarily balanced. How swingy the results are obviously depends on the dice used for initiative -and hence core mechanic, unless initiative uses a different die roll (not uncommon). This is usually combined with an initiative rolls each turn, instead of a single roll each combat, although it would be possible to only grant extra attacks on the first round (e.g. due to surprising the victim).
(Possibly there'd be some way to handle this non-linearly, such that a higher roll gives 'diminishing returns' in number of bonus actions - e.g. extra actions might be timed to occur only on specific counts set by a table, such as at # of attack-squared initiative numbers...1 for 1st attack,4 for second, 9 for 3rd, 16, 25, 36...).
Another variant is Legends of the Wulin using match-counting (ORE style) mechanics - extra 'sets' on initiative allow minor actions only. (attack rolls also generate extra sets, but these instead add extra effects).
If used with ‘side-based’ initiative, a single high roll can grant several monsters bonus attacks and so smoke the PCs. Might be used to treat Two Weapon Fighting as a bonus to Initiative (considered but not used as an option in Midian Dark Fantasy). Or, a character might be able to take a penalty to attack to get an initiative bonus, with an ambidexterity feat offsetting this penalty for two-weapon users. This would certainly require an initiative roll each round though, or a fixed order where characters could roll to attempt to 'push initiative' each round.

Another variant, in Alternity, is for a low initiative to lose bonus attacks - Alternity has 4 phases (Amazing, Good, Ordinary, Marginal) depending on whether a character rolls under 1/4, 1/2, or full action check result, or fails the roll completely. Each action requires one phase, so a character with 2 actions who rolls poorly and acts in the Marginal phase only is reduced to one. Most variations of this delay bonus attacks to later in the round.
(as an aside I have seen the exact opposite of this system used in boardgames, though it doesn't make a lot of sense - in 'Conquest of Planet Earth: the space alien game' players roll their number of action points (1d6, 1 rolls again at +1), and the player with the lowest number of action points goes first.
 
*One action; a character can opt to take multiple actions, but if so both actions take a penalty (e.g. Talislanta, Storyteller, Savage Worlds, Star Wars D6).
In Marvel Super Heroes (FASERIP) similarly the character can make a Fighting FEAT check to make multiple actions, but can make only one attack (at a penalty) if they fail the roll. Usually multiple actions in this variant are simultaneous, though Star Wars delays extra actions i.e. all primary actions are resolved first, then secondary, etc. much like high-level fighter attacks in AD&D. RuneQuest variant ElfQuest lets characters with skills over 100% make two attacks at half skill with the second attack delayed 3 strike ranks.
In some games, this option applies with some actions only e.g. D&D allows multiple actions at a penalty for Two Weapon Fighting.
One elaboration is to adjust the multi-action penalty based on what weapon a character is using i.e. a short sword (speed 3) might allow two attacks both at -3, while a two-handed sword (speed 7) might take a -7 penalty if used to make two attacks. Talislanta usually has a -5 penalty, but certain skills such as Zandir Swordsmanship or Arimite Knife Fighting drop extra attacks to -3. Another variant may be the Superbabes system for "Do It Twice" - here a character can make twice as many actions if they successfully make a Dex ("moves") roll with d20 under the stat. Failing the roll does not cost the character an action, but attempting the roll costs 3 fatigue points (power points), in addition to the costs of the other actions.
Balancing the math of this option is trickier as it may be possible for players to calculate they can increase their odds of hitting by acting twice at a penalty. In games like this there is (indirectly) synergy between Luck points and multitasking; a character is more likely to pull off two actions when they use luck. (Compare with games such as 4E D&D, where 'action points' are a daily resource granting extra actions directly). HERO 6E has a 'multiple attacks' option which adds a defense penalty instead (1/2 DCV) -  likely to discourage its use by strong characters against lots of minions who otherwise couldn't hit.
Magic under this might treat a spell as just a normal action (a multitasking character may be able to cast e.g. 2 spells as separate actions), limited to one spell regardless of other actions, or can use multi-task rules for multiple targets, extra Energy Bolts from one spell, etc.
(See also 'Combat Moves', pg 5 - section for multiple-actions)
An article for FUDGE here (https://web.archive.org/web/20060824063025/http://www.fudgefactor.org/2005/05/speed-as-augmenter.html) discusses adding a 'Speed' skill (specific for each other skill) which discounts penalties and at higher level can offset penalties for more than 2 actions.
Multiple action penalties are sometimes assigned equally to both actions, or for sequential actions there can be an increasing penalty - e.g. defenses might be at -0,-1,-2, etc. [e.g. TriStat dX -this also has an 'extra defenses' power each level of which cancels penalties on that attack, with attacks after that taking penalties normally]

*set number of multiple actions. Fantasy Dice for instance gives characters a simultaneous primary action + secondary action. Secondary actions cannot include movement (unless the first action is a dodge); if the first is a defense it has to succeed for the second action to be an attack (counterattack). Actions apart from counterattack can't use the same arm. Some actions e.g. sprinting forfeit the secondary action. Supers RPG 'Infinite Power' gives characters 2 actions each round that can be used to move, attack, use a skill, or use a power, but the same action (e.g. attacking) can't be repeated.

*a number of multiple actions based off an attribute e.g. Agility (Synnibarr) or in Alternity off average of Con+Will (? - a bizarre attempt at balancing the usefulness of stats - this is also partly dependent on initiative roll in Alternity, see above). Where based off a stat, a designer has to be careful as this introduces a massive breakpoint between “1 action per round” and “2 actions per round”, and a slightly less serious one between 2 actions and 3. Multiple actions are sometimes based off a separately bought up stat (e.g. SPEED in Hero) instead.
Synnibarr is also interesting in that the character who wins initiative gains a bonus attack on segment 1 (slightly odd in that the same roll gives varying numbers of attacks based on what everyone else rolled).
Multiple actions sometimes occur all at once, or can be handled with phases (HERO) or initiative passes (Palladium) where everyone cycles through attack #1 in initiative order, then attack #2, etc.
The Fantasy Trip gives missile combatants with high DEX more attacks - the larger the bow, the more DEX is required for a second shot. It uses not raw DEX but 'adjusted' DEX (adjDex) including assorted circumstance modifiers e.g. armour. Crossbows get +1 Dex used prone - so its possible a x-bow man could reload faster that way.
Arduin Grimoire has a system based on comparative DEX: if your DEX is double an opponent's you get 2 actions, etc. It uses DEX-countdown to resolve when, with the second attack occurring at 1/2 Dex. Monsters with multiple physical attacks like claw/claw/bite always get that number of attacks regardless of their DEX, but delays them the same way i.e. a monster with just 2 claws would get claw #1 at DEX and claw #2 at 1/2 Dex; differently to how AD&D would do it with a 'routine' all done at the same time and only high-level fighter attacks staggered.

Fireborn has an interesting, if cumbersome, system where a character gets physical actions equal to their "Fire" (as the element; equivalent to Str) attribute. A series of actions is scripted, and a dice pool (Fire + bonus dice moved from other stats if desired) is rolled vs. the defenders' pool with each net success carrying out one of the scripted actions in order. (The main issue being that individual actions don't have separately calculable chances of success, e.g. modifier for skill rating). For example a character with 'Fire 3' might do a Dash+Jump+Strike.  Characters can choose to script 'Power' before a Strike (+5 damage, but the attack is more likely to fail), or 'Press' afterward (+2 damage), and can make multiple attacks with a 'Ready' (2 Ready for a medium weapon, 3x for heavy - the extra action cost helping put a brake on extra attacks despite a largeish number of raw actions). Effects like 'knockouts' also count as added-on actions, rather than being a hit penalty etc. Because opponents can't counter movement outside their reach, successes for Dash or similar are subtracted before attacker and defender rolls are compared.
(Heroic Golden Turbulence is also similar, but less developed, and with fewer actions due to a smaller dice pool to start with, as well as including both attack and defense).
(after some thought, I think the system here is probably too complex for the payoffs it gives - combat results being not tremendously different to other systems. Much of the system could be duplicated in e.g. a Savage Worlds type game without the dice pool, with a rule that a character can add a move or similar either declared before the roll at -2, or at a cost of each [4 pt] raise generated after)
Note this system tends to give extra movement for higher-rated characters (most systems with multiple actions try to  inflate movement per turn less). Because each turn a character can make several actions, whole bonus actions can be given out more readily (e.g. "If you have shuang dao and Weapon Use (elite) edge, you may Feint or Defensive Feint once each turn without using a mental action to do so").

*Strike ranks - see above. Strike rank systems can run into problems with low-speed weapons getting too many attacks if not balanced carefully (a drop of speed from 4 to 3 in a 12-segment round moves a character from 3 attacks to 4 attacks, while going from 3 to 2 moves a character from 4 attacks/rd to 6 attacks/rd.
One patch is to have modifiers apply to base number of attacks rather than speed and use [segments in round/number of attacks] to work out a characters speed, instead of modifying the strike rank of weapons directly.
 
*Actions bought with initiative e.g. Feng Shui - actions cost a number of initiative points to complete – characters count down from their initiative e.g. an attack taking 3 initiative might start on 10 and actually complete on 7 (or be executed immediately, but with the next attack not allowed until 7). This is similar to Strike ranks, except counting down instead of up. Feng Shui type games tend to give fast characters higher initiative points and so more actions, whereas strike rank systems tend to reduce the time required to make actions and have a round with a fixed number of segments. Feng shui also lets characters take 'snapshot' actions - the normal 'shot cost' of 3 initiative for an attack can be reduced to "2" at -2 to hit (fairly severe in its d6-d6 system) or "1" with a -5. 3-cost actions can be performed at count 2 or 1 without extra penalty, though longer actions carry into next round.
 
*Action Points – various of Leading Edge Games’ RPGs use this; An interesting version of this is also seen in the freerpg JAGS (http://www.jagsrpg.org/). In JAGS number of action points are determined by “Reaction” ( DEX). The length of an action determines how many action points a task is (i.e. Full Round = 10, Medium = 7, Short =3). Unless an attacker wins initiative by a significant margin, they can be interrupted with a shorter action i.e. a “Charge” is a Long action (8 points) and so can be interrupted with a normal Attack (Medium action, 5 points). This folds something similar to 3E/4E D&Ds “attacks of opportunity” into the normal action system. A downside is that a player needs to know action costs of various actions on their turn and weigh up the relative costs; it also makes Dex/Reaction very valuable. Action points are good for handling detailed movement allowances (i.e. "crawling = 2 APs per 10ft" and so on).
Rolemaster (RMSS) gives characters an activity % (a character gets "100% activity" each round), with various actions using up variable %s of activity. (actions are separately defined as snap, normal or deliberate for initiative purposes).
 
*Dice actions + automatic actions. DC Heroes allows characters one of each. This is fairly good since action types are defined by the system (if you roll dice for it, its a dice action). Lifting an object would be an automatic actions (weight = STR), as would running (distance = DEX) unless the character wants to lift something super-heavy or run particular fast which requires the character to make a Pushing attempt.
This approach also combines interestingly with the ability to take multiple actions at a penalty (Masterbook). Running + Shooting is possible, but automatically gives a multi-tasking penalty to shooting rolls.; lifting a too-heavy weapon automatically penalizes attack rolls.
(DC Heroes is interesting in that while characters all get one action/round, some PCs can do dramatically more with it. Thanks to multi-actions and logarithmic movement rates, Superman can fly halfway around the world and smack a bunch of guys with one action. It also has interesting 'superspeed' rules, where any noncombat action has a base time measured in APs; Superspeed APs deduct from these and so and with enough points in it, someone can build a house as a combat action.).
 
*MERP % Activity- MERP 'moving manuevers' use a dice roll on a chart to determine % activity that a roll uses. A low roll may mean the manuever is successful, with moderate rolls meaning an action takes a full round (100% activity) and high rolls meaning the manuever consumes less time, with remaining % activity being spendable to perform other actions. (Another note - Rolemaster in one of the companions had a skill for multiple attacks, while may be a precursor of 'iterative attacks' in 3.x D&D)
 
*rolled number of actions e.g. Cthulhu eating d3 investigators per round.

Number of permitted actions may change under some circumstances. D&D treats "surprise" as special; 3.x allows only a standard action (i.e. no movement except by replacing the normal action) in a surprise round; 1E AD&D is the opposite and allows a character to make a set of melee attacks each segment on a surprised foe.
AD&D also allows extra actions against certain opponents i.e. a fighter can make attacks equal to their level against 1-1 HD creatures or 0-level humans (a legacy of the Chainmail combat system?). This is something other games handle more deftly; DC Heroes for example lets a character make a "Multiattack" by taking a hit/damage penalty, applying the attack result against mobs of foes simultaneously (larger the mob, the greater the penalty).
Palladium reduces number of actions for characters who are spellcasting, compared to normal melee actions - which synergises in an interesting (if unclear) way with their Dodge system to make it harder for a wizard to dodge or parry midspell - they are less likely to have extra actions to spend to do this, assuming the action has to come out of a lower number of actions per round. (Rifts also has different ROF for weapons like bows compared to melee attacks, which is mostly just confusing since using a bow presumably shouldn't alter how many Dodges a character can make a round).(Edit note: I have now seen an online Rifts game where it was houseruled wizards could just cast spells at the same rate as melee attacks, 8 attacks = 8 spells! wheeeeee).
Special abilities can also grant extra actions in specific circumstances (e.g. Cleave) or characters can sometimes spend points for additional actions (4E Action Points). Extra limbs/weapons can also grant extra attacks (see 'Two Weapon Fighting' in the combat moves section (http://www.therpgsite.com/showthread.php?p=497810#post497810), next page for a list of variants).
Games sometimes include abilities which allow open-ended repeat attacks- e.g. Blade Cascade in 4E D&D (Unerrata'd) or Flying Windmill Kick in Feng Shui - either let a character make attacks until they miss. This sort of ability can be dangerous to design since there could be combos with abilities that increase to-hit bonus (Elven Accuracy in 4E, generally speaking luck points..) dealing up to unlimited damage.

The allowed number of actions per round plays a part in determining what combat actions are defined in the system. A game which allows only a single action per round may have to define additional basic action types to cover what would be combinations of multiple actions in other systems - perhaps compare "Two Weapon Fighting" as normal multitasking of two attacks, vs. 4E D&D "Twin Strike" as a defined power, or Charge as a defined action in say 3E D&D, vs combinations of Run+Wild Attack in Savage Worlds.
 
A game can also have fairly abstract 'actions' - where something that might be a separate action in another system is merely a result of extra success. For example, a very high attack roll might kill multiple opponents (Anglerre 'overflow' w/ cleave ability), or perhaps weirder uses of bonus combat successes in Heroic Golden Turbulence.
Conversely, something that might be resolved as a separate action may also just turn into a bonus, rather than being resolved with another roll. 4E TWF just gives a +1 to damage for having an offhand weapon, and Tunnels and Trolls just turns an extra weapon into bonus dice (see Damage post specific system notes for details). The Lone Wolf gamebook series has a Mind Blast type character ability, that just gives a bonus to Combat Skill instead of being resolved as a series of extra rolls of psychic attack vs. psychic defense or anything like that.
 
Splits between attack/defense are sometimes modelled at the level of actions (a character can either spend an action to attack, or on Dodging; Palladium), sometimes through selection of combat manuevers (a Wild Attack gives a bonus to attack and penalty to defense; Savage Worlds), or through point allocation (a LegendQuest character can apply Skill Levels toward attacking or toward Parrying [a particular opponent], once per round - part of a general idea that a skill level can be used 1/round that also shows up in spell Control Levels and the horsemanship rules)
A game may give out separate 'attacks' and 'reactions' - notably in 5E D&D a character might have 4-5 melee attacks but still only one 'reaction', so their attack power increases independently of defensive power (compare to Palladium where being faster always increases both, though special abilities like extra plusses to Dodge or 'automatic Dodge' allow one-sided increases).

Games may also distinguish between 'actions' and 'attacks' e.g. 3E and 5E D&D where one 'action' can give several attacks; AD&D refers to 'attack routines', where a bonus routine might be multiple weapons or limbs. 'Bonus' actions may be given out as full rounds/normal actions, or be limited to single attacks. Inconsistencies here potentially generate problems (5E D&D: normally a 'bonus action' gives only a single attack to fighter-type characters e.g. two weapon fighting, scimitar of speed; whereas, 'quicken spell' etc. can let a whole spell be done as a single bonus action, giving the equivalent damage of 4 attacks from an 'eldritch blast' or similar spell).

Its not uncommon for games to distinguish between 'physical' and 'mental' actions - characters may exist who can perform bonus mental actions but not physical actions, due to limitations of physical form. GURPS has a 'compartmentalized mind' advantage (from the Lensman supplement, which had it from the original books), at least one 3E D&D race with multiple minds can do it (the synad, though limited in x/day). 2nd Ed. AD&D deities are noted as being able to perform 2 (demigod), 5 (lesser), 100 (intermediate), or unlimited (greater god) tasks simultaneously by divine rank, and subject to limitations of physical form, presumably to allow them to handle assorted plots, prayers and communications in their portfolios.

Special: 'Number of attacks' is only very rarely directly tested as a game mechanic. Cadillacs & Dinosaurs [Twilight 2000] has an 'initiative' (1-6) that represents combat experience, and so has rolls to avoid 'panic' made with D6 under initiative rating if severely injured etc. (the normal game system is d10 roll under stats 1-10); a failure meaning the character freezes for a Phase for each point failed (they can drop prone after one Phase has passed).

Generally, if everyone gets several attacks a round (Palladium), it would probably be better to just switch this for shorter rounds with fewer actions per round ('When everyone is special, no one will be').

Action systems where a character gets to do X several times, or just do Y once normally, is going to give characters a strong incentive to do X. For instance, this would include 5E fighters with say 4 attacks a round (mitigated slightly by having at least a few options that can be performed with an 'attack'), or worse FUDGE characters who have purchased a SPEED skill specific to another skill e.g. who can 'Knifethrow' 3x/round without penalty or do anything else once. This could be particularly a disincentive against 'improvised actions' - doing anything interesting in combat that's not directly on the character sheet but instead use of terrain/situation - for powerful/high-level characters , since power of normal attacks or spells is 'scaling up' along with number of them.  
Action-point systems where characters get discounts on particular actions can increase potential # physical attacks but still allow a character to 'mix and match' - less incentive to just do the same thing over and over. Avoiding this problem might contribute to bloat in special abilities, again as in 5E where Eldritch Knight characters have to get a 'cast spell+attack' separate action to keep spellcasting competitive with their 4 attacks.

Dice Rolling Note: Systems vary in how many dice rolls are required per combat round (or just per combat - a game could have one-roll resolution without rounds, e.g. Full Light, Full Steam).  
This depends basically on:
 a) the number of stages involved in resolution (e.g. some subset of: initiative, attack, defense, hit location, armour bypass, damage, soak)
b) the number of actions (sometimes not the full set of stages is required per action, e.g. one initiative applies to all, or one 'attack roll' in a dice pool system might be split across multiple attacks, or a damage roll is made with a flat bonus for extra attacks that hit), and;
c) how many dice are actually in a 'roll' e.g. d20 vs. dice pool.

“Finally, and brace yourself, everything and everyone has 20 hit points. Yes, a Confederation of Worlds light infantry commando who has spent the last twelve years choking down steroid pills the size of softballs who could walk naked across the Satan’s Armpit dessert [sic] (still in shape for cocktails later) has as many hit points as Don Knotts in “The Incredible Mr Limpet”. But to make you feet (or perhaps even feel) better, we’ll call them something else...hmm...how about Damage Levels? Yeah! Now that sounds important!” – HOL.
 
PCs, typically being mortal, tend to get physically injured and occasionally die. Games may have parallel systems for handling mental and/or spiritual damage as well – including fatigue, psychic damage and spell use; possibly even results of “social combat”.
 
The most common basic approach for handling damage is that characters have a resource, “hit points” which when depleted means they are killed.
 
Depending on the system Hit Points may be a pure resource (lost when a character takes damage) or it may be designed to also function as a score (aka a “gauge”) for the purpose of other game effects for example, in Tunnels and Trolls, normal physical damage is subtracted directly from a character’s Constitution and the current value is used for Constitution checks – such as the character trying to hold their breath, resist poison or make a saving throw against a death spell (as a side effect of this large monsters, which have a CON multiplier, are particularly good at holding their breath). Mutant Epoch works similarly, with current Endurance being looked up on a table to perform a 'Hazard check' such as resisting poison. (Note after playing Mutant Epoch - the table lookup for attributes looks unwieldy at first, but actually stat checks don't seem to be made that often, e.g. combat uses a different subsystem and doesn't need use of the table).
Comparatively, D&D sometimes attempts to use “hit point checks” (e.g. the “Death Touch” granted power in 3E perhaps, or the Power Word spells) but this typically works badly because hit points are not scaled in a fashion that works with any particular dice roll. T&Ts approach is also nice in that dealing damage to CON is balanced against damage to any other attribute – DEX damage from slowly being petrified, STR damage from fatigue, Intelligence damage from mind blasts or Luck damage from a curse – eliminating the need for a condition system as seen in other games.
 
Games with Multiple types of Hit Points
A couple of games including Palladium, Star Wars Saga, Marvel Super Heroes, Amazing Engine and Alternity use multiple varieties of Hit Points –“hit points + SDC” or “wounds + vitality” or “mortal wounds + lethal wounds”. Most of these multiple-type-of-HPs systems are aimed at making characters “brittle” since often a good attack will bypass the larger pool of lower-grade hit points and zap a PC in their Wounds stat - though for Palladium few attacks can bypass SDC and the distinction between HP types is fairly minor (SDC having been added primarily to bloat up PCs’ HPs in modern games, so they could withstand gun damage). Marvel Super Heroes had a Health score based off several stats combined, plus a Kill result or being dropped below 0 could result in a character losing Endurance ranks. Alternity build off its multiple HP subsystems to have a couple of interesting mutations representing redundant internal organs and the like. On the downside it required tables to determine what damage type an attack did - an ordinary attack would have 3 separate damage ratings listed, effects that dealt damage on a miss (i.e. dodges vs. explosions) needed 5, and even inanimate objects had multiple HPs - e.g. "the canister can be broken by 4 points of wounds or 2 points of mortal damage".
(EDIT NOTE: this sort of system does have a psychological advantage in that a GM can deal minor attrition damage - not possible if wound levels are quite granular, as well as major damage where necessary.)

(Note that systems which just have large pools of HPs, particularly where these just inflate with level, can run into realism problems where situations that should be automatic death (stabbed in your sleep; falling from a great height; smothering a grenade with your body in Palladium) only cause a flesh wound. This can require the GM to overrule the HP results to give a death result, which can have rules (like 'coup de grace' in 3E). Multiple HPs can fix this (if Mortal Wound health boxes increase more slowly), as can tight control over HP inflation/fixed # HP systems).

Note that here I've been talking about games where the two different HP tracks are equivalent in scale - so that a character might take 10 points off HP-A or 10 points off HP-B. A slightly different case is if the system has say an arbitrarily large hit points score and also gives a character a few 'wound boxes' or similar, perhaps with a critical filling in a box or perhaps with a number of hit points damage filling in a box also. 'Dragonborn' IIRC does this (as does the vanished ROAR game where characters had a fixed 5 'Life' levels in addition to normal damage hurting their CON). This can be a reasonable way to calculate wound penalties or the like in a normal ad hoc HP system.

Hit Points are also sometimes divided up across various hit locations, as in Twilight 2000 or Runequest. This system may or may not be used for NPCs, since it requires more detailed tracking, even though the resulting maimings may be fun. This setup can cause complications for tracking 'systemic' damage - Roma Imperious (IIRC) has no core HP system and so even blood loss is resolved as being damage to a specific location, with some rules charting how this spreads through the body. HarnMaster uses specific injuries but also has a separate 'blood loss' statistic which is tracked.
 
Fixed HPs (i.e. all characters have the same # hit points)
Some systems use fixed hit points + soak rolls – as lampooned above in HOL; here everyone has the same number of Hit Points i.e. 7 health levels IIRC for Storyteller or 3 “Wounds” for PCs in Savage Worlds (though SW characters must first be “Shaken” to take a Wound). To represent character’s different ability to withstand injury, damage itself is reduced for tough characters (via a soak roll or a "Toughness" threshold); though soak rolls are sometimes found in other designs as well (Warhammer, whose 1st edition was famous for the ‘Naked Dwarf’ effect ). The Buck Rogers: High Adventure Cliffhangers game –not to be confused with the Buck Rogers XXVc game which is an AD&D variant - apparently has a system where characters have only one hit point; PCs must pass a Stamina check any time they are injured, or die.

Wound Penalties
Fixed HPs i.e. where all characters have the same # hit points frequently form a condition track (referred to as the “Trauma Gauge” pattern in Kirk’s RPG design patterns) – individual health levels may be named (Bruised, Maimed, etc) and have increasing wound penalties on all checks. This is realistic but can lead to a “death spiral” effect since the penalty usually affects all checks (not just Constitution-based checks like in Tunnels and Trolls). FUDGE has a slight variable on this where a character gets a limited number of named injury levels: there may be multiple boxes at the same level (e.g. "Scratch" levels) and taking one too many hits of that severity causes the wound to overflow and be recorded against the next level. Old gamebook Cretan Chronicles  had an interesting death spiral kludge in that being seriously wounded reduced a character from rolling 2 dice to 1 die, but this cancelled out if both sides were crippled (preventing lengthy stalemates).
Penalties may sometimes be reduced by an advantage or feat (usually a fixed amount), or a skill (e.g. Aberrant has a endurance skill letting a character roll [Stamina+Endurance] and reduce the penalty by the # successes).

Soak rolls
These are rolls by the defender to reduce the amount of damage, sometimes representing toughness in an alternate way to having different HP totals. A soak might be only sometimes successful (Savage Worlds), or the roll may nearly always succeed but have to be rolled to determine how much is stopped (Storyteller).
Soak rolls are particularly common in dice pool systems since soak is a form of ‘effect’ which these handle well.
Savage Worlds also has a "soak roll" where a character expends a luck point, aka a "benny", to try to roll their Vigour, absorbing one wound per 4 points of the roll.

Personally, I used to hate soak rolls since for WW a quite lengthy set of dice rolling for hit/dodge/damage/etc could end up with no damage due to soak, and since it didn’t make sense to me that being stabbed could result in no damage. Nowadays I don’t mind the Savage Worlds approach however, and have come to terms with the idea of a fully soaked hit just being a “flesh wound”.
 
Another note on soaking: HP-based systems are generally fairly predictable; a large number of hit points will take several rounds to plough through. Sometimes critical hits are added on to neutralize this invulnerability, although...this is an example of a subsystem working at cross-purposes with the main system (why not just have hit points that inflate less dramatically in the first place).
A soak-based system is more capricious; it is sometimes possible for a very poor 'soak' roll and/or high incoming damage roll to drop a fairly tough target in one very lucky hit. In many die-pool games these sort of events are quite rare though (e.g. a result of 0 successes on 8d10, target number 6 will only come up on 1 in 256 rolls).
A couple of minor perks of soak systems are that they're also good for representing cases where a character's ability to take damage will change rapidly (such as from shapechanging) without current wounds being affected; similarly some games have abilities that let a character sometimes exchange their 'soak' stat for a different stat (such as 1/round using Dex to 'roll with punch' instead of using a Con-based toughness value). A HP system does the exchange less deftly (e.g. by having HP based off an unusual stat all the time).

Occasionally a system that doesn't use soaking normally will find a situation that requires it and improvise something. A couple of Tunnels and Trolls solos allow CON saves, with the amount failed by becoming damage (in Captif D'Yvoire, for instance), though this is more or less just a general mechanic for saves which happens to be using CON in this instance. 5th ed. T&T Gunnes allow a Luck save with amount made by/missed modifying damage, since the damage of a bullet 'varies tremendously depending on where it hits the victim' - other weapons don't get this.
Palladium in 'Dead Reign' notes that zombies are resistant to damage, and gets a "natural Armour Rating (A.R.) of 14 reflecting its ability to soak up or shrug off most kinds of damage" although this has the problem that it runs off the to-hit roll rather than the damage roll, and a zombie is as likely to shrug off an SMG burst as a punch.
 
Finite soaking: very rarely a system has soaking while runs out after use. Dying Earth is one example of this - a character makes a "Health" roll to negate an injury, reducing their health pool by one; otherwise they are injured (-2 to all actions, on d6). The soak dice themselves function much like "hit points", although they are rolled instead of fixed in value.
(Savage Worlds soak costs a 'bennie' and so also work like this).

True20/ Mutants & Masterminds instead of having HPs has a soak roll called a "Toughness save" (d20+modifiers) made vs. a variable DC based on the damage of the attack and with how much the roll is failed by determining effects (usually an accumulating penalty but eventually collapse or death). Because of the d20s variability, this may make combat more "swingy" than a normal HP system, or a dice pool soak.

Toughness Thresholds
A 'Toughness threshold' is sometimes included in a damage calculation as a way to consider opponent's level of vulnerability. It can be used to replace a variable # of hit points, just as soaking does (Savage Worlds), or HP may vary as well (Warhammer). It is similar to 'soak' but as I mean it here suggests using a fixed subtraction, rather than a roll.
Savage Worlds for example calculates a 'Toughness' at 2 + 1/2 Vigour die; armour also adds to this.
 For Savage Worlds the system reduces HP tracking for minions nicely and so is good for mass combat, but with the trade-off that it requires lucky rolls to bring down big monsters, making that more hit and miss (though a party can operate tactically to help bring down a big monster). (as noted by CRKruger) The variation between characters due to Vigor [4 points between d4 and d12] is more than the bonus provided by Heavy Armour (+3) - the 'Naked Dwarf' effect.

Specific Injuries
Yet another way to handle wounds is by “specific injuries”: e.g. in Amber, Rolemaster. Most of these (Amber excepted) also have a HPs system for blood loss and the like, but most damage is via descriptive effects like “grazed knee”, “left leg disabled” or “skull crushed”. The HP system normally just causes characters who fail to die from serious injuries to eventually collapse from minor damage, though Warhammer combines a HP system with specific injuries in an unusual way; a character only loses Hit Points (“Wounds”) initially, but after this buffer is exhausted starts to roll on the critical damage tables.
More commonly, specific injuries are tacked onto a HP system via critical hits, or for attacks which do over a certain amount of damage (Earthdawn injuries over a certain threshold have varying effects based on their hit location though HPs are not normally tracked locationally; 2nd Ed. AD&D’s Fighters Handbook had “numbed” and “useless” results for called shots to a location from attacks dealing over ¼ the victim’s total HPs). CHILL (but not other Pacesetter Games' RPGs) has a semi-specific system where most attacks will generate abstract Wounds of varying degrees based on success level of the attack roll, in addition to targets taking HP ("Stamina") damage.
Adding specific injuries onto a HP system is sometimes considered problematic at a conceptual level - an uneven level of abstraction since some wounds involve broken bones, bleeding effects etc. and other "wounds" -those just causing the HP number to go down -don't, as well as having large HP numbers fail in their role of providing protection to characters.
 
Specific injuries can also be fairly abstracted, as “conditions”. (e.g. see scenario mini-game “Lady Blackbird” http://www.onesevendesign.com/ladyblackbird/ (http://www.onesevendesign.com/ladyblackbird/) ?)
FATE has a system of 'consequences' whereby stress (damage) can be voluntarily converted into fairly narrative complications like 'dangling off a cliff' or whatnot, instead of being subtracted from the stress track. (a strange hybrid of specific injury and soaking?).
Hackmaster (the revision) subtracts damage from HPs normally, but also records each wound separately (which affects wound healing).

Additional Notes
 
*Hit Points & other hit-point-like resources: Exalted has a wound level system, plus gives characters a separate pool of power points ("Essence") which fuels various Perfect Defenses. Characters usually need to use perfect defenses to block various (massive-damage-pool) effects, making the power points pool in some ways analogous to "hit points".
 
*Multiple systems: D6 Space actually has two alternate damage systems, giving the GM the choice between a hit point system and using soak rolls (perhaps for compatibility with Star Wars). 3E D&D's Unearthed Arcana has an optional 'Toughness' system (like Mutants & Masterminds' system) which can be used to replace hit points.
 
*Luck: As well as physical toughness, "Luck" frequently factors into how well a character can absorb damage. Different systems handle this intangible in very different ways: D&D assumes that 'luck' is part of a characters' Hit Points (a luckier character would have more). The Tunnels and Trolls characters CON represents physical durability only but the T&T character has a separate Luck score that will usually reduce incoming damage indirectly, via additional Combat Adds and better saving throws. The Savage Worlds character's "Wounds" are also wholly physical, although the scale for them is fuzzier (a damage roll under Toughness may 'injure' a target descriptively, but has no mechanical effect); the Luck factor applies via Bennies powering Soak Rolls.
 
Secondary 'wound boxes' on top of HPs: As an interesting case of (probably bad) game design accidentally creating a secondary 'wound box' system, there are 3.0 D&D vorpal weapons, which could cut off someone's head on a critical hit, often on a 15-20 result (keen scimitar) or even 12-20 (with keen + the improved critical feat stacking in 3.0). Epic-level characters could get 4 to 8 attacks a round (with two weapon fighting), resulting in many epic level monsters having evolved multiple heads to survive; effectively a being has a special 'wound track' where each head is one 'wound', with the regular HPs (bloated to crazytown) being irrelevant. A couple of monsters also had extra vorpal resistances (sirrush); or weapon immunity in 3.0 could also stop such weapons working (if a monster needed a +6 weapon to hit the +5 vorpal weapon wouldn't work -  though barring the GM having handed out a +6 weapon that's non-vorpal as well, this shuts down the warrior completely).

Death's Door
Many HP systems consider a character to be only incapacitated at 0 hit points, and die at some negative number. A few systems instead treat a score of 0 as death, but have character's collapse at a small positive number. Systems vary considerably in how wide they set the margin, depending on how lethal the system is; Dragon Warriors has [d6+5] health points and a death result of -2, meaning quite often a hit [about 2-5 damage] will just kill a seriously injured character outright. 3.5 uses -10 (and Pathfinder -CON); 4E uses negative [half normal HPs]. 5E does not track negatives (minimum is 0) but characters start making "Death saves", actually fairly good for keeping suspense in dying though this also necessitates more rules to provide automatic death in extreme cases, and it makes magical healing very effective as it will bring someone around automatically despite 1-2 failed death saves, starting at 0 instead of a negative number.); Marvel Super Heroes likewise does not track negatives, but a character losing all "Health points" begins to lose Endurance ranks instead. Mutant Epoch has several categories (Incapacitated but conscious i.e. can still use mental mutations, incapacitated but stable, incapacitated and dying - with the exact thresholds depending on a characters [Endurance+Willpower]. Palladium and AD&D 1E/2E (optionally, for -6 or worse) have permanent impairments for characters reduced to negative HPs; Palladium has a table for this).
Shadowrun 4 lets characters buy extra "Damage Overflow Boxes" as an advantage, while DC Heroes has an 'Invulnerability' power which kicks in to recover damage automatically if a character with it (e.g. Superman) would be killed.

The main technical issue associated with having negative HP thresholds is PC/monster consistency. It is usually more fun for combat to include a monster being taken out as a decapitation or the like; that a monster technically isn't dead until -10 HP is something alot of 3.5 DMs are going to overlook when describing a final blow (I had one DM describe an NPC as losing an arm when we were fighting her - and then we decided to just take her prisoner). One of the more interesting logical workarounds within rules is Advanced Fighting Fantasy's Death Door system; a Hero reduced to 0 Stamina begins losing LUCK points at 1/round, finally perishing at 0 Luck; monsters do not have LUCK scores (though they may substitute Skill instead for involuntary checks such as resisting spells) and so can be described as being slain immediately at 0 Stamina. Another good compromise is the systems that require some sort of check to continue functioning at 0 - luck rerolls and the like can help PCs stay functioning (or just be incapacitated), while a monster may be more likely to fail and be dispatched without having to linger in the twilight before death. Spawn of Fashan has 'cling to life' rolls, but notes that is 'a product of a strong will developing from intelligence', so doesn't apply to most (non-sentient) creatures.
A system may sometimes skip 'death's door' for specific effects e.g. 5E disintegrate destroys a target reduced to 0 HP, rather than have it become dying; or a mind flayer extracts a targets brain if it can reduce their HP to 0. This makes these attacks particularly lethal; in the sense they bypass a portion of the hit points (the 'underground' half of a 5E characters HPs) they slightly resemble 'aggravated' damage or damage that 'goes straight to wound points'.
Death at '0' may be mathematically easier to calculate any 'overkill' with, e.g. if a cleave-type power lets a character apply excess damage to a different target (lower numbers of HPs, e.g. just a few wound boxes, would also help).

Objects
Objects may have HPs, as creatures do. Systems where high STR is supposed to be modelled, such as supers game, may want to instead have "break DCs" or similar to separate object and creature destruction subsystems, as realistic damage generation from super-strength may result in target creatures getting reduced to a thin paste unless object HPs are set extremely low, and so lead to an arms race with regard to defensive powers, or balanced super-strength will give little ability to punch through tanks (GURPS Supers).
Damage to objects may reduce checks relating to the object (e.g. Repair rolls, Drive rolls, etc).
 
Partial List of HP Calculations
Some of the numbers given below are here because they show interesting design in and of themselves, others are listed to give context to the list of damage calculations by game (next post).

Arbitrary HP Score (the most common design)
D&D: Usually 1 dice per level (d4 to d12 by class), plus Con modifiers. 1st level maximized in some editions. AD&D replaced dice with fixed points (no Con modifier) after "Name" level (usually 9th or 10th). A house rule I'd seen was to have an extra Hit Die for "0-level" (e.g. race-based hit die) - this is also used in David Johansen's Dark Passages D&D variant, and in Dungeon Crawl Classics/Mutant Crawl Classics (where characters start at 0-level).
Monsters have mostly arbitrary (or CR-based) numbers of Hit Dice, with d6s in 0D&D, d8s in AD&D; Maybe partly because dice size is standardized, small monsters may have 1/2 or 1/4 of a HD.  They use type-based dice in 3E, and size-based dice in 5E (something similar to this idea first having been floated by Gygax for his never-written 2nd Edition; its interesting in that # size categories is thus influenced by # dice steps possible, perhaps interesting as a two-way interaction since the rule both sets # categories and couldn't exist if # of categories wasn't in the ballpark of what would work for it).  
4E has fixed HPs based on monster level (much higher than base PC HPs, possibly with a x2 elite or x4 solo multiplier).
Low HPs in 0D&D/AD&D are arguably buffered by lots of NPC hirelings, making CHA almost a source of extra HPs :)
D&D almost never uses wound penalties: late 2E 'combat and tactics' has specific injury criticals, and 3E in rare cases (GM option, when stepping on caltrops) may have specific injuries. 4E often had conditions occur as a side effect of 'powers'. One place exact HP mattered in 1E, was magic sword use; a character worked out average HP/level and each level worth of HP reduced their 'personality' by -1, possibly letting a magic sword take them over if heavily injured.
Carcosa: as 0D&D, but hit points are re-rolled between encounters to increase unpredictability (i.e. replicating some of the automatic features of using soak rolls more awkwardly).
Arduin: started out as a series of fan or '3rd party' 0D&D supplements, but went to a revised HP system - base by race (largely size-based), +Con score, + 5 for fighting classes,  +1 for 2nd/3rd/4th level, +1 per level for warriors (1 per 2 levels or 1 per 3 for others). "People now have a chance to run any character or characters on any expedition they choose without regard to difference in levels of experience. They can have their 1st level warrior stand shoulder to shoulder with a 10th level lord and hold the gate together! Just as in real life young and inexperienced Warriors accompanied older, more experienced fighters."  
As a fairly haphazard early (modular) game its sort of unclear whether monsters are intended to also convert to this - it could be argued that one reason for the revised system was to prevent 'high level fighters having three times as many HPs as the dragon they were fighting' in which case the monster should be staying the same, and new monsters appearing in the same book as the new HP system have Hit Dice normally. 'The Arduin Adventure', intended to replace the core 0D&D rules to use with the supplements, does give more HPs to some monsters (e.g. orcs go from 1 hit dice to 34 hit points); it has a slightly different HP system again of [CON score +20+level].
Some of Hargrave's problems with HP inflation may actually be due to level inflation - the class tables in the original Arduin go up to level 100.
Gamma World: CON in six-sided dice is traditional from 1E to 4E (weapons do AD&D damage but powered weapons doing large amounts also exist). 4E adds 1d6 per level advanced, and has classes...Enforcers get +Con HP initially, and add CON modifier each level advanced. GW characters convert to AD&D keeping all their hit points (!) i.e. 35-60 average at 1st level. (as stated in the AD&D DMG for 1st ed. GW, and the same rule applies for 4th Edition according to Dragon #183 conversion rules).
Monsters have lots of (usually) six-sided hit dice, set by race rather than CON (2E listed ability scores for creatures). (though if it hadn't, its HD per CON idea would've made it easy to represent things like the 3E 'tauric' template that adds component races HD together).  
Palladium (in general): generally Hit points = Physical Endurance (3d6) + d6 per level (including 1st).
-Original Palladium Fantasy characters Original or revised Palladium Fantasy did not have SDC. Race affects PE and hence HP heavily e.g. at 1st level normal elf 2d6 PE->3d6 HP, human 3d6 PE->4d6 HP, dwarf 4d6 PE->5d6 HP. Multi-classed characters could scam extra HPs by going up level in multiple classes, getting them more levels more cheaply.
-TMNT characters had SDC based off Size Level, plus any physical skills (choice of somewhat restricted due to skills being allocated on background table).
-Heroes Unlimited characters had SDC based off power category, + super power bonuses, etc, plus more physical skills.
-Rifts/Robotech include 'MDC'. Base SDC is by class (from 3d6 to d4x10). Even a roll on the background table can give 'scaly skin' (+3d6 SDC).
Monsters e.g. in Rifts may instead have up to several hundred MDC, or more (with deities having HPs that look like modest lotto jackpots).  Inflation of numbers over time largely erodes the value of PE (Physical Endurance) as an attribute (on the flip side, damage output, Strength went up due to inclusion of physical skills and then 'supernatural strength' - but PS does not affect MD damage). The MDC system can optionally be dropped to have an SDC-based game (Conversion Book guidelines), such as for characters travelling to 'SDC worlds', though this generates weirdness since the straight MDC/SDC conversion it suggests drops some characters to 1/100th their normal hit points pretty arbitrarily, leaving some characters still overpumped (e.g. Juicers get a huge SDC bonus - normally insignificant in effect - that doesn't divide).
Palladium's inflation sometimes is 'uneven' in what's increased. As HP increases damage also increased, and the margin of error between unconsciousness/death [-PE] narrows from quite wide to almost nonexistent.
13th Age: Base value 6-8 by class, + Con modifier, x3 multiplier at 1st level. The multiplier increases by x1 up to 4th level, by x2 up to 7th level, then by x4 up to 10th level (game max.).
Synnibarr: d6*100 life points per level, plus CON (rolled on d20, minimum 8)*10 at 1st level only. +bionics bonuses (potentially into the thousands of points, to a cap of 50,000). Bionics add to general LP pool, despite limbs having locational HP, i.e. a bionic arm helps against being shot in the head. Optional system replaces with life points = weight.
BRP: average of SZ (2d6+6) and CON (3d6). Divided by location in Runequest.
Marvel Super Heroes: Health = STR+AGI+END+Fighting. (usually damage = opponent STR). At 0, unconscious and begin losing Endurance ranks.
Fuzion: Base Stun hits = body (1-10)*5. Base Hits (killing) = (body*5). Characters can reallocate up to 1/2 between these at chargen.
Toon: 1d6+6 hit points
SenZar: = character CON (5-15) x experience level. Death at -CON.
Monsters use the same formula but get +/- d10 or d20 to the total (GM choice)?- presumably for variety [fixed CON given for each].
Dragon Warriors: d6+class modifier (+9 barbarian, +7 knight, +4 sorcerer). Unconscious at 0, death at -3. The random roll replaces having a random-roll 'Constitution' - it doesn't have CON, instead instead using Strength for e.g. rolls against poison - a houserule I've seen is to roll a 3d6 'Endurance' score and use [End/3] instead of the d6 roll for HPs.
HERO (6E): body base 10 (+1 per character point), stun base 20 (+2 per character point). -Body equals death.
Hero characters will usually have a 'Physical Defense' (or Energy Defense) that reduces damage slightly; in 4E PD was derived as (Str/5) and ED (Con/5), while they're fixed base in 6E.
Amazing Engine: varies by setting. Faerie, Queen & County, Stamina = (Willpower+Reflexes)/5, Body = (Fitness/5). Attributes are up to 7d10, +20. Bughunters get an additional +10 to physical stats and a /3 divisor.
Talislanta(circa 3E)- About 10-16 base HP depending on template (12 is standard), +Con (average 0), +2/level. Extreme template HPs range from 4 (ferran) to 22 (monad).
Unisystem: (Str+Con)x4, +10 life points. Stats are rated around 1-6. "Hard to Kill" can add extra life points (1-5 pt merit, +3 per pt, also adds to checks to survive at negative LPs).
Superbabes: HTK (hits to kill) =(d6 per level)+ Muscles bonus (up to +220 at 1000 Muscle) + Health bonus (+600 at a max. 1000 Health) + Moves bonus (+60 at max. 500 Moves) + Int bonus (+10 for mindless, +0 average, +5 for a deific 300) + Will bonus (+55 for a 500) minus Personality and Looks penalty (up to -30 from a max 300 in each; up to +10 for scores of 0).
Icons: Stamina = [Strength+Willpower] (note: No Endurance stat. Determination can also be spent to stop damage.).
Cortex- Life Points equal Vitality stat +Willpower stat (scores are rolls from d2 to d12 so using maximum i.e. d8+d8=8+8 = 16 LPs.) When total damage exceeds LPs, the character must make an average Vitality+Willpower roll to stay conscious; difficulty increases each round. Wound (as opposed to stun) damage can also apply a penalty to this.
Over The Edge: roll double normal dice pool of most combat oriented trait, or take [7x pool] as hit points. If multiple traits, some or all can be rolled (specify in advance and take highest).
Demonspawn gamebooks: Life Points = sum of all attributes (there are seven rolled on 2d6x8;  Strength, Speed, Stamina, Courage, Luck, Charm, Attraction + Skill which starts at 0 and gains one per combat) = average LPs of 392. Being sexy helps noticeably - since there are two charisma scores (Charm vs. males and Attraction vs. females) which each add 1:1 to LPs. There is also a "Power" score for using magic, which doesn't add to PC LPs, but does for some monsters (e.g. Demonspawn). Monster difficulty is usually reduced by low Charm/attraction; very tough monsters can have very high Courage or Stamina for more LPs with little other combat effect (one 900-LP giant skunk monster has 200 Courage, 400 Stamina) - a way for the GM (well, the book) to fudge monster hit points where desired.
Starcluster 3E: "Constitution" = Str + Coordination + Agility + Endurance (stats averaging 7-8), multiplied x10 if using d100 or d10+bonus, x4 if diceless, x2 if multidice additive. (damage varies depending on which game resolution system is chosen). Penalties accumulate for each 25% of Con lost.
Hong Kong Action Theatre: reportedly has two sorts of damage - 'Form' (Toughness attribute)(physical injury) and Focus (Chi attribute)(fighting spirit). Player allocates damage between these as desired - Form reduces Speed/Skill, Focus reduces Cool and use of special abilities.
FantasyCraft: (damage similar to D&D). Characters have Wounds = CON (x size multiplier; 1 med, x1.5 large which is available for some PC races at 1st level e.g. drakes, giants), plus Vitality of up to [12+Con mod]/level. Minor NPCs instead make 'damage saves'; this is a slightly wonky mechanic as its a 'damage based DC' - see discussion of these in next post - although the problem doesn't affect PCs/special NPCs. Tougher non-special NPCs may still make 'damage saves' require multiple failed saves to kill (...basically invalidating the point of not tracking hit points, although it does allow 'kill minor NPC' feats/powers to work against them at reduced effect). Critical hits allow characters to spend an action die per failed save applied. Weapon feats often cause autofails based on different stats being higher than the target (Con - hammer, Int-knife, Wis-staff, etc.).
Hollow Earth Expedition: HP = Body (1-5) + Willpower (1-5) + Size (avg. 0). Characters are unconscious at 0 and die at -5 (-7 w/ Diehard). Total HP for creatures can be negative if Sz is low in which case the effect is ignored until affect they take damage i.e. a -4 HP creature dies immediately if it takes damage.

Stress Track
Fate Core: a character has physical and mental stress boxes for 1 damage /2 damage, with Physique and Will skills giving extra slots (for 3-damage at +1, 4-damage at +3, and an extra mild consequence slot for +5. They also can take a mild, moderate or severe consequence from damage, reducing it by 2, 4, or 6 respectively and each time adding a (negative) Aspect. Characters recover all stress (but not consequences) between action scenes and probably will 'concede' conflicts without dying. NPCs have fewer stress boxes, depending on plot importance. [side note: see thread here (http://forum.rpg.net/showthread.php?728874-FATE-Core-Not-Sure-About-the-Extra-Stress-from-Physique-Will) debating if characters should all have the same stress track for 'spotlight time' fairness).
Shadowrun 1E: 10 wound boxes (Body stat roll used to soak damage). NPCs may have less - being taken out by a Light, Medium or Heavy wound only ("Professional rating" 1-3).
Storyteller e.g. Vampire: a number of named wound levels (Bruised, Crippled, Incapacitated, etc). The only way to get an extra wound level basically is the "Large" merit.
Limited number of levels makes this handy for running wound penalties (which inflate seriously at Crippled). 1 damage = 1 wound level vs. soak so damage often varies between complete bounce and 'chunk salsa' effects, as opposed to other games' death spirals. Each level gives a particular wound penalty; some rolls are exempt from wound penalties e.g. Arete rolls in Mage are initially only about 1-3 dice, so wound penalties don't affect it. The unrealisticness of damage 'bouncing' for high soak is somewhat mitigated by PCs normally being supernaturals; physically human creatures (including Mages) can only soak 'bashing' damage, not lethal.
Aberrant -a Storyteller-derived superhero game, this was similar but had serious problems with damage and soak scaling; a PC could be built with soak similar to a regular human ('baseline'), while energy blasts could go up to 20 or 30 dice. Health Levels were the same as Storyteller, although aberrants could make a skill check to negate wound penalties and could buy extra health levels (redundant internal organs).
Apocalypse World: 12 segments, normally shown as a 'clock'. Derivatives may modify this, e.g. Dungeon World is more D&D-esque, with the main notable difference perhaps that characters can often get free 'kill' results vs. lower-level opponents (+1 to your level if you have the Vorpal Sword).
(AW doesn't use its HP as a track very much - e.g. to determine whether injury worsens on its own. It does show soaking, a common feature of fixed # HP [stress track] systems, in that characters can take an attribute penalty to absorb damage, albeit rarely).
Savage Worlds: PCs have 3 wounds with a "fourth" wound meaning a roll for incapacitation, -1 to rolls per wound; 3 bennies which can be spent to roll a Vigour check to resist wounds. Most NPCs have only one wound.
Forgotten Futures: named wound levels of "Bruised", "Flesh Wound", "Injured", "Injured" (there are two 'injured' levels), "Critical". Unlike most stress track systems, wounds just use descriptive labels i.e. a weapon might deal an 'Injured' result. An extra result at the same level is moved down to the next stage i.e. a second Bruise gives a Flesh Wound instead. See also damage calculations, next post.
Fireborn: characters have 'minor wounds' equal to their 'Earth' score, and then wounds at -1, -2, -3, etc. up to -8(dead). Thresholds of [Water x 1,2,3 etc.] determine if a wound is equal to -1, -2 etc. Minor wounds give no penalty (-0), once all wounds of a given level are filled a wound moves up to the next stage.

Attribute Loss
Tunnels and Trolls: = character CON score (base 3d6; x 2/3 if elf, x2 if dwarf or hobb, +level or magic boosts). Death at 0.
The Fantasy Trip (pre-GURPS): HP = STR . Generally 8 to about 16; in Melee STR and DEX add to 24, TFT clone at darkcitygames has 3 stats and uses base 8 for each, with 8 discretionary points. Monsters may have STR of up to 50 or so (giants).
GURPS: HP =Health (3-18, bought with points). -HLT means roll HLT or die. Automatic at [-5*HLT]. 4E uses STR instead of HLT.
DC Heroes: damage is subtracted from BODY attribute; body also reduces damage taken (calculated with a table). The damage reduction can also be provided by armour or martial arts powers; characters are sometimes made harder to kill with the Invulnerability power, giving an immediate check to 'heal' damage taken.
Maelstrom: characters have an Endurance score (base 30 + discretionary points, rolled against as a percentage). Characters are unconscious at 0 and dead after 100 damage total.

Roll Penalty
Cortex+ e.g. Marvel Heroic/Smallville: 'stress' is rated at up to d12. It equals one of the dice in the attacker's dice pool when damage is generated, and can then be used as an extra die by the victim's opponents. More damage later either supercedes (if higher) or adds one dice step; the system is interesting in that it can give a probability adjustment based on damage for either the total damage taken, or a single individual wound. There are mental and emotional stress tracks as well as physical, making powers like 'invulnerability' less overpowering.
A minor peculiarity of the system is that since attack roll and damage are separate numbers chosen from the same dice pool, a high attack correlates with less damage and vice versa (instead of a high attack getting more damage).
Marvel SAGA: cards are also used as HPs. (NPCs don't have cards and so just have HPs, I believe).

Specific Injury/ Locational HP
One Roll Engine: 4 wound boxes to the head, 10 to the torso, 5 for each limb: potentially +1 box to each for a high Body stat.
Age of Heroes: 'location points' (LPs) determined by cube root of mass in each hit location (listed on a table). 'Cumulative hit points' are calculated with LP x a multiplier based off CON (4.0 for an average score) + flat Willpower bonus (=half willpower).
Rolemaster: hit points based off 'body development' skill rank, capped by race however. Early RM had a die roll for each rank bought, later RM had a fixed amount (based on race) per rank. As a skill it is indirectly affected by class (development cost) and the stats determining available Development Points. Raw HPs are less important in RM than in many games due to commonness of crits.
Cadillacs & Dinosaurs: NPCs 20 points. PCs have stats rated 1-10 and a 'hit capacity' of chest (STR+CON)*3, other locations (STR+CON)*2, and head (CON*2). (Presumably a character with high STR and low CON would have a head that looks like an apple). Locations are disabled at 0, and blown off at negative of normal.
Amber: GM defined damage (wounds are described and all effects are up to the GM)
Puppetland: character sheet has a 'jigsaw' picture of the puppet. Each time it is damaged, a piece is coloured in. (thanks to TristramEvans).
PDQ: damage reduces a characters 'qualities' and are down when all qualities are zero. The first quality lost has a story effect related to it ('Punching Spiderman in the Mary Jane').


General patterns here: 1-10 stat range (e.g. d10 mechanic) tends to use either HP generated by a multiplier, or a subtraction operation on all incoming damage, or locational points. D20 most often follows a D&D model (rolled HP + Con mod per level). Die pool systems often use rolled soaks, sometimes with fixed # health levels.

Working around the HP system: a HP system should provide a 'workable' HP total for any character that can play, more even if everyone should be involved in combat. In e.g. boardgames, characters with small HPs may have some other workaround (abilities that let them burn off items or cards instead of taking damage and so extra 'virtual' HPs, and RPGs can likewise have spells that do that - i.e. Phantom Armour for the 1E illusionist).

He rolled the percentile dice again. The numbers blazed up at him. Eighty One. High damage, even for an immortal.
-Bimbos of the Death Sun
 
 
The other side of the HP system is the damage system. Damage in most systems is an example of an effect system; it is usually the most involved effect system in an RPG because precision is required – the stakes are by default character life or death, leading to inclusion of detailed modifiers for things such as weapon modifiers (1), attacker Strength (2), and sometimes hit location (3). Damage usually includes a random variable (4) and may include a skill/to-hit bonus.(5).
 
(1) Weapons: In HP-based systems weapons are often assigned different amounts of damage (exceptions including OD&D and Fighting Fantasy; potentially HERO which is more complex but where, IIRC, a weapon’s specifics can be designed by the player able to pony up enough points). Some systems give weapons multiple possible damage ranges e.g. Harnmaster separately defines Edge, Point and so on values for weapons (a detail most games are happy to ignore or abstract into the damage roll – like maybe a 1 on your longsword damage means you hilt-punched the orc in the snout); Palladium’s Ninjas & Superspies includes various unarmed damage ranges for one-finger-strike, punch, kick and so on, though fails to offer much incentive to use lower-rated attacks.
All weapons being equal does give a player more freedom to customize to fit their concept, without ending up using something that’s sucky because the game designer failed to properly understand how a khopesh is meant to be used (the stupid shape is to go around an enemies shield, not so you can make free trip attacks; thanks, whoever wrote Sandstorm...), but this removes a layer of the crunchy/tactical elements of character design; it is generally better to design weapons to be equal rather than identical; a task often approached by adding different armour penetrations, special abilities, special drawbacks or attribute requirements to weapons, something designers manage with varying degrees of success. Of course, it can also be argued that some weapons (e.g. whips or lucerne hammers) should be uncommon choices because they aren't that good. (Some systems like 3E include special abilities like feats etc. that can power-up weaker options.

 
(2) Hit Location: some systems will modify damage for vital locations struck (e.g. head = double damage), while others assume this sort of thing to be part of the damage roll; for others damage points aren’t changed by location but the effects of X amount of damage might be different i.e. different limbs may be disabled, or a character may have less HPs in some areas (such as the head e.g. in Twilight 2000, Runequest).
One example of what not to do with hit location would be the mind-boggling Swords’ Path: Glory (discussed here: http://www.therpgsite.com/showthread.php?t=21194 (http://www.therpgsite.com/showthread.php?t=21194) ); it uses hit location tables that cross-reference a rolled Impact and armour type to determine exact flesh depth penetrated and hence whether bones are broken, arteries slashed or so on. Unlike Rolemaster this was almost wholly a raw HP system – the hit location was randomly determined and final output of the table is simple a number of damage points and a shock roll % rather than a specific injury, making the outcome not much different to just rolling a damage die (compare the principle of Black Box design http://www.enworld.org/forum/general-rpg-discussion/226856-simulationists-black-boxes-d-d-4th-edition.html (http://www.enworld.org/forum/general-rpg-discussion/226856-simulationists-black-boxes-d-d-4th-edition.html) ). Also, SPG was meant to be plugged into a system where HPs inflated rapidly with level, despite its HPs being completely physical rather than representing “luck” or “rolling with blows” , and didn’t allow for any way to select hit locations or otherwise improve damage from character skills/higher attack rolls, making it in many respects then, less realistic than say Storyteller (?...though the idea of a layer of 'impact' calculation before damage calculation, something shared with HarnMaster, could have potential uses...?).
 
Hitting a specific hit location may only be available as a result of a "called shot" in some games (2nd Ed. AD&D, Unisystem, Savage Worlds), or may be a result of a good hit roll (an idea that works better if attack rolls are DEX-modified, rather than STR-modified), or might be generated with a separate random roll (Runequest, Deadlands).
A "separate" roll can sometimes be generated as part of another roll i.e.
*Warhammer 1E/2E reverses the tens and ones places of the d100 to determine location. The future 40K games e.g. Deathwatch run into complications with autofire weapons such as bolters where a single hit roll can generate multiple hits (a success is one hit, +1 hit per 10% of attack margin, up to the full ROF); in this case the hit location roll is used for the first shot and a table lists where 2nd, 3rd, etc. shots land - following a sort of arc across the body e.g. Head is always Head/Body/Legs (or something like that).
As noted by Rob Muad'Dib later:

QuoteTop Secret/SI(Designed by Douglas Niles and published by TSR way back in 87, it used all kinds of cool/innovative bits in its design--ads/disads, stun/wound dmg marked as /X, luck points, etc) pulled two result from attacks for close combat/melee. You'd roll under your Attribute (plus small skill bonus), if you succeed, your damage was based on the tens die (a Price is right/blackjack mechanic) and the ones die determined hit location.

*One Roll Engine counts matches in a dice pool as successes for that number i.e. if you rolled 7,6,6,6,5,4,4,1 you got either three successes (damage) against location 6, or two successes (damage) against location 4. Potentially this method could be used with a damage roll in some games, if damage is generated additively from a set of dice, without having to use OREs core mechanic for all actions.
If randomly generated with a separate roll, hit location may be generated for just some results (e.g. hits that are criticals, or that do more than a certain amount of damage) or for all results. A rolled outcome might be modified in some circumstances e.g. it may be possible to 'block' a hit to the head in melee by taking a hit to the arm instead. HarnMaster arranges locations on a table lowest-to highest (with odds/evens determining left/right) so that a bonus or penalty can be added to the location roll for 'aiming high' or 'aiming low', without fully specifying where a blow is aimed.
Synnibarr has a rule where hit locations for shots are rolled but dealt to a % of hit points, which would work except that cybernetics add huge hit point bonuses to the general hit point pool (i.e. a character can be shot in the leg, and not disintegrate solely due to having an incredibly tough robotic arm).
 
How the hit location system works has a major effect on combat description by the GM/players. The GM is freer to improvise description without locations, whereas with more detailed rules the player might get to describe results more (based off the dice rolls/mechanics).

A couple of other determination methods use a silhoutte or body map: Aces & Eights' "Shot Clock" uses a d12 to generate scatter around a prechosen location (which is hit without scatter if the attack roll is sufficiently high), while Millennium's End uses an “overlay” (showing how much roll is made/missed by) over a “body map”.
Hit locations mostly provide a more realistic game, at a cost of more mucking around, but do tend to generate issues with certain damage types such as electrocution, shock, or poison – even falling – which are hard to allocate to single locations. Some systems may use different location tables for melee and ranged weapons.
I’ve occasionally thought that in cyberpunk type games where “organlegging” is popular, hit location tables might be useful for the GM to help determine what “treasure” is salvageable out of defeated opponents...

(3) Strength modifier: the other common modifier applied to damage is for Strength; exceptions include 0D&D pre-Greyhawk, HarnMaster - with slight variation appearing in the most complex version, HarnMaster Gold, Rolemaster, and Legends of Anglerre; Amazing engine which claims Fitness adjusts it but doesn't say how much; 4th ed. D&D where various modifiers might apply; as well as the simpler Fighting Fantasy or Maelstrom which don't have an equivalent score. Tunnels and Trolls just gives more 'adds' for STR, so it improves to-hit and then indirectly damage based off difference between attacker and defender. Rolemaster adds Strength modifier to offensive bonus (to-hit chance) which indirectly ups damage and criticals (STR modifying result here is possibly weird as it gives specific, highly accurate and deadly strikes on high results). Shadowrun 1st Ed uses Str to modify target number of defender's soak roll.
This tends to make Strength a fairly important statistic for damage in most games. Modifier is normally just an addition to damage, though Synnibarr gives characters a damage multiplier and Savage Worlds increases the step die rolled (the Strength die). A couple of games (Magic Quest, Legend Quest) have STR bonus based off # Str points above STR-minimum to use a weapon, instead of an absolute modifier (notably affecting dual weapon use since using two weapons has cumulative Str-required, so using them reduces Str damage bonus). D&D 3E applies 1.5x Str mod to two handed weapons and 0.5 for offhand weapons, so that TWF can't apply 2x Str mod easily; optional rules (Savage Species) extends the progression to x2, x2.5 etc. for monster weapons used three- or four-handed. (This sort of proportionality can be less messy with die pool/variable TN systems).
In a system, occasionally a weapon might get an extra bonus beyond the normal plus from Str, e.g. City of Terrors for T&T has an item, the 'war gauntlet' that 1/day power punches for 1d6 damage per Str point (whereas a normal fist is 1d and gets +1 'add' for each Str point above 12; the Gauntlet presumably gets that as an extra bonus as well).
GURPS calculates a character’s # d6s rolled for damage depending on Strength and whether the weapon is “Thrust” or “Swung”. The Forgotten Futures RPG was interesting in that Str only increased the probability of more damage rather than adding more damage automatically since it increased odds of a higher result (different damage descriptions are given for a 2d6 roll under ½ the Str (Body) value, a roll under full Str value, and rolling over).
Systems may “mirror” the role of Con in determining hit points and role of Strength in determining damage; one might add and the other subtract damage equally (Warhammer). Or to try to build a system where a character can normally take 3 hits before dying, a character might add [1xStr mod] to damage and [3xCon mod] to HPs.
Breaking this parallel leads to a noticeable balance issue in 3.x D&D, where a low Con cripples even a high level character (20th level = 20x Con modifier to HP). This sort of one-sidedness also occurs in “Aggravated Damage” (Storyteller), where the attacker still gets Str but the defender doesn’t get a soak roll using Stamina.
Crossbows in D&D tend to be weaker than other weapons due to not adding Str modifier; later D&D versions added +Dex for parity, while Palladium (in their medieval weapons & castles book) gave crossbows a built-in equivalent STR. Another game where this really shows is Scion, where melee weapons can get Epic Strength bonuses (see here (http://transitivegaming.blogspot.com.au/2007/10/scion-guns-vs-melee.html)).
See page 7 (post 69) for more on weapon Str minimums.
Large creatures don't always get enough raw bonus from Str to represent how nasty they are, so may get some sort of size bonus to damage (maybe equivalent to weapon type e.g. in 3E where size steps up damage dice). BRP e.g. Call of Cthulhu bases 'damage bonus' off a combined total of [STR attribute + SZ attribute] rather than STR alone.
 
*(4) the random variable; most systems use random roll of some kind for damage; exceptions include games where to-hit roll modifies damage instead e.g. Talislanta (see below), Dragon Warriors (damage set by weapon, no modifiers), and Tunnels and Trolls (damage = difference between attackers and defenders’ rolls; an odd system in that extra weapon damage dice also add to a character’s chance to hit).
Rolemaster uses the attack roll on a table to determine hits of damage (no separate damage roll). High rolls generate criticals off a different table; the attack roll (modifier by attack and defense skills) determines what sort of critical is generated (A to E or so), with a new roll then being made on the critical table.
DC Heroes has attack success adding to damage, but also often generates a 'variable' nonrandomly, through attackers or defenders expending Hero Points to raise their effect or resistance values, or use of Hero Points to eliminate damage directly with 'Last Ditch Defense'. (cf. post on 'safety valves').
Games with fixed/fairly fixed damage ranges can have larger variables in cases where some of the normal damage modifiers/rules don't apply that well. Aberrant for instance has Teleport error (landing inside an object) deal 1d10 health levels of damage (rolled directly) when most rolls instead use a dice pool. A 3.x pit trap begins with a roll of d4 to see how many spikes the character lands on, then gives each spike an attack roll/damage roll as a dagger (which could perhaps mostly be abstracted to a single larger die if desired, although that would cause DR issues).
Highly polar rolls can work better for generating interesting results. For instance, a GM might use a damage roll for a missed attack to see how badly damaged a computer console is, which gives fairly fixed (uninteresting) results if the damage is also along a fairly narrow range.

*(5) the to-hit or skill bonus; Shadowrun 1E has fixed damage, modified by attack successes; in it weapons have varying "Staging" which is how many successes move a weapon up a damage code -light to medium, medium to serious, etc. Weapons with low Staging are more beneficial for highly skilled characters, however Staging is also the # of soak (Body) or Dodge successes by the defender that will drop the attack back a code so these weapons are less effective on high-Body targets, or high Quickness ones. A later edition of Talislanta has fixed damage by weapon, with 1/2 damage (partial success), x1 (normal) or x2 (critical). Storyteller (oWoD) adds successes to-hit to the damage dice pool.
The to-hit add to damage can be thought of as one way to represent character skill. D&D doesn't add a bonus from the to-hit roll (except via criticals) but skills may apply a bonus to damage directly i.e. extra 'sneak attack' dice, BECMI weapon mastery, weapon specialization, or monk +1/2 level to damage in 1E.
Note: post #28, above, has more about 'effect' in general- flow of data from margin of success to result and so on.
Note that if a high dice roll increases damage, that can offset combat options or builds designed to roll lots of attacks at a penalty to 'critfish' for 20s or the like - a penalty to the main attack lowers damage, while an attack with a penalty deals less damage.

Damage-based rolls
A very few systems have worked out how to take a damage value, and use that to determine a success chance/probability of related events. For example, in Marvel Super Heroes an energy blast doing 30 points of damage would be a Remarkable amount of damage, and that value could determine the likelihood of the blast setting a building on fire (i.e. using the Action table, 30 damage would give a normal success on a 36+ on d100..). Other systems have attempted to set damage-based DCs (consider 3E D&Ds “concentration checks” for spellcasters taking damage, Coup de Grace saving throws, or a high level rogues’ Defensive Roll ability) but this generally works poorly since damage is not scaled appropriately to give a d20-based DC.
Essentially systems run from a Success Roll (die roll for success/failure)-àEffect; taking an Effect output and converting it back to a success chance is working backwards, and so is difficult. MSH works for it since attacks deal fixed damage; Mutants and Masterminds should allow damage-based checks as well, since its damage rolls are just DCs for checks. Savage Worlds almost but not quite manages it, since its damage roll is on a slightly different scale to other checks - the sum of 2 dice, instead of best of 2 dice (the original 1st printing SW had damage as simply a trait roll, and in some respects would function better for this than the modern system). A dice pool system could in theory handle a conversion back from Damage to Success roll, if the damage dice pool and normal task die pools had similar numbers of dice.
Comparing say SW-1st printing and MSH, these work differently in that MSH has damage equal to 'attribute' (from which a check probability can be worked out), while in SW-1st printing damage is simply a check itself - game mechanically there's no difference between rolling unarmed damage and making a Strength check to twist someone's head off. The SW system has most of the advantages of MSH i.e. capability to use damage as a DC for an opposed roll, but also allows damage randomization. Similar systems could (theoretically) work with damage that directly reduces attributes (like in T&T), whereas MSH's system isn't particularly compatible.
In a game like SW where damage is a 'check' there isn't much difference between a sword stroke and a save-or-die effect. In some ways its damage checks are better for that in that a SoD often doesn't consider all of the toughness bonuses a creature should have, such as size bonuses and the like.
One Roll Engine is perhaps scaled well to use damage as an opposed roll too (as damage simply equals to-hit successes, plus some weapon bonuses) though I don't know if any particular mechanics are built off this. Earthdawn is another system where damage is a normal task die roll (Strength + weapon specific modifier is used to work out the step die), though the final result is normally subtracted from hit points rather than being used for opposed rolls, normally; Air Blast uses damage vs. Strength for knockdown (in ED 2E), most other knockdowns etc. are complicated by considering Wound Threshold however.
 
Further thoughts on damage-based rolls
Actually, considering further there are probably 3 potential mechanisms providing usefully scaled damage amounts (from the damage roll of individual damaging attacks):
1) damage from one hit is on the same scale as attribute (fixed/proportional to attribute, say 3-18 if the system has stats that are rolled with 3d6), and can be assigned a check modifier accordingly, using the normal attribute bonus chart or attribute check rules. If not attribute, it could work if scaled as a skill check or other check.
2) damage is rolled as a check, identical to other checks (if it equals to-hit successes, or is a separate Strength check with limited weapon modifiers, as in original Savage Worlds, etc). The damage can be variable and is used as the target number for opposed rolls.
Or 3) damage is generated by a 'damage check' which is identical to other checks as above, but then a final amount is generated from this, not necessarily equal to check result e.g. actual quantities of damage can be assigned via a table. Make the damage check function consistently as an opposed value may limit some of the operations that would normally be possible with a table, like using an alternate table for smaller weapons; it also suggests that e.g. damage reduction/armour should apply to the check result rather than output damage number.
Setup 3) of course adds a table - and in the middle of combat - but generates fewer constraints to the designer with regard to how Hit Points must be scaled, and how the damage check must be scaled (the two things that have to dovetail with each other in the case of the other options).
A few systems use ad-hoc translations of damage to success chance, usually badly: the 2nd Ed. Complete Fighter lets the 'sap' manuever have a 5% chance of KO per point of damage (regardless of defender HP), while Superbabes has damage forcing the target to roll d% under its current HPs to not be knocked out. Modern Savage Worlds sometimes uses [roll penalty = number of wounds] e.g. cremefillian ingested poison in Low Life; maybe gearing down the damage too much?
(Hypothetically, you could imagine a system which has damage set up to work as a check value, and damage that isn't - call these fixed and unfixed damage maybe. In this case extra bonuses could give more damage, but at a cost of having the damage become 'unfixed' and no longer be useable for dealing stun, knockback etc. etc. That could be associated with e.g. weapons vs. spell damage.)

Elaborations
If rolled separately, critical successes/failures on damage rolls could have other effects, like weapon breakage (e.g. a '1' for damage = a weapon breakage).

As an idea, a range of different special results could be generated for 'criticals' without a table, based on damage rolls, e.g. 'doubles' might 'roll up', each maximum die causes pushback and multiple maximum dice makes a target drop prone.


Legends of Anglerre (FATE) has a mechanism for damage where the overkill on creatures ("overflow") is directly applied to other creatures (if there's a stunt like Cleave) or converted into additional effects (movement, etc.). LoA is perhaps especially good at handling this since it lacks a second roll for damage or other damage modifiers i.e. for weapon type (explaining how using a greatsword increases movement would be difficult!); amount by which an attack roll succeeds becomes damage directly. In other games, T&T has no term for "overflow" but likewise lacks a separate damage roll and so readily e.g. lets damage be split between multiple targets.

Older systems in particularly may sometimes model blood loss as ongoing damage from injury, which accumulates until a wound is properly treated (e.g. LegendQuest). Because of extra book keeping this is rarely seen nowadays. In more recent games the Roma Imperious system had interesting blood loss rules, further complicated in its case by HP being divided up by hit location, meaning blood loss was also from particular locations, rather than being systemic. D&D 3E retains bleeding for dying characters only, who lose 1 HP per round until they stabilize, apart from a couple of specific weapons/monsters. A game may also abstract progressive weakening with occasional rolls to see if a character collapses, instead of continuing damage.

Other Effects of Damage
In addition to HP damage, attacks might also cause 'knockdown' or 'knockback'. Systems here include DC Heroes, MSH (special colour result), High Colonies (based on damage before armour subtraction, if greater than Str - so lots of bullets can knock a character down), Runequest (I think replacing impales on special successes with some weapons?), and Rifts occasionally more or less by GM fiat (or whatever cases of GM fiat Kevin wrote down).
 
A damage 'threshold' can have other effects as well. D&D and some D20 variants have 'Death by massive damage' [for 50+ points, or a size-based amount] adding a save or die to large damage amounts. Some special attacks might also trigger based on N+ damage e.g. in Rifts the 'Xiticix killer' has a tentacle that enters and reams a target for extra damage if the original damage roll is 12+; in some games crits or Str bonuses etc. may modify this, or a 'base' amount only may be considered.

Critical hits - see page 14 (post #136 (http://www.therpgsite.com/showthread.php?p=567848#post567848)) for more details on critical hit systems.
 
Multiple dice for damage are reasonably common, which can scale up problematically at times. One comment in regard to scaling for systems e.g. 4E D&D here (http://forum.rpg.net/showthread.php?703186-D-amp-DNext-latest-L-amp-L-and-quot-tactical-module-quot/page12)

Quote from: YakkThere are people who think that if 1d8+4 is an appropriate amount of damage to take when you have 20 HP, then 10d8+40 is an appropriate amount of damage to take when you have 200 HP. In reality, the first has a huge random component (anything from 25% to 60% of your HP can be taken off in a blow), while the second is highly predictable (40% to 55% is the equivalent range) and takes 5+ times as long to evaluate. An example of this is the 4e damage per level charts, which presume "half dice, half fixed" has the same meaning at level 1 as at level 30, significantly making level 30 combat less exciting.

Some sample damage calculations, grouped into categories (roughly parallelling the 'effect' categories in post #28 on pg 3):

Fixed damage
Fixed damage (per shot that hits) would potentially work well with a system where a roll determines how many attacks hit, which could then be applied as a multiplier. Fireborn is something like this (but is somewhat more complex and listed under 'dice pool systems' below)
Fighting Fantasy: 2 damage regardless of weapon. (Test for Luck for 4, or 1 if this fails). cf. Advanced Fighting Fantasy below (Table-based). In rare cases damage may be rolled - e.g. Space Assassin has blasters which do 1d6. Weapon type usually doesn't modify; an inferior weapon may penalize "Skill" (the rules in the books sometimes just treat losing a weapon as generic 'damage' to Skill, rather than an ongoing modifier; in which case picking up weird alien nunchucks/a sharp piece of fruit/a walrus as a weapon and then drinking a Potion of Skill to restore lost Skill, might be interpreted as meaning you are now proficient in weird alien nunchucks/fruit/a walrus).

Marvel Super Heroes: damage = STR or weapon material strength, whichever is lower, or power rating for powers. While damage is fixed, special success on the attack roll may add a Slam, Stun or Kill result. Being fixed, the damage has no problem with scaling up to cosmic level without choking on too many dice - a class 3000 energy blast just does 3000 damage, instead of having to roll 30d6 (or whatever).
Dragon Warriors: fixed base damage by weapon (1-6); Str also adds a bonus to damage.
BESM 3E : mostly fixed damage, although damage is doubled on a margin of 12+ and tripled for 18+. Characters add 'attack combat value' (to-hit bonus).

Varying Die Type [i.e. an independently rolled die]
0D&D: 1d6 damage, regardless of weapon. The Greyhawk supplement adds alternate weapon damage and Strength modifiers/exceptional Strength for fighting men, as well as 'large-size' damage for weapons (e.g. a longsword is d8 vs. an orc or d12 vs. an ogre - maybe it does more damage cutting through more flesh, or this may be a game balance thing); 1st ed AD&D is basically the same as that. Swords & Wizardry White Box (a clone) has d6+1 for 2-handed except staves, d6-1 for small, with +1 damage on a critical.
(flat random damage IMHO is perhaps not optimal since its not much more effort or complexity to instead use a weapon die, or have a calculation off something instead of an arbitrary expression).
A few spells/effects use alternate systems e.g. fixed damage (a hellhound's breath doing damage equal to its HD in AD&D) or damage modified by AC [moving through the very pointy Plane of Minerals doing damage equal to d4+AC (not including Dex adjustments).
D&D 2E/3E: 1d4 to d12 +Strength modifier e.g. d8+Str mod for longsword. Potential critical for double damage on 19-20 (3E) or on 20 (2E). Strength modifiers start at 12+ in 3E and 16+ in 2E. Spells typically deal d6 to d8 per caster level. 50+ damage in one hit optionally forces a saving throw vs. death ('death by massive damage').
D&D 4E: variable # of weapon dice (by power) + key ability modifier + any additional special effects. Max damage on critical, +d6 per weapon plus. Some powers do damage on a 'miss' [=ability mod]; some feats likewise give that with weapons such as warhammer or scimitar, to balance their lower (+2, vs. normal +3) proficiency bonus.
Overall inflation in ability mods over D&D editions has tended to make the actual weapon die roll less and less meaningful (vs. 0D&D where a low roll might just scratch the orc, a high roll kill it); this changes the whole dynamic of combat from a series of life-or-death die rolls to a slow 'grinding' process (in part prompting need for more complex manuever systems to spice it up, although these are also good for involving player choice).
Black Streams: this is an interesting (free on drivethru) rules supplement for AD&D intended to let single PCs take on a dungeon solo. It takes the normal damage roll and vs. PCs steps it down [1= none, 2-5 = 1 damage, 6-9 =2, 10+=4]; PCs use the same table but deal damage in 'hit dice' e.g. a roll of '2' would deal 1 HD of damage and so kill a 1 HD orc. They also get a bonus class-based 'fray die' that works similarly.
Runequest/BRP: base by weapon e.g. d6 or d8 +damage bonus from [total STR+SZ] on table, with normal ratings giving +0 extra damage.
Savage Worlds: Explorer edition/Deluxe - Str dice + weapon damage dice (i.e. Str +d8 for sword). +d6 if hit roll succeeds by 4+; maximum rolls reroll and add. Shaken if roll exceeds toughness, +1 wound per 4 over. Str also heavily limits what weapons a character can wield, and so affects damage substantially (although a higher Str die can still roll a 1 - in unarmed combat particularly, Steve Erkel can 'roll up' and outdamage Arnie. Compare this to Forgotten Futures below, which has a slightly similar effect from a table).
SW 1st printing/2nd printing -Str trait roll (including wild die) + fixed weapon bonus. 1st printing gives +2 from per each 'raise' to hit (4 over Parry) (this was reduced in 2nd printing to encourage called shots). PCs had a big advantage on damage since they get both a wild die to it, and are more likely to get a 'raise' on the hit roll as well.
(see nDervish argues here (http://www.therpgsite.com/search.php?searchid=509047) that damage scaling in SW tends to not work at higher levels due to the fixed 4/wound being a narrowing gap as number of dice increases).
SW damage does tend to generate occasional blowouts since there are several dice which can 'roll up' separately. A houserule might be to limit one die to rolling up; potentially you could even limit rolling up to the bonus die added from a 'raise', so that open-ended results become quite rare.
(I also was recently working on a SW-derived system which was one-roll-only; in this a weapon did damage equal to either the Fighting die result (including rolling up as normal), or a separate damage die (usually larger, and including step increases for Str). 'Light' weapons dealt damage equal to the fighting-die only, with no extra damage roll; this has an effect of reduced 'critfishing' for TWF as this had two chances to roll up the Fighting die, off both attack rolls, but no damage die explosions.)
Ample Polyhedra: One friend's homebrew rpg "Ample Polyhedra" system, had a damage system reminiscent of Savage Worlds: characters had 1-4 'wounds' (1=Extra" to 4="PC") but instead of wound divisor being a set /4, each character had a 'toughness number' which was the divisor. A complication with that was that to keep criticals valid, critical dice were then also increased for high Toughness to cancel this out, making large creatures vulnerable to being stabbed in vital places e.g. Toughness 4 = +d8 damage on a critical (raise on attack roll), while Toughness 6 would give +d12 on a critical - even more damage so as to maintain a 50% chance of an additional 'wound'. A houserule proposed was to have normal damage wounds calculated using the Toughness as divisor, then add a separate critical roll not adjusted for Toughness i.e. d8 vs. TN 5 to get +1 wound added on to the final wound count.
The game treated armour as a toughness bonus, but this only helped against the first wound (a character with base Tf 6/+ armour 9 would take wounds on 15, 21, 27, etc.).
Cortex: damage = attack roll - difficulty, + probably a damage die (d0 unarmed). Strength modifies weapon damage only indirectly, by boosting the attack roll (for Str-based weapons). Str also does not limit what weapons a character can use.
Toon: almost all attacks do 1d6 damage, no Str [Muscle] modifier. The 'incredible strength' schtick, which has a fixed base instead of being Muscle-based, lets a character do +3 damage on a successful skill roll but gives combat penalties if the skill roll fails and opponent Fight roll succeeds. A few weapons do extra damage e.g. rayguns 2d6,  bazooka d6+2.
Warhammer 2E: d10+Strength modifier +(fixed) weapon modifier, 10s explode (if a separate Weapon Skill roll is made, IIRC); subtract target Toughness.
Later SF Warhammer games this inflates with multiple damage dice sometimes e.g. base 2d10+5 for a bolter, with +1 dice & drop the lowest for its 'tearing' quality (greatly increasing chance of a 10 occurring and rolling up), increase # Wounds, and some creatures with Unnatural Strength or Toughness (e.g. Space Marines) double those modifiers.
Dungeon World: like 13th Age below, weapons deal a hit die based on character's class.
Talislanta: combines step-die with a basic table (d20+modifiers, 6-10 partial success, 11-19 normal, 20+ critical). In e.g. 3E most swords would do d10+STR score; with a 'partial success' damage is reduced by half and with a critical the damage is doubled. 4E just has fixed base damage, adjusted for the table in the same fashion. Spells deal around d4 per spell level (potentially outpacing HPs), again with a damage multiplier from the table.
Ork!-the RPG: this uses a d4 to d12 for stat rolls (skills checks roll a number of these dice equal to skill rating 1-5, and add them). Combat is a raw attribute roll ( i.e. one die) of attacker Str ('Meat') vs. defender Con ('Bones'), with armour/weapon each adding up to +5 bonus; this same modifier range is normal for opposed rolls, though the modifier is fairly harsh for stat rolls as these use only 1 die. Damage = one level per 3 points of difference, round up (characters have six wound levels, including the uninjured health level).
Amazing Engine: step die with a 'margin rating' (roll under this on ones dice of the attack d100 means "Body" damage rather than "Stamina"). e.g. knife d4/3 margin, club d6/2. Fitness (basically Strength) theoretically adjusts this, but how much is not listed! Margin rating can be adjusted by called shots or armour.
Maelstrom: varies by weapon e.g. staff d6, spear 2d6, sword from 2d6 to 5d6 by cost. There is no STR attribute.
Mercenaries get a special proportional damage bonus - d6 per 10 damage or fraction, counting rolls of 1-3 and ignoring 4-6 (a blackjack die pool!). This is then a two-step process where initial damage has to be rolled before the number of dice to roll is known (e.g. 10 damage would roll 1 bonus die, 11 damage = roll 2 bonus dice). Ignoring the effect of rounding up, this gives about a 10% average increase in damage (+1 per bonus die).
Metagene: uses a variable dice based on strength. What's interesting here is they slowed down the progression by going d4,d4+1,d6,d6+1,d8, d8+1,d10..etc..not necessarily a great choice, every 2nd increase has exactly the same average but different distribution (i.e. d8+1 and d10 are both 5.5).

Die Pool (additive)
GURPS: variable number of D6s based on STR and whether weapon is swung or thrust.
The Fantasy Trip: variable number of D6s, by weapon; weapons useable are limited by character STR (roughly similar results to GURPS); only unarmed damage is adjusted by Str directly. Crits deal double or triple damage (4 or 3 on 3d6).
Cadillacs & Dinosaurs: firearms deal a number of d6s; monsters typically have a number of d6s (basically arbitrary; most are not rated with Strength). Melee/thrown weapons d6+Str score or half Str score.
13th Age: variable die type/additive. Damage is one die/level, with damage die based off class rather than weapon to allow free weapon selection, + [ability mod*tier]. Monsters deal a fixed amount of damage instead.
Star Wars D6: damage of multiple D6, for melee weapons this is a Strength check (+possible weapon bonus dice). Notable because this uses the same mechanic as normal task rolls. Targets roll Str to resist (+ armour?), with difference (on a table) determining if a character is stunned, wounded, incapacitated, mortally wounded or killed (3 wounds generate an incapacitated, incapacitated + a wound = mortally wounded).
Tunnels and Trolls:. available as free download on drivethru; extract of the core rules from the solo adventures here [URL="http://www.freedungeons.com/rules/]http://www.freedungeons.com/rules/[/URL]. Roll weapon dice (d6s) + combat adds (+1 per point above 12 in ST, DEX, or Luck) - [same total for opponent] = damage (before reducing for armour). Damage is finely defined by weapon 'adds' allowing for huge weapon lists (e.g dirk 2d+1, broadsword 3+4, scimitar 4d, warhammer 5d+1, greatsword 6d); where D&D has 'dagger: d4', T&T has a whole table of dagger types ranging from 'Dirk: 2+1' to 'Scramasax: 2+5', and same for other types.
In 7E and later, 6s deal automatic 'spite' damage. [T&T combats can be very one-sided, so PC resource attrition through the adventure may occur mainly through 'spite' or through loss of spell points [ST/POW]).
Missiles do much more damage (opponent total isn't subtracted from combat total) but require a Dex roll to hit, and come with the problem defense that a miss means defense is 0 and melee damage against the archer becomes probably fatal (though in a group situation, this is mitigated by friends contributing to attack or taking a share of damage). A DEX roll can also be required to hit very agile opponents (Blood Bats in the 5E rulebook adventure) or dodge the attack of larger monsters - GM discretion- so that opponent roll again isn't subtracted.  Monsters that don't fight normally and have to take the full attack of PCs are usually given a very high CON by fiat (e.g. the Con 90 giant mosquito in solo adventure Amulet of the Salkti).
Poison in T&T is very common and can multiply the final damage e.g. x2 curare, x4 dragon's venom. Early versions of T&T added the multiplier to initial die roll; I think later versions applied multiplier to final 'hits' instead, so that poison didn't increase chance of hitting, though this generates adjudication problems as characters would often be using two weapons - with only one actually poisoned - or adding their totals together in mass combat.
A couple of magic weapons -i.e. the Hero and Hopeless Swords, from the Naked Doom solo dungeon- generate a fixed attack each round, instead of rolling dice. This is also the case for one common attack spells (Take That, You Fiend). TTYF deals [IQ attribute*spell level] damage, a horrendous amount; this is especially bad in 7E where a character's level itself is often [IQ/10], making a TTYF deal damage approximately equal to [IQ-squared/10]
As the 'attack roll' is made up of weapon damage dice, it limits a lot of possible manipulations of the dice pool - it doesn't make much sense to 'split' the pool or spend dice on combat moves since most fancy manuevers shouldn't be easier with a greatsword than a dagger, unlike if the pool represented fighting skill.
Superbabes: base damage d6 (punch) to 20d20 (clobbered with aircraft carrier) + Strength bonus measured in dice with an irregular progression (at higher levels, generally +d6 per 50 for a maximum of +22d6 at 1000 STR). The "Hit 'em Harder" power adds a further +d6 per level with a specific weapon (in example characters up to +6d6).
SenZar: weapon type generates a 'Damage Class' (base DC is set by weapon, can be modified by magic weapons), plus Str adds bonus dice; these are added together to get up to several D10s of damage. Some weapon enchantments can deal x2 or x3 damage; the system gives separate damage bonuses for a Natural 20 to hit (x2) and rolling 10 over the TN (maximized damage) - quite often both happen at once. 1st level characters are very squishy but gain HPs rapidly -  a strange feature of the advancement being that while there's no balanced mathematical progression, characters dealing level-inappropriate piles of damage will level faster (by killing oversize threats) until they die or catch up in HPs. Spells instead deal fixed damage (= power points spent, max. cost capped by spell level), and monsters have what sort of dice they roll for damage fiat-assigned directly, rather than going via 'damage class'.
Infinite Power: damage is (like other rolls) a set of d8s added together, 8s add and roll over. A total over opponent 'damage limit' inflicts one 'hit' and 4 hits takes out a character. (This is based off the quick start rules but it seems there's no benefit to increasing damage beyond enough to hurt the target).
HERO: d6 Stun per point of damage class (e.g. per 5 STR). Body damage = 1 per die (except that 1s rolled on the stun dice are worth 0 damage, and 6s worth 2 damage). Typical combat is fairly nonlethal because chargen is complex, and due to genre conventions. Killing attacks do more Body but less Stun - in 6E, Body damage equals the full roll and multiply by d3 to determine Stun dealt.
Fuzion: multiple d6 additive. Dragonball Z for Fuzion apparently runs into hundreds of bonus dice, apparently with defensive dice subtracting (?) and average normally used unless a result is likely to be significant. # dice (or fractions like -1 per 10d) can be used directly in some calculations like penalty for combat manuevers or energy costs, rather than damage itself. The scaling issue shows the problem fitting DBZ to Fuzion rather than using a custom system (e.g. Marvel or DC Heroes for instance are better adapted to this sort of scaling problem, but their setup is intrinsic to their damage systems rather than something that can be just added on in a sourcebook.).
Other: Someone's DIY system on rpg.net here (http://forum.rpg.net/showthread.php?771239-Weapon-damage-scaling-by-strength-Lite-Rules) has a table cross-referencing Str and weapon type, with the peculiarity that rounding off means optimal weapons shift around as Str goes up/down.  

Die Pool (Count successes)
(Dice pool games as above tend to have fixed wound tracks; partly 'soak' is easier with these, but also arbitrarily-large HP pools would require correspondingly large damage dice rolls - its more OK to go from roll d8 at 1st level to 4d8 at higher level, than to go from 5d10 to 20d10...)
Storyteller: [Str+weapon bonus] dice, counted at difficulty 6. Bonus damage dice from success on attack roll [Dex+Melee]; subtract target soak successes[Stamina].
Storyteller-descended Aberrant usually is similar (though soak reduces the damage pool without being rolled). IIRC one interesting case was that a teleport error would deal 1d10 damage (very unpredictable compared to the usual range).
One Roll Engine: damage = number of matches on attack roll (to location determined by the actual number) + weapon bonus damage.
Shadowrun 1E: damage set as Light (1), Moderate (3), Serious (6) or Deadly (all 10) damage levels, by weapon. Weapon skill roll extra successes equal to weapon 'staging' rating increase damage to the next step; weapons also define the target number to reduce damage for soaking with body dice ('power level'). Dodge dice are spent and add as bonus dice to the Soak roll (using the same target number!) but also cancel the attack completely if more successes are rolled than attack successes. Dodge dice have to be rolled separately (or colour-coded) due to their ability to cancel hits completely, so there isn't really any simplification from having dodge/soak be intertwined.
Surgery rules tie into the damage rules e.g. an organ transplant leaves a character with a Deadly wound. This works generally better than it would in a overly-variable-HP system, where X damage will kill some PCs and be a scratch to others, like high-level D&D fighters.
Blue Planet: a set three damage dice (d10s) are rolled against a TN of [base damage + Strength - target Toughness] giving a wound severity of 0 (glancing blow), 1 (minor), 2(serious), or 3 (critical). Each wound forces a stun roll (Will check) with a penalty equal to the severity; critical wounds also force a Fitness roll to avoid dying.
Arkham Horror is really a particularly complex boardgame, but system-wise is interesting since its virtually the 'count successes' version of Tunnels and Trolls. A character rolls their 'fight' score as a number of dice (5s or 6s are successes, with a blessing lowering TN to 4 or curse to TN 6. Weapons add bonus dice and the successes equal damage - if the monster isn't killed it deals damage. Therefore like T&T hit/damage is a single roll, though only one side rolls. Two weapons simply stacks the damage bonuses; one weapon (the axe) has a +3 bonus instead of +2 used two-handed. The 'marksman' skill lets a character reroll a fight roll once per game turn. Monsters can be 'physical immune' or 'magical immune' in which case a weapon of that kind adds no bonus, but the base Fight dice still always apply.
Fireborn: weapon base + an attack 'sequence' will include manuevers that add pluses to damage (e.g. Press +5), or that can instead give an extra attack. A peculiarity is that the detailed damage amount is then compared to a 'threshold' which will convert it back to a 'minor wound', or -1d penalty, -2d penalty, etc. The effect is that damage amounts are fine-grained and look important (this weapon does 8, that does 9) but will frequently end up having no game effect (a kick for 4 or mace for 7 damage might both be a -1d wound for a Water 4 opponent). Or a -1 wound might become -2 instead because -1 wound level is already used up). An issue might be that attack 'sequence' might be metagamed to choose either multiple attacks or a 'press' depending on exact damage thresholds, if known?

Base + Margin of Success (or Table)
Rolemaster: damage by attack roll on chart; possible critical rolls on high attack.
Army of Darkness (Unisystem variant): STR x weapon multiplier i.e. [Str+1] x3 for sword. Add attack success level (determined by table, generally +1 damage per 2-3 over minimum success value of 9+). Core unisystem uses varying dice types. The Buffy unisystem variant also notes that life point damage for shots/stabs is doubled vs. humans (after armour, though largely just extra addition in low-armour genres; halving armour vs. bludgeoning and revising damage calcs might've been better).
Unisystem tries to speed up combat by streamlining dice rolls, despite the hit roll adding to damage. NPCs or monsters use their average attack roll to work out the normal 'success level' of attacks and add that to the base damage, resulting in the same damage every time, while PCs refer to the table.
DC Heroes: fixed base found by comparing STR/target BODY on a table (0 if evenly matched, up to full attribute if resistance is zero), plus bonus damage from a high attack roll.
Over The Edge: attack roll (multiple d6) minus defense roll, difference is multiplied by a weapon damage factor (no Str score exists/ is factored in, unless its defined as an ad-hoc trait and used as the attack roll). Armour works as rolled absorption.
Fate Core: damage ('shifts' directly equals the difference between attacker Fight and defender Fight roll, or Provoke vs. Will for social combat. Weapon and strength provides no direct modifier - relevant Aspects are potentially createable but would typically affect damage via increasing attack roll rather than modifying damage directly. One example stunt, My Blade Strikes True, forces a target to take a consequence rather than simple stress, 1/combat.
Forgotten Futures: (freerpg, link here (http://www.forgottenfutures.com/game/rules/ffutures.pdf)) damage roll uses the normal resolution system (2d6 under stat). A roll is compared to Body (i.e. Str) or weapon "effect" for weapons such as guns, and each weapon has a table listing a result for if the roll is under 1/2 Body, under full Body, or over, with damage being one of four levels (Bruise, Flesh Wound, Injury, or Critical). For instance a rifle deals a Flesh Wound on a failed roll, an Injury on a success, with a critical of Critical/Kill (target rolls Body to avoid being killed). Armour modifies the "effect" number. Note that since the 2d6 roll is non-linear, the 'critical' result is less common, and that (as noted above) high 'STR' (Body in FF-speak) only increases likelihood of more damage, rather than giving a direct bonus.
Feng Shui (2E): Str+x by weapon or power base damage [usually +1 to +4], - opponent Toughness = wound points. Wound points may be used as a modifier e.g. 'Vengeance of the Tiger' lets character riposte after taking damage with plus to hit equal to wounds taken (probably unbalanced, but followed by a Con check with the same number as a penalty to avoid exhaustion).
HOL: . Weapons have a base Wounds, then weapon "Anguish Factor" (minus target Armour) is cross-referenced with a d6 'intensity' roll on a table to get a damage multiplier (which however only varies by x1 from the roll though e.g. a 4 adjusted anguish gives 1-2:x1,3-6:x2). A high attack roll adds +d6 to anguish factor. As noted above, characters all get 20 Health Levels.
Advanced Fighting Fantasy uses a simple 1d6 roll on a weapon-specific table e.g. a sword by roll in order is 2|3|3|3|3|4|5 (the last number, for 7+, is available only with special bonuses). This gives slight variation while keeping range of damage mostly compatible with original FF (where damage for a successful hit is always 2). See notes on "game hybridization/how to" - overcomplicated by back-compatibility with a very simple system. AFFs two editions handle 'Strength' differently; in 1E this gave +1 damage while in 2E it became a feat (equivalent) rather than a skill, and also IIRC just gives a +1 to the roll on the table i.e. much less of a bonus - the table downsizing the effect similarly to say Fantastic Futures' tables.
Chill: chill has named result levels like 'scratch' or 'critical', generated by attack result on a table, which fill up boxes on a health track that's generally similar to e.g. Fudge or Storyteller. Each result also generates an amount of 'stamina damage' which is set by the result level e.g. 2d10 or 4d10. System has some redundancies therefore, also, Str or weapon type don't modify damage.

Other Attack-Roll Based
Unknown Armies (d% roll-under), firearms do damage equal to the attack roll if you roll under your skill, up to a maximum for the specific gun. A roll of doubles (11, 44, etc.) gives automatic maximum damage).
(T&T above could potentially be grouped with this inasmuch as it too has wholly attack-roll-based damage, albeit that the attack roll is multiple dice additive).
The miniatures game 'Silent Death' apparently (http://forum.rpg.net/showthread.php?564518-No-more-damage-roll) uses a 3-die roll to hit (sometimes different dice types). Weapons are rated as 'low', 'medium' or 'high' damage, indicating which of the 3 attack dice is used as the damage roll also e.g. on a 3+4+5 attack that hit with a 'low' weapon, damage would be 3. Doubles indicated these added together, building in 'criticals'. (If you rolled 4,4,5, you could do more damage with the low weapon than the high one, 8 vs. 5.


General Note: Damage being a different subsystem to other mechanics can affect the value of stats modifying damage and/or hit points. Multiple damage sources can make e.g. Str bonus irrelevant, but more often a different subsystem scales up the importance of STR. In an extreme case, a Marvel Super Heroes character for instance uses attribute score for damage and table lookup to-hit, so a one-rank shift in Fighting stat might give +5% to hit (increasing damage per round by 10%), while the same increase to Strength might increase damage by 50%, 100% or more.

Thoughts in closing: many people consider it logical that the attack roll influences the damage - which can also in many games factor in character skill. Some core mechanics do not easily support this, and/or the additional calculations involved can be annoying or slow. Attack and damage being somewhat disconnected is sometimes desired e.g. Savage Worlds does this to encourage 'called shot' attacks. Its also argued that, for example, having damage only slightly influenced by margin of success makes random gunfire dangerous despite e.g. darkness or movement penalties, supporting an illusion of realism.


See also: damage for miscellaneous situations (falling, immersion, etc.) is dealt with in post #55.

Describing damage: most GMs are generally in favour of giving colourful descriptions of what damage looks like to players. Note that games with hit locations and etc like limit the GMs ability to extemporize here. Games where there are a lot of small damage quantities coming off an arbitrarily large HP pool are a dampener on description since it tends to be irrelevant and happen all the time; a player is more likely to notice/care if they have only a few 'large' hit points.

(http://i1239.photobucket.com/albums/ff507/BSJ17/wolvievssentinel2.jpg)
 
The usefulness of armour in a system is partly determined by genre concerns (desire to make limited armour feasible for barbarians or swashbucklers, for instance), and partly by 'realism' (weapons may be made quite deadly, but with armour offsetting this by being especially good at stopping damage).

Systems for handling armour:
 
1) Armour as Target Number (to-hit number) – D&D, Palladium Fantasy – here an attack roll to hit must be over an armour-based target rating to hit. Palladium also lets characters roll a “Parry” and use the highest of that and the armour rating, while D&D stacks any “parry bonuses” onto the base to-hit required. The Palladium approach makes armour less useful at higher levels but also removes a synergy between DEX and armour in D&D, that actually makes high DEX + high armour more powerful if you can manage to get both together (through mithril or Graceful armour etc). Palladium armour is also limited in how much damage it can absorb before being destroyed. However...perhaps the main benefit of armour as a target number is that it removes the extra 'subtraction' step of armour as DR, making it easier to roll a large number of attacks for an orc skirmish etc. In the case of Palladium, having to roll damage on the armour however slows down the system enough this benefit is lost.
D&D as it evolved became more realistic, with AC getting more increase from dodging. Having a single AC represent a mix of both led to twice as many factors at play on the same number, with a tendency for AC to vary dramatically.
AD&D AC, while usually used as a target number, rarely might instead apply as a modifier to raw damage ("Characters who fall into the pit are hit by a number of spikes equal to their AC. Each hit deals 3 damage and requires a save vs. poison.." - Egg of the Phoenix).
More on DEX mod: note that 5E D&D balances 'Dex mod' by having heavy armours not apply it, while medium armours are capped at +2; generally AC is very constrained. One 0D&D variant, Arduin, didn't apply Dex modifier to AC; this is somewhat justifiable perhaps in that defensive benefits are modelled in other ways, with high DEX granting the initiative and always giving the option to parry (otherwise not possible), and giving more actions (could help to parry).

Armour as target number tends to scale badly for SF games as it makes guys in super-armour incredibly hard to hit – often even with futuristic weapons since these do tons of damage but don’t often get hit bonuses, but doesn’t offset damage if they do get zapped...so combat becomes miss, miss, miss, miss, miss, vapourize). Note that if a system gives a character bonus damage for a good attack roll, a raised armour TN will reduce bonus damage, also.
Armour in D&D adding to AC also led to Strength rather than Dex adding to hit rolls. This occasionally generates additional messing around n the games system i.e. being “entangled” separately penalizes to-hit (Str based) and Dexterity), and maladapts it for supers games (Strength becomes very powerful, but enormous Strength is a superhero genre convention; also two super-speedsters would be unable to hit each other, while a super-strong brick easily hits a speedster).
A houserule for Palladium here  (http://www.telluri.com/lin/palladium/mdc.html)(adapted from Heroes Unlimited) takes out MDC but adds categories of half/full/no damage based on strength level/damage type (potentially streamlineable to a linear roll a la Savage Worlds but more improvised).

(Possibly the origin of armour being treated as it is in D&D, decreasing chance of hitting rather than absorbing damage, might be a legacy aspect due to armour more or less predating hit points - in the wargame figures might have a roll to be taken off the board in an armour-based fashion???)

2) Armour as damage absorption – probably the most common system in RPGs, here armour gives a penalty to damage; either a straight subtraction, or rolled (e.g. extra “soak dice”, counting successes in some Storyteller games). (In theory armour in a dice pool game could also modify the number on a die needed for it to count as a “success”, reducing damage by a proportion, but I don’t think I’ve ever seen this). The main drawback of this method is that small weapons may have trouble getting through armour. Variants include:
*absorption can be rolled in other fashions e.g. armour may subtract e.g. 1d6 from damage (or a related step die [Alternity]); Lord Vreegs' Celtricia game gives armour a base protection, divided by [average of 2d6], meaning armour is on rare occasions seriously perforated. Rolled absorption mitigates the problem of smaller weapons having trouble penetrating, at least slightly, at a cost of more rolling.
Rolled absorption may also allow multiple layers of armour to be accounted for separately - each layer gets a roll and the best is taken - without this excessively increasing armour defense value. (a similar effect could also be achieved by having armour affect the damage roll, e.g. roll damage twice and take the worst).
*GURPS (IIRC) gives armour both a to-hit and an absorption, a combination of this and the above method.
*Synnibarr gives armour a damage divisor (from one to four “tenths” i.e. from /10 to /10,000, and then up to four more for armour) but is also destroyed if it takes too much damage (an ablative system, see below). Creatures such as dragons sometimes got scales that worked as extra 'armour' on top of their normal armour, to balance them with PCs who could have up to 8 'tenths'.

Note if a game is 'PC only rolls' (e.g. Dungeon World), then armour will probably work by absorbing damage since most other options don't work e.g. there's no 'hit roll' by monsters to affect; armour as extra HPs may still work.


*Table-based. Rolemaster (and Sword's Path Glory) cross-reference armour on the damage tables when calculating damage. This is basically a form of absorption, although the table allows greater control of the final results - i.e. less likelihood of all damage being negated. In Rolemaster, critical hit severity [A to E] is also reduced.
Absorptive armour synergizes badly with fixed weapon damage (e.g. in Marvel Super Heroes, its frequently possible to be unable to injure a highly armoured opponent; this isn't helped by a good attack roll).

3) Armour as extra HPs (ablative); Palladium’s high technology games - Rifts and Robotech –do this since attacks can’t get through armour until its been reduced to slag. For Palladium this was a fairly good expansion of the base system since it built off an aspect of the armour rules in its earlier games (the armour’s damage capacity) and also avoided the usual trap of Armour as Target Number systems where armour classes go off the scale. For a normal Fantasy RPG system, this approach would perhaps be unrealistic.
This approach is also an interesting "game balance control" tool for the GM in Rifts; upgrading a puny character's armour effectively jacks up their hit points.
Most of the time this approach has damage taken by armour lost permanently (eventually you buy a new set), though "The Black Hack" (D&Desque) has armour points that recover after resting, with the (thin) rationalization that a tired or wounded character can't use armour as effectively. Most versions of this rule, obviously, your armour is destroyed and needs to be replaced every 5 minutes.

4) Separate Armour Bypass roll – rarely seen (since it adds an extra die roll). Dragon Warriors has this; a successful hit roll is followed by a roll of another die vs. an Armour Factor. For example plate = AR 5; a sword would roll d6 and have to beat the AF i.e a 6 equals damage. This can be used to give weapons varying armour penetration. In DW, it does tend to add “whiff factor” (excessive miss rate), and unlike D&D type systems, higher level/combat skill gives no direct bonus at getting through armour.
This sort of mechanic is good for representing e.g. multiheaded weapons (triple-flails or African throwing knives); each blade or head can roll a separate die. Max rolls/1s could also be used to represent e.g. weapon breakage or impalement.
Villains & Vigilantes uses a d100 bypass roll; if the roll fails the damage is absorbed by the armour, reducing its %.
JAGS gives armour an ‘armour save’ on 4 Jags dice (d6s with 6s counting as 0s) to convert Penetration (PEN) damage into Impact damage, though not to stop damage entirely. PEN damage >4 is doubled as it reaches a character’s vitals.
CHILL integrates 'armour bypass' into the damage roll directly - damage is rolled, with a roll less than armour on a location bouncing off, while higher rolls instead deal full damage. This systems limits the full benefits of a bypass system i.e. weapons can't be low-damage but high-penetration, but is relatively simple. Perhaps some weapons could potentially be kludged to have a separate 'effective damage' for bypass purposes.
Free rpg Zenobia (http://zozer.weebly.com/free-rpgs.html) has an armour save where a dice pool of 1-6 d6s (depending on armour type) is rolled, and any 6s negate the hit. It has a 'Hard to Kill' skill which operates as Armour 1 and thus, gives a 1-in-6 chance of negating damage completely) - probably showing how treating toughness as armour is especially bad when armour is bypassable instead of damage-absorbing.

An Armour save/bypass roll could also be used that just gives a reduction of damage, rather than negating it; this may be a good way to represent "partial armour" without hit location (credit to David Johanson for this).
 
5) Armour as Parry
Supers! (Hazard Studios) has armour which is basically rolled as a defense i.e. it functions as a "Parry" when a characters opts to use Armour instead of a different defensive power (if defending with something else, the armour rating is ignored). Supers! Armour can be used multiple times, unlike other powers used in defense, but at -1d each time. Relative multiple of the attack over the armour defense sets the damage inflicted.

Other Elaborations: HarnMaster attempts to model characters wearing multiple layers of different armours, but with this tending to generate, IIRC, excessive defences – such as system probably requires diminishing-returns to be built into the benefit from the total armour points.
A few systems have also attempted to use “piecemeal” armour – per location (for post apocalyptic games in particular it may be fun to get that road warrior feel by strapping some old tires onto your body for extra defense). The 2nd edition AD&D Fighters Handbook again did this, but with a cumbersome system of adding fractional AC bonuses for mixing and matching armour types; it works better in systems with hit location rolls.
Most armour systems give characters penalties for wearing armour; if different armour by location is used penalties should perhaps be calculated off different locations i.e. head (helm)- perception checks, body – swim/climb (most suit weight being there), arms – manual dexterity, legs – speed.
 
Aberrant has armour piercing attacks (reduces Soak by 2/attack success) as well as aggravated damage (ignores soak entirely, but had reduced damage base); conversely armour can have the Impervious advantage, making it more expensive (=probably lower armour value overall) but letting it ignore these effects.
 
Early AD&D is somewhat infamous for the "weapon vs. AC modifiers" table, which cross-referenced armour type with weapon to generate a to-hit modifier. This is generally criticized as being unnecessarily slow (some character sheets try to solve that by adding a few lines for weapon type on character sheet) and it also suffers slightly in that monsters usually don't have an equivalent armour or weapon type listed. It does however add a degree of tactical calculation and verisimilitude into combat, as well as being a part of the balance of the game - some weapons, notably crossbows, have benefits if using the table that made them seriously inferior when the table was ditched in 2E, and in addition multiple weapon proficiencies become more useful as it gives a character the option to switch between weapons (the table is cut down in 2E, but a later rule where characters get more weapon slots for Int could lets high-Int characters indirectly earn to-hit bonuses if both rules are in use, encouraging less stereotypical fighters). The table itself primarily reflects weapon type (bludgeon, slash, pierce) though it also adjusts for 'encumberance' of armour i.e. unarmoured types can get larger bonuses against slow weapons like two-handed sword (i.e. can dodge better).

CORPS has armour with an x/y rating, where 'x' is stopped and 'y' is converted to nonlethal.

General Considerations:

Scaling: How armour ratings are scaled is an interesting question that varies, typically depending on the damage scale (if absorptive) or the to-hit scale (for AC systems like D&D's). Most games have relatively fixed damage which also sets the scale for armour (set to not make it too powerful); open-ended damage systems struggle with armour scaling to an extent i.e. in Tunnels and Trolls armour can stop excessively large amounts of damage since damage is based off the difference between both sides' combat totals and could be any number.
 
Access to Armour: typically either all characters can use it (sometimes with it inflicting penalties), or proficiency in it may be based on class or skill selection. A few systems also have Str-based armour use: Tunnels and Trolls gives armour an explicit Str-required (wizards can wear it, albeit that in 5E and earlier, spellcasting fatigue might mean they suddenly can't move after casting a spell).  In theory a game with Str-requirements only for armour with add a plus to Strength from class.
Savage Worlds makes armour extremely heavy, meaning that characters wearing it are likely to suffer encumbrance penalties unless they're strong or have an Edge that increases cargo capacity [Brawny]; while tightly integrated this does make encumbrance a bit less optional than in other games. It incidentally, also deters strong characters from going around mostly naked (the fantasy barbarian archetype)...the last thing your barbarian character wants is the Brawny edge.
Another compromise system is Atlantis (based on Talislanta's "Omega System")- the quick start (http://www.atlantisrpg.com/images/AtlantisQS.pdf) includes an 'advanced militia training' which doubles STR (min +2) for determining armour penalties.
Dungeon World has a derived 'load' (encumbrance) rating which is modified by class and affects armour worn, as well as there being specific class features that can reduce armour weight.
Armour may interact positively or negatively with character skill. Palladium's Parry rules mean that a high Parry makes armour redundant, while Tunnels and Trolls has a skill that doubles armour protection, and 2E Dark Sun had an 'armour optimization' skill which let a character slightly boost AC to compensate for limited armour available.

Balancing unarmoured characters: while the benefits of armour are in part determined by how good the designer makes armour in the first place, some characters may also get extra niche-protected benefits while not wearing armour due to their concept e.g.
*The swashbuckler kit in 2nd Ed. AD&D (the kit) got a +2 to AC while not wearing armour; later Skills and Powers had this a selectable fighter ability (plus human characters could purchase a tough skin for AC 8, nonstackable with normal armour).
*The 1E AD&D monk likewise got an improved AC due to 'defensive ability', which only worked when unarmoured.
*barbarians in 5E D&D add [Con mod] to AC i.e. 10+Dex mod + Con mod.
*The Dragon Warriors barbarian class is balanced on the assumption they wear less armour than the knight, but have more HPs. (They always have the higher HP base, but take penalties when wearing heavier armours).

Armour and effect on other probabilities: armour that reduces damage can affect probability of other special effects via use of damage-based rolls (see above). Ad hoc adjustments can be used in other cases e.g. 3.0 had a monk "Flensing Strike" feat which let a target save vs. having strips of skin torn off/pain effects with a special save bonus equal to natural armour bonus, or whips have a rule where they just can't damage opponents with armour or natural armour.

Armour spikes get rules in some systems - 3E notably uses the grappling rules. Savage Worlds' Fantasy Companion notes that charging doors, or falling over, may result in getting stuck.

Armour & Agility/Dexterity Penalties
Armour's weight may inflict a flat penalty on Dex-related tasks. This can include Dodge rolls, initiative, any Dex-based roll. Savage Worlds as noted above just makes armour heavy and applies encumberance penalties (good as small dice sizes make any penalty substantial, such that rolling multiple minor penalties into one is a good idea), while Tunnels and Trolls 5E applied an (optional) DEX multiplier. D&D generally just caps max. Dex bonus to AC (3E and later) in heavier armour; early D&D may give specific penalties (Wrestling, thief skills) as well as probable penalties by GM fiat.
The Fantasy Trip is notable for especially harsh DEX penalties for armour, which also seriously affects to-hit chance (at worst plate = -6 Dex). The penalties are so serious, and combined with a hit roll that's normally on 3d6 and hence nonlinearly increasing, that there's an incentive to have heavy armour worn by lithe agile high-Dex characters so they can still hit, while the beefcake dudes should be as naked as possible.

Hit Locations: armour may be varied by location in games which have either location rolls or 'called shots'. Another approach is to reduce total armour value e.g. a character who takes off their helmet might have a reduced armour rating and reduced perception penalties.

SHIELDS
Shields typically operate as a bonus to parry or as armour, depending on system. Conan D20 divides AC into Parry AC and Dodge AC, with the bonus for a shield being +4 Parry/+1 Dodge (helping vs. ranged attacks). Savage Worlds gives shields a Parry bonus, but they instead act as armour vs. ranged attacks (as these ignore the character's Parry rating). Tunnels & Trolls simply treats shields as armour (a problem with its system is that characters take damage based off difference in attack totals, so usually a shield does less than using an offhand weapon). Arrowflight (1E) reportedly treats a shield as armour if a character gets any successes on a defense roll, or if the hit happens to strike the shield arm hit location).
Dragon Warriors gives a shield an extra roll (a 1-in-d6 roll to negate a successful blow); this gets kludgy for magic shields as it does not scale up for those, which instead add a Defense bonus. [a penalty to the attacker's roll]. An elaboration for this might be to adjust the roll for certain classes or whatever (knights might get a 1-on-d4 roll, say) -  although, this sort of roll which gives a fixed chance - completely unmodified by attacker ability, be they Joe the Peasant or the god Thor - has the potential to break if modifiers are allowed, since bonuses can never be offset or countered.
3E lets tower shields (but not other shields) plug into the 'cover' rules if the character sits wholly behind the shield.  
 
A couple of systems limit how often a character can use a shield (each round). In GURPS Man-to-Man, shield 'passive defense' is the readying time of the shield. Likewise for Sword's Path Glory: it varied readying times for shields, with a reduced parry based on how many initiative impulses have passed since the shield was last used (calculated as a multiplier to the base parry %). (SPG also has multiple 'tracks' for weapon and shield initiative, so a character might get to choose between doing a shield-parry at a penalty, or making a weapon parry and delaying their next attack).
More abstractly, 2E D&D limits how often a shield bonus can be applied for small shields (all shields add +1, but a buckler can only be used once/round). Systems with specific weapon skills usually rate shields with a skill percentage for defense, rather than a flat bonus. This sort of rule could support multiple use of shield bonus each round in line with weapon multiple attacks, where those are skill based.
Systems which represent facing typically limit shield bonuses to front/side attacks; 2E D&D has an option to strap a shield on a character's back, but this applies a penalty on to-hit rolls.
 
Some systems may model shield degradation e.g. giving shields their own limited 'hit points' (Runequest IIRC). In this case a shield may be useful to prevent a weapon taking damage from parrying.
One houserule on the internet for earlier D&Ds, 'shields shall be splintered', lets a player opt to let a shield absorb an enemy blow that should have hit, breaking it..
 
Legendary Lives (http://www.hauntedattic.org/legendarylives/LegendaryLives.pdf) has an odd system for determining shield-defense where a characters [DEX+shield size] determines its parry bonus in each hit location separately. This staggers increases across multiple categories (a point of DEX always adds to defense somewhere, without giving a huge bonus) and perhaps realistically gives a lower shield bonus to the weapon arm and legs.

Some systems may model the effects of weapons (such as flails) that are particularly good at getting around shields by reducing the shield bonus.
Like armour, shields can sometimes get spikes (e.g. spiked bucklers; Tunnels & Trolls includes the 'madu', or horned shield). Generally these are handled with two-weapon fighting rules.

Special Abilities
Some special abilities may mimic the effects of armour. e.g. the Angel in Apocalypse World gets 'Battlefield Grace: while you are caring for people, not fighting, you get +1 armour' or 3E monk: add +Wis mod to AC. In systems where armour is a TN (D&D, Palladium) Dodging and Armour are basically the same and these are perhaps more common.
An early (081712) 5E D&D playtest included fighter manuevers which let a character roll their 'expertise die' and reduce damage by that, only when wearing armour or using a shield (despite these things normally raising AC instead of soaking damage).

Tunnels and Trolls gives warriors the ability to absorb double value for armour (i.e. leather would absorb 12 hits instead of 6). Deluxe backtracks from this slightly (sometimes seen as a problem due to lengthy ties in battle), with the doubling kept but considered to be armour 'abuse' and requiring saving rolls by the warrior to prevent the armour degrading. 'spite damage' also bypasses armour, and warriors get extra dice in combat per level. Overall the problem is mostly one of warriors being a bit broken initially (or as soon as they can buy full plate) while wizards dominate the endgame more.

Monster special abilities: As a weird variety of DR, AD&D 2E had a monster called a 'chronovoid' which took 1/2 damage per magic weapon +1, or 1-3 spell levels. Hence a nonmagical weapon did nothing, a +1 1/2 damage, a +2 full damage, a +3 1.5x damage, and a +4 double damage. (I know D&D normally handles armour as an AC raise, but I otherwise don't know where else to put this). Pondering, maybe this monster would be easier with double HPs (say, roll d12s and allow it a Con modifier) and then use x2, x3, x4 rather than x1.5, etc.  Something more fine-grained might've been better for spells, e.g. 25% per spell level, although that would be hard to implement.

recent edits: The Black Hack; DW 'load'(*); Rifts armour and game balance (*), chronovoids (*)

(http://i1239.photobucket.com/albums/ff507/BSJ17/image022.jpg)
Image: Island of the Sirens (http://robbdaman.deviantart.com/art/Island-of-the-Sirens-D-and-D-Map-279815339) map for the D&D Minis wargame; triangles represent hampered terrain.
 
Systems vary considerably in how detailed movement considerations are; discussion of existing systems in this section needs to be considered with the caveat that different groups played games with different emphasis on it –for instance most versions of D&D can be played with or without miniatures/counters, at least if the GM is willing to handwave the occasional fireball area and decide randomly which PC a monster attacks.
Where miniatures are used, distances may be measured, or a grid may be used – in hexes as in GURPS or in squares as in D&D. (In theory, a surface could also be marked with equilateral triangles). Squares are less precise for diagonal movement but may allow placement of larger figures better (a Large figure fits weirdly on 3 adjacent hexes). Larger figures such as horses cause issues since where they take up irregular areas (3.0 D&Ds 2-square-long horses) detailed rules for facing/turning are also needed. GURPS has some very intriguingly weird Large creatures e.g. GURPS Lensmen has player character races including “1 hex humanoids”, “3-hex” Rigellians, 10-hex-long Velentians (arms in hexes 2,4,6; 1 hex reach; 40 hex wingspan), 7-hex-long Delgonians (arms in hex 2, legs in hexes 3 and 5), and elephantine “4-hex” Dhilians.
Using miniatures, sometimes a figure just affects/threatens all sides of it equally (is assumed to just turn where necessary) as in 3E D&D, while other games have characters select a 'facing' which will specify flank and rear squares which might not be shield protected, can't be attacked into or take a to-hit penalty, etc.
3E has an abstract 'flanking' where multiple opponents on opposite sides get a hit bonus, whereas Savage Worlds just gives extra opponents a 'gang up' bonus.  

Movement in some miniatures systems grants the defender an additional attack (HarnMaster, D&D), while in others (DragonQuest, Warhammer Quest) the defender instead must pass a roll to disengage. In the case of 3E/4E D&D, movement out of individual 'threatened squares' generates a bonus attack, while for 5E (or AD&D) movement out of an opponent's entire threatened area - i.e. leaving their reach, not just moving around inside it - gives the bonus attack.
 
Miniatures show statically a melee situation that is actually dynamic and constantly shifting; combats in systems using them to excess tend to be very stationary and punish movement harshly . Attempting to add swashbuckling movement back in to a minis system results in a more complex sets of “interrupts” and special powers or skills, with (in my opinion) a final result that combat is still less fluid than if miniatures were not used at all. They also consume setup time and effort. On the plus side miniatures do help adjudicate ranges or inclusion of PCs within areas more fairly, can add a tactical dimension, and can reduce GM book keeping if used right e.g. in a mass combat they can be useful for tracking better how many opponents are left and which are wounded, and act as visual props that add interest to a game.
 
Miniatures are less required in games which are abstracted (such as Tunnels and Trolls). They are also more problematic when dealing with chases, vehicles or big monsters (3.x/4E rules for “move action” rules do pursuit poorly – e.g. with turn-based movement and pursuer’s attacks reducing their movement ). Marvel Super Heroes got around this sort of thing by using hexes, but having “areas” which were a massive 40ft across. Somewhat related to this, The Gaming Den (tgdmb.com) has in its archives some discussion around the idea of abstract-sized areas that upsize with party level. Warhammer 3E uses abstract 'zones' to handle distances; 13th Age apparently does likewise and includes rules meant to mimic positioning effects abstracting, such as having multiple-target spells either affect d3 targets or d4+1 with collateral damage to allies (at player option).

Movement rules may include penalties for 'hampered terrain' (e.g. these cost double movement to go through). Some houserules I've seen cover how dead monsters can act as hampered terrain (and how large monsters may crush things when collapsing).

Exact positioning is also perhaps more useful in a game where there are a lot of area-type explosions or blasts. (As a side note, blasts sometimes just extend out through the area, or sometimes have diminishing damage from the epicentre).


 
EDIT: 3-D movement: 3D movement (space, air or underwater combat) makes miniatures slightly trickier. Theoretically 3 objects in a space define a plane, and can be represented on a 2-D surface e.g. for space combat where a defined "falling direction" isn't necessary. More than 3 objects may need representation of height up when placing the miniatures (and actual distance between objects will be affected, technically - square root of [height diff squared+horizontal distance squared).
Flying objects can work vs. each other (with appropriate scale) but probably requires a separate map to the ground-based battle.
 
Movement rates in systems may be racially based (i.e. dwarves get move 9" in AD&D), or based off an attribute i.e. Speed in Tunnels and Trolls, or DEX in many systems. Marvel Super Heroes has movement based off Endurance, somewhat mysteriously.
Games with "action points" may have movement rates which vary indirectly as a result of characters having different # action points (IIRC, JAGS).
 
In a number of systems, characters have randomized movement each turn. Examples include:
*Savage Worlds, where Running lets a character move [Pace+d6] tabletop inches (Normal non-running movement does not require a roll).
*Masters of the Universe, where characters can move d6.
*DC Heroes has fixed base movement based (=DEX), although movement can be Pushed with expenditure of hero points and a roll.
*The HeroQuest boardgame (d6 squares).
*2E AD&D, where characters could make a series of Str checks to attempt x5, x4, or x3 normal speed (x2 is automatic).
*Rolemaster, where moving required an agility check on a table.
 
Rolemaster/MERP movement was fairly time consuming, with standard movement requiring a [d100+modifiers] roll on the Moving Manuevers table to determine how much of the turn is consumed by movement. (Also, God help you if horses, stairs, or jumping is involved - any attempt to go up stairs during an adventure can theoretically end in a broken neck).
Original RM (1st/2nd ed) had a flaw in movement rates, where moving at x3 or more base speed increased manuever difficulties. This increased the likihood of rolling a result that reduced movement to 80% or less, so that trying to move faster would slow down a character. The tables were further tinkered with in (I think) Companion V.
 
Proponents of rolled movement tend to like it because of possible variation introduced to combat - by making movement less predictable, precalculation of options by players is made less clear. It also makes the combat movement work for basic chases without too much extra effort. On the downside, its an extra roll; and many of the systems above generate amounts of movement that are extremely variable.
 
According to this (http://forum.rpg.net/showthread.php?561909-Running-skill), Spanish game 'Far West' "had the Speed (Velocidad) skill; you rolled d100 under it if you had to run. No degrees of success or actual speed, though; either you ran faster than the opposition, or you didn't." Shockingly abstract / hard to convert into anything useful.

(Far West here, and Rolemaster, and maybe AD&D, illustrate the problem of trying to apply normal resolution system to movement/chases - its usually a bad idea since characters should be able to try to run faster without it failing entirely. Replacing the normal core mechanic with a simple die roll of dX+Y feet/squares moved is probably better, though a different mechanic does make interpreting any sort of skills boosting movement more complicated).

In some systems depending on how initiative factors into movement, some of the same effect as random movement might be introduced by the initiative roll (e.g. with per-segment movement and the like).
 
Fireborn (see combat manuevers) is somewhat interesting in that it has a 'roll' for movement as part of the total attack sequence roll, requiring attack successes be spent.

3E is interesting in that it doesn't have either rolled movement or variable movement rates between characters - all humans for instance have a movement of 30ft/turn. Consequently chases don't work well. This also interferes with combat tactics like running away from a mob and fighting them one at a time as they catch up.

Reach
Reach is easy to handle in square/hex mapped games as being able to hit targets further than the adjacent square - at least, the huge 'reach' of very big creatures or polearms can be handled, although differences at human level are going to be handled less well.
Some games may have more detailed reach e.g. Age of Heroes has weapon length rules with shorter weapons must make an attack to successfully close in.
On the other extreme, 13th Age ignores reach more or less, but has a "Reach Tricks" feat applying ad hoc benefit - 'once per battle, tell the GM how you are using your weapon's reach to perform an unexpected stunt such as an opportunity attack against an enemy that disengaged then moved, strike a nearby enemy not engaged with..' or perhaps parry attack on an ally or the like.

Cover
While perhaps this could be considered a form of armour, cover is something that typically is a concern in games which take tactical positioning (and hence movement) seriously so I'm sticking this here. Cover may absorb damage, provide a to-hit penalty, be rolled against a separate check. It sometimes is considered to block particular hit locations, in which case a location roll might determine whether the cover works. Some 'indirect-fire' weapons, such as grenades, may be able to go around some forms of cover. Cover rules may also intersect with vehicle rules i.e. a character may have cover inside some sorts of vehicles. Effectiveness of cover may depend somewhat on 'readied action' rules or whether move/shoot/move to duck down again is allowed, as well as degree of attack penalties for 'snap fire' vs. aimed shots and what weapons occur in a given game (e.g. it may be a bad idea to hide behind SDC cars in Rifts).

Doorways
Doorways can be a 'choke points' (in military terms) - limiting how many opponents can engage. This is more of a concern in games where multiple opponent rules are very harsh - e.g. while T&T combat is very abstract, it directly adds the attack of extra opponents so 2 skeletons might be an automatic win for the PCs, 3 a fair fight and 5 an automatic loss (depending on relative stats). The last time I played this, it led to lots of attempting to get skeletons through doors one at a time and therefore necessitated lots of GM judgment calls (that started turning into ad hoc rules), in what was theoretically a very simple system and indeed as a result of its combat being simple.

Chases
Unisystem has a slightly interesting chase system (e.g. from Buffy):

QuoteChases: Movement concerns may also arise during a chase scene. First, you must decide how much of a lead the chasee has on the chaser. We suggest granting +1 per Turn of head start. Then have the two racers perform a Dexterity (doubled), or Dexterity and Sports Resisted Action. The winner gains +1 per Turn. So if the lead sprinter started with a three Turn head start (+3) and the chaser won the first Resisted Action, the lead would be down to +2. Once the lead is eliminated (brought down to 0), the chasee is caught; if it grows to +5, the chasee gets away.

(This roll is in spite of normal per-turn movement being fixed at [Dex+Con] per turn).

Movement system fails
You'd think it would be fairly straightforward, but movement systems tend to generate a few possible issues e.g.:
3E elusive target: when an opponent attempts to hit you and misses, they instead strike someone 'flanking' you. The problem is, unless they have reach, a flanking opponent is 10' away and so can't be hit.
3.5 Trample: 3.0 worked (horses were 5x10, not 10x10cubes) whereas in 3.5 two adjacent opponents make this malfunction.
5E D&D lightning bolt -by RAW this hits grid intersections, not squares, so doesn't hit anything if fired directly ahead. http://forum.rpg.net/showthread.php?747894-5e-So-it-s-been-out-for-a-bit-what-issues-are-people-having/page8 (http://forum.rpg.net/showthread.php?747894-5e-So-it-s-been-out-for-a-bit-what-issues-are-people-having/page8)
D&D 4E reportedly has issues with diagonal movement of rectangular shaped vehicles/objects - cf. here https://forum.rpg.net/showthread.php?776802-4e-Diagonal-Movement-of-Vehicles (https://forum.rpg.net/showthread.php?776802-4e-Diagonal-Movement-of-Vehicles) (although I'm not sure I understand the problem).

Especially ignoble mention also goes to D&D Basic (BECMI) Immortals rules; this made Immortals theoretically 4-dimensional creatures (as in, having four spatial dimensions), making the goings-on very difficult to conceptualize.

Less seriously, Champions apparently rounds up movement on 'half moves' (really a math issue) so characters often buy an extra inch of movement to add an inch to half-moves. (reference (http://www.therobotsvoice.com/2013/06/the_10_best_superhero_role_playing_games.php))

See here  (http://www.therpgsite.com/showthread.php?p=858973#post858973)for further discussion on movement/facing/tactical combat e.g. The Fantasy Trip as an example (Skarg).

I've done a lot of game design, and so I have leafed through your posts a few times.  Wanted to say I enjoy them.  Makes me understand the reasons I have done certain things, seeing them in context.

Thanks, Lord Vreeg :)
 
Edit note - adding link to Feel of Combat notes here to keep the topic together.
 

Quote from: RobMuadib;512932FEEL OF COMBAT
Oh yeah another thing that bears mentioning with the more abstract systems with increasing hit points is how normal threats (i.e. falling) become trivial (the old saw about high level fighters being able to jump off a cliff and get up and fight with no ill effects.) So you have to add kludges like the massive damage rules etc.
 
Another thing is the overall speed and feel of combat. Does it resolve quickly, or does it end up like D&D combat with everyone hacking on each other for several rounds, etc. You should design it for the effect you want out of combat. Do you end up with lots of corpses in a gritty system, do people cut and run after getting wounded. Does everyone just get knocked out and roughed up like in Super Heroic systems. Each type of system works better for some things than others.
 
The more heroic the game system, the less lasting effects of damage there should be, and the more of a beating character's can take. While gritty systems can end up with lots of dead character's, often to the extent that combat is effectively MORE deadly than real life, lots of people die every time there is combat, instead of people getting wounded, fleeing combat and dying without medical attention. Indeed, because most game systems don't include any morale systems, lots of fight are to the death, while in real life, people cut and run if possible.
 
Another thing is on Impairment, in real life, people can be wounded and not really notice any significant effects of the wound due to adrenaline, unless a bone is broken, the body part is mangled outright. In some famous cases of suspects on PCP, they can take over a dozen gunshots to the torso and not even be slowed down. (In reality people only drop immediately if they take major damage to the CNS (Brain, spine, neck), or the heart is directly damaged) People can be shot without realizing it. While at the same time they can drop for purely psychological reasons, or die of shock from a shot to the foot.
 
Most often impairment is used in RPG's so people can be beat down and rendered ineffective, the death spiral, instead of just eventually dying. Incapacitation is used to make for an effective end to combat, without necessarily people dying, especially in Heroic/Super Heroic realities. Needless to say there is HUGE amount of variation in combat systems.

As a general note on combat, as well as level of lethality, combat systems vary in abstraction - systems can be abstract so that 'fiction' is generated built around interpreting die rolls and changes in numbers, or detailed which maximizes the amount of player tactics that can be brought into play. (see post # 197, problems of abstraction level (http://www.therpgsite.com/showthread.php?p=753326#post753326)).

In terms of 'tactical' design, I saw this here (http://forum.rpg.net/showthread.php?559596-Game-mechanics-choice-and-tactics) which I found interesting:
"I suggest that there are a large class of players who don't want to be tactically challenged, but do like engaging a system and generating a result that's in some way their own. It's okay if the decisions that they want to make are largely obvious, so long as they aren't endlessly repeated. If they have to react to a changing situation, even if the best choice is pretty clear, they feel good about it. There's something satisfying about making the right decision, even if it's not terribly hard to make the right decision. As long as you're actually making a decision, and not just repeating a script."
4E D&D for instance I've seen condemned by hardcore wargamers as "tactical illusionism", since the choices generally aren't arduous, but it would support the need of this sort of player - they don't want anything hard, but want a medium between complex strategy and being a meatbot whose function is to roll hit and damage dice for the fighter.

btW, LOOKING AT DAMAGE, AND ARMOR...

Have you looked at said catagories with non-normal bell curve distributions?

Or with armor as damage absorption combined with target number...or with the damage absorption also a range?

also do not see continuous init systems under initiative...not to complain, just enjoying this thread, and that is what I have used for 20+ years.  Hackmaster and  i think exalted also have used it.

No problem, appreciate any input.
I'll go back and add 'continuous' to initiative systems when I have time (Sword's Path Glory does that as well...with three separate tracks, for weapon arm, shield arm and movement...).
 
Not sure what you mean by 'non-normal bell-curve distributions' w/ regard to damage sorry? I will go back and add note of rolled armour absorbtion though- hopefully I the same thing you're thinking of e.g. rolling d6 for how much damage your armour takes (like Alternity or Agon).

Quote from: Bloody Stupid Johnson;497779No problem, appreciate any input.
I'll go back and add 'continuous' to initiative systems when I have time (Sword's Path Glory does that as well...with three separate tracks, for weapon arm, shield arm and movement...).
 
Not sure what you mean by 'non-normal bell-curve distributions' w/ regard to damage sorry? I will go back and add note of rolled armour absorbtion though- hopefully I the same thing you're thinking of e.g. rolling d6 for how much damage your armour takes (like Alternity or Agon).

You have it.

I also use (along with critical hits) a dividig dice with protection and damage to change the normal distribution to more of a long-tailed distribution.  

So tiny dagger like a dirk might do 2d6+1/d10 damage, a broadsword might do 1d10+16/d6, and a really slow doublebladed broadaxe may do 3d6+19/d4.

All protections are divided by the average of 2d6 ( I know it sounds obscure, but it works really well to give me the distribution I want)

Hmm, hadn't considered how to give long-tailed distributions with dividing dice before, though it makes sense I guess multiplying (as with the d10xd10 distribution) and dividing give the same sorts of results, but with rounding down smoothing it out a bit...? I do wonder if you graphed it out if there'd be a simpler way to get that effect ? Anyway, thanks again.

***EDITED TO ADD THIS IN, IN SEQUENCE


Core mechanic & Combat manuevers

Currently I've been musing over how core mechanic affects choice of what is a combat manuever in the system - potentially working through this may let us work back to pick a core mechanic that better suits what you want. (questions that are usually quite far apart and so not usually a consideration at the outset (Unless a designer is rebuilding an existing system perhaps, since then the total existing structure is visible).  

General Notes
*Active defense (i.e. separate roll to dodge or parry) is generally possible for any mechanic since you could at worst can use the RQ approach where both roll (parry success = attack is blocked). If 'players only roll'  then opponents can't have active combat manuevers, obviously, but 'players only roll' could be an add-on for basically any mechanic.
*Often there's a choice between having a manuever declared before a roll is made, and having an extra effect result from a good attack roll. Manuevers that are better than a standard attack can be either:
-declared a priori before the roll, with a difficulty adjustment.
-occur as an extra effect or option after the roll, as a result of a good 'effect' (hitting by X, spending successes, etc).
A given core mechanic may be slightly better at either applying a difficulty adjustment (i.e. favouring pre-declared actions), getting a measureable effect out (i.e. favouring choices after the roll, good at both - so either is fine - or generally bad at both. In this last case (where neither is good), that perhaps suggest a more abstract system, or options to be balanced so that doing something all the time isn't an issue. Abilities can also be resource-based (you have a 'shoot them in leg' power useable N times/day), or might require mechanical investment in feats/skills to perform. At worst an extra roll may be involved (e.g. for hit locations).
The sort of tasks requiring difficulty adjustment includes in particular 'called shots' or the like, as well as what I'd called 'going for broke' in general (Power Attack type mechanics*"Automatic Action" - skips whatever the dice mechanism is, so can appear in any system. (Main system distinction - are automatic actions determined by 'take 10' or similar, or are these a fixed category?). As noted under cutting down excess rolling, very variable results can require a diceless resolution to break bizarre results. Movement, grabbing or lifting might be forced to be automatic instead of being too random. So movement is probably more likely to be an automatic fixed amount given a high-variability roll (d20, changing die types). SW has a fixed base but a variable 'running die', reducing divergence by the large base value.
*Pushing: existing cases - DC Heroes, Masterbook- known examples are generally universal-table games. Its a roll to increase what's basically a fixed effect to start with. Relies on having effect-output (and translating that back as a boost to a raw value) so  most feasible with universal-table type games; possibly also count-success systems (though its a. tricky as dice-pools are fairly small/granular and b. usually these are rolled rather than fixed, and 'spending willpower' or a safety valve mechanism fills the niche instead).

Additive
Additive systems usually don't use the core mechanic for damage rolls - and damage rolls could be more relevant to some sorts of combat manuever design (? - e.g. where damage is used to work out check difficulty)
*handle better attack>more damage translation badly, so, "armour bypass" or "power attack" type manuevers are more likely.  'Backstab' or 'Coup de grace' need specific combat options, instead of occuring  automatically as a function of attack successes giving more damage.
*More likely to have manuever declared 'a priori' (before rolling).  Games where you pick assorted manuevers after rolling usually work with more granular "effect" numbers for math convenience - compare the complex manuever systems (Heroic Golden Turbulence, Fireborn ) are often found in success-count systems; additive systems are more likely to require choice of a manuever before rolling, though there are exceptions (Dungeon World's multiple options for Moves; Dragon Age which gives stunt points after the roll equal to the [d6] 'dragon die' if doubles are rolled).
Grapple, disarm - abilities that take out an opponent bypassing its HP - tend to be more problematic with heavily inflating HP pools, occurring in many additive systems.

Multidie Additive
Wide variation in character's  likely average roll - the 2D character won't beat the 6D character in a fair fight- which could perhaps encourage building tactical 'you lose' situations into the manuever system to compensate and let powerful characters be taken down if they fail to defend or otherwise make a huge tactical blunder. (Tunnels and Trolls, for instance, has a number of situations where the defender doesn't get to roll and consequently takes a ton of dice to the face). System supports rolled movement fairly well, if you're into that.
This same concern can apply in other games where there's a heavy bell-curve/determinacy in results: Amber (diceless) may be an example although it relies on player/GM ingenuity rather than a codified mechanical system.


Roll-Under
Opposed rolls generally speaking more difficult. Properly speaking, its just where both sides roll that's a problem - RQ has a "resistance table" that handles conflicts with a single roll - but active defense (both rolling) isn't as easy. [see opposed roll notes for specific problems in e.g. Cadillacs & Dinosaurs]. Speaking of RQ specifically, the resistance table also handles [attribute vs. attribute] not [skill vs. skill] which has large numbers of possible numbers, though roll-under systems that aren't d100 could work. Overall, Grabs and the like (i.e. opposed Str) are possible but slightly more complex than in additive games.
Other Notes:
*Roll-under doesn't let a difficulty modifier be applied as easily for defender skill, so usually it has an active roll for the defender [Active Dodge or Parry], defaulting to unmodified % otherwise. (an exception being Dragon Warriors, where 'defense' points can be penalize to reduce Attack score - still a nuisance, but where calculations that'd be annoying anyway are merged with some tactical decision making than in any other case would just be pure extra complexity). Generally in roll-under 'called shot' type effects may be more acceptable (aiming for something at -10%, for instance), that being slightly easier to apply.
Arguably, 'Active dodge/parry' is slightly more difficult as well,  except that any success being a total block (a la Runequest) may be OK. 'Blackjack' resolution is also possible.
Like additive, has limited flow from attack into damage so likely to have backstab, coup de grace as defined manuevers.

Dice pool:  success counting
Makes "burst fire" type mechanics more awkward, due to number of dice.
TWF - works, can be implemented multiple different ways (e.g. TN increase vs. split dice pool).
Changing controlling-attribute for tasks in combat problematic just since since weighting of attribute on checks is very high (being able to switch up stat+skill is a feature of this, but done at-will breaks combat - the high Int characters are not going to stop Feinting or whatnot).
Difficulty in these games can be applied by shifting TN, penalizing dice pool, or requiring more successes: the first two options would require advance declaration of combat manuevers that would cause a penalty.
(You could also potentially have a choice, where a penalty is dice before rolling and successes instead if announced late).

Success-counting systems especially struggle with tying automatic actions to the randomizer (if they aren't just a fixed category) since no # of dice gives a final 100% chance- requiring ad hoc rules like oWoD Storytellers' "you can succeed automatically if your dice pool is equal to or greater than the difficulty". If multitasking 'splits' dice pools or raises TN to perform an action, an automatic action may need a fixed 'cost' in dice assigned to perform, or a stat to roll/default difficulty assigned.  Games with varying TN could have automatic actions be 'TN 0' in which case successes = dice pool, unless there's also a 'reroll 10s' or similar open-ending rule.

Dice pool: match counting (e.g. ORE)
Hard to apply difficulty modifiers before the roll (modifiers are major, maybe too major), hence 'going for broke' (power attack) not as workable as an option. (ORE specifically might add a minimum 'height' to a roll to get a move to work, however, IDK that its easy to work out what sort of bonus damage would work as a trade-off, and/or such a mechanic might reduce the final # successes and so be counterproductive). Conversely, manuevers where there's a bonus to hit but lower damage would also be difficult.

Dice pool: take highest
*Multiple actions: can't have a 'split dice pool' attack action, since highest roll will be in either subset (i.e. there's no effective penalty).

Dice pool: resource dice pool (e.g. DiTV)
Works more for 'extended' actions. Lends itself to lots of opposed manuevers (spending a die to 'reverse the blow', etc.). If this is the universal resolution mechanic for a system, combat moves tend to be designed somewhat abstractly so that they also work for other events - social combat, "skill challenge" type stuff, etc.

Changing-Dice-Type
With single-die, is handy for resolving multiple attacks/ opponents. Single die gives very unpredictable results on opposed ability checks e.g. grabs (grapple), though resolution could be more complex (e.g. just having a die type comparison to see who is stronger, perhaps with a shift up of die type for a "raise"/crit on the attack roll). Generally a 'crit' type result happens if a roll is X points over the target difficulty (crits can't happen on dice maximum since chances of this go down as dice get larger) so there needn't necessarily be a 'backstab' option.
Other variations (take-highest or changing die/die pools that count successes) operate more like those options.
If difficulty in the system is normally applied by shifting die type up/down, then that forces declaration of combat manuevers in advance.
(One game of this type I'd designed which used a cortex-type [stat die + skill die] for skills, kept combat to single-die by splitting a die each to attack and defense, letting the player customize how aggressive their stance was and also allowing 'full attack' and 'full defense' type options by spending both dice on one thing. It also ended up with a clunky method of exchanging 'steps' between the dice.)


Universal-Table
These are more likely to have certain manuevers appear as 'special effects' of good result levels, rather than declared upfront - e.g. knockback (DC), or the "slam", "stun" or "kill" results of MSH (FASERIP). That, combined with the ability to tables to calculate odds for very large base numbers, add to the appeal of this mechanic for the superhero genre.
MSH's subvariety of UT again doesn't consider opponent stat at all. [i.e. doesn't support a "simultaneous attack" type combat option].
Active dodge is more difficult (asymmetric results due to ad hoc penalties from a roll) - kludgy.


Summary
Summarizing the meanderings above and overgeneralizing a bit we get final results for the common options of:
Roll-under: requires 'active dodge', backstab and/or coup de grace rules.
Additive: usually before-the-roll combat moves. Requires backstab/coup de grace rules.
Count successes: leans toward after-the-roll (success spending) manuever options, multiple attacks slightly painful.
Match-counting: more heavily favours after-the-roll (success spending) manuever options.
Universal table: leans toward after-the-roll 'special success' manuever options.

"My Limit Break involves a moose, the demon Baphomet, and a Kuiper Belt object. It takes four hours and you can't skip any of the cutscenes."
-Pintsize

Below is an list of combat special attacks/actions from various systems.
In most games, a character can freely choose a special attack, at least from those abilities they know. A couple of systems have other limiters; 4E D&D gives characters a limited list of powers which are generally 1/encounter, while Dragon Age has characters roll an attack roll first, with a high roll giving more “points” to spend on stunts. 13th Age has "flexible attacks" where a character gets a set of moves with fairly metagame triggers (e.g.: odd natural dice roll to hit, even natural dice roll, natural 16+, X on the escalation die) which tends to mean fighters will have one or two combat options available depending on their roll, which ones available varying from round to round. The "Escalation Die" is particular interesting - this is a d6 used as a counter for rounds passed, which can also be spent as a to-hit bonus and so favours characters using powerful attacks until later rounds.
TORG favoured certain actions depending on a pick of cards from the Drama Deck. 5E D&D limits some (4E styled) manuevers to the "battlemaster fighter"; these use a supply of manuever points recharged by short rests. The Street Fighter Storytelling Game had special manuevers which had prerequisites to learn (like Punch **/Kick ***) and then cost 'power points' to use (similar to using magic in many games; PP cost also varied depending on combat style).
It is also possible to encourage mixing-up of manuevers by making sure terrain effect/circumstances modify them heavily (or different monsters). A move may also add a bonus to a different move that follows immediately.

Some systems make various moves more difficult based on realism concerns, while others may use a more 'cinematic' setup. Options also sometimes need to be balanced considering other rules e.g. grappling is traditionally an issue in D&D given that it can largely bypass the HP system, the primary defense of higher-level characters.

Simple, single-action-per-round combats can potentially be described very complexly if desired (there's less chance that narration will accidentally trip a mechanical 'lever') but often there's not much player incentive to do so. [Mechanics: *roll* success! Description: "Fighter takes a swing at the orc, the orc deflects the swing with a buckler, the orc stabs at the fighter, the fighter dodges and counterattacks BAM! the orc is hit."] Sometimes "stunting" (a rule where any cool description gives a bonus to an action) is used to replace a detailed combat move system to interact with. GM improvisation is also a possibility.

Specific weapons may add bonuses to specific moves (swordbreakers, "Da Dao" swords with rings in the non-cutting back edge for disarming) or be useful for specific moves only (nets).


Various combat actions might be designed so that various options are relatively balanced against each other. Equally, it may be acceptable to have the vanilla 'I attack' option be the best - this is OK if other options will sometimes become better for various tactical or other reasons - some or many options being 'edge cases' for specific situations. Games sometimes balance subsets of actions against each other with different action types e.g. x,y and z are 'minor actions' or 'bonus actions' which are intended to be less good than a normal attack action. This does give slightly more design complexity - potential for creating fairly randomly distributed 'trap' options where some character abilities arbitrarily synergize (different action types) and some don't (as they use the same resources). The same problem applies even with just one action type (e.g. the fighter/wizard who has to chooses between casting a spell and swinging a sword) but tradeoffs are more straightforward/apparent  to the designer.
Games with lots of character options can run into problems where resources are dumped into winning by optimizing particular weird options (3.x D&D for instance having highly specialized spiked chain/improved trip, 'ubercharger' or grappler builds) - resulting in player interest in character building but relatively uninteresting gameplay.
 
 
Basic Attacks
 
*Attack: the character makes a normal (melee?) attack. In some systems the character may need to split a bonus between “attack” and “defense” initially, while others assume normal attack/defense unless a specific action is taken.
Some weapons may use different sub-actions for attack e.g. “Automatic fire”, or “Continuing Beam” fire may be a different action.
4E D&D has a no-frills 'basic attack' which is used for opportunity attacks or bonus attacks, but is less powerful than a character's normal turn (where they may use a 'power'). Classes without Str/Dex as workable scores sometimes were 'taxed' by needing an at-will power that would fill the role of a basic attack. Characters which were dazed, charmed or otherwise handicapped might be limited to only making basic attacks temporarily.
Attack rolls can be based on a skill, an attribute (Marvel Super Heroes), or a level-derived number (D&D). Rolls may be directly opposed (e.g. in initiativeless games like Tunnels and Trolls),  against an armour-based number (D&D), against a fixed number barring rolled dodging (e.g. Storyteller; Palladium is a crossbreed of this and armour-based), with a penalty based on allocated defense points (Dragon Warriors), or against an automatically scaling parry value. Monsters may not get to roll in some games e.g. Dungeon World (the players roll Defy Danger instead, or may take automatic damage in some cases). Ranged attacks sometimes use a different system (cf. "Shoot", later in this post).
A couple of games lack a true 'attack roll' e.g. T&T (see Damage for description), 3:16 (roll is just made for how many enemies are killed). (and Fireborn calculates a # of attacks that hit, without individual 'hit rolls' - see 'TWF' later this post). In cases where T&T needs attack-roll based resolution e.g. to see if a monster can pull off a special move, it may add an extra fixed-odds roll (e.g. the snakebeast entangles on 1 on d6), an extra Saving Roll, or 7E had extra effects based on 'spite' (# 6s rolled in monster dice pool). Monsters also sometimes just automatically did something (e.g. there are monsters in Amulet of the Salkti which had sparking armour that automatically blinds a character for 5 DEX damage if they're hit; something that could perhaps have worked off 'spite' if that had been invented at the time). tl;dr - the single-roll resolution generates a lot of edge cases where trying to figure out a result becomes a bit tortuous.
Call of Cthulhu for a couple of outer gods has a peculiar roll for attack, where a die is rolled on a table to find a god's (e.g. Azathoth's) skill score is, for that attack. This is sometimes 100% but overall could be replaced by just a single, average, percentage.
Extra Difficulty on an attack roll is sometimes represented with an extra roll, for instance 3E D&D has a 'miss chance' % due to darkness or invisibility - kept separate to the main hit roll to prevent high skill levels offsetting it i.e. so these circumstances are always a problem.
 
*Skill Attack:: cf. 'Skill Defense' below. An attack roll using skill is not usually a distinct action type, really, but I'm leaving this here for the sake of inclusion. Some games which ordinarily do *not* use skill rolls for attacks do allow a skill to be used under specific circumstances. For instance, FantasyCraft (to quote Pedantic on rpg.net here (http://forum.rpg.net/showthread.php?768082-Interesting-AMA-with-Jonathan-Tweet-on-reddit/page8):

QuoteCompare that to something like the Spear Mastery from FC, which lets you substitute your Athletics check for an attack roll, which leads you to look for ways to boost your athletics check, which leads you to using the englightened skill ability from the Explorer class, and then you notice you can use Sword Mastery to perform spear tricks with swords and so forth.

Here as skills have a higher maximum value than the (fixed-level-based) attack bonus by class, using skill increases the attack result (particularly useful to classes with a poorer base attack). It would also be possible as a mechanic to substitute a skill roll for an attack roll under specific circumstances (Ride when attempting a trample, etc.), given a mostly-unified system for skills and attack rolls.

"Glancing Blow"- 4E and early 5E had attacks which could be pulled off as a side-effect of an attack, but dealing lower damage. 4E contained a number of attacks which dealt [ability modifier] damage even on a miss; 5E early playtests (081712) included similar fighter moves 'Glancing blow' and 'Jab' which deals damage equal to the 'expertise dice' spent to power the maneuver, instead of the normal [weapon+Str mod] result. An attack roll was required in early 5E. A similar power doesn't appear in the final 5E fighter's list of manuevers, with the equivalent option possibly turned into a simpler 'half damage on miss' great weapon fighting power and then dropped due to controversy.
As well as these there was a similar missile attack, "Snap Shot" which did [expertise die] in damage but rather than being a bonus attack following an attack action, could be taken on a turn used for something else, e.g. moving.
5E later on in the "Unearthed Arcana" column added a "fell handed" feat which gives partial successes on damage rolls - if a character misses due to disadvantage but the higher roll would've hit, then they deal reduced damage equal just to [Str mod]. (This has a mathematical flaw in that a character's chance of doing at least some damage actually increases with disadvantage, due to rolling two dice - the same chance as if they had 'advantage').

Most systems of course would just use the description of a 'glancing blow' for a normal attack with a low damage result - a poor roll for damage, low attack roll not giving much of a damage bonus, failed Test For Luck [Fighting Fantasy], or good opponent Soak.

*Shoot - generally uses the same mechanic as melee combat, but not always, e.g. as a consequence of the roll not being resisted by defender skill; Fighting Fantasy uses opposed rolls for normal melee (both sides roll 2d6+Skill), while ranged attacks roll under skill on 2d6. Metamorphosis Alpha uses a different mechanic for missiles to remove AC as a factor (2d6 with TN set by range, instead of d20 vs. AC), as does Tunnels and Trolls which uses a Dex roll to hit, whereas normally for melee attack/damage is one opposed roll with the difference giving hits (see "Damage" post, multidie additive system examples, for how this works). For attacks on PCs e.g. in 5E T&T, a PC may be allowed a Luck roll to dodge an incoming missile (consistent with how traps are handled, and since monsters by default lack “Dexterity” ratings - sort of an early version of the 'player's only roll' rule). In Deluxe T&T, wizards are normally limited to 2 die weapons, but can use larger weapons if they lose their 'combat adds' - with larger ranged weapons they hit as often as warriors (uses unadjusted DEX roll), but do much less damage.
"Supergame" (1980) apparently used a d6-vs.-d6 roll to determine to-hit instead of a formula or table of [attacker skill/[attacker skill+defender skill] as a percentage; it also rolls a hit location for 'fire combat' only to determine damage multiplier, instead of rolling a multiplier directly.
Thrown attacks may use the same rules as bows, etc; Savage Worlds has separate Throwing and Shooting, while Atomic Highway puts thrown attacks under Athletics.
Savage Worlds uses skill rolls for both melee and ranged attacks, but with target numbers being calculated differently for ranged attacks (usually making it easier to shoot, barring cover). Shield bonuses, as noted under shields, apply a Toughness bonus against ranged fire in SW, instead of a Parry bonus which is irrelevant.
Ranges frequently vary by weapon.
Systems can use exact measurements or (as in Warhammer 3rd, HOL) a highly abstract range/range bands  (HOLs ranges are “Really Not Far”, “Not Far, Really”, “Closer than Really Far”, “Really Far”, and “Really Really Far”).
Some systems adjust penalty (as well as maximum range) by weapon e.g. 3.x D&Ds “range increments” - which is probably easier with less abstract range.
Others systems may adjust throwing distance by Strength (Palladium).
DC Heroes has a particularly neat exponential equation which determines maximum heft/throwing distance for supers characters;
Weight (in APs) + distance (in APs) = STR score
e.g. Silver Age (2E or 3E) Superman (STR 25) could hit a baseball (Weight 0) 25 APs of distance (32000 miles/orbit), throw a battle tank (weight of 11 APs i.e. 40 tons) 14 APs of distance (16 miles), throw a 20 AP weight (a 25,000 tonne submarine) 5 APs of distance (100 yards), or just lift a 25 AP (750,000 ton) object.
Shooting is also not infrequently modified by attacker movement (e.g. Palladium, 'shooting wild' penalty if attacker is moving) or defender movement - some games penalize ranged attacks vs. moving characters and some the reverse (e.g. 3E characters without the 'Run' feat lose their Dex bonus when running, the reverse of most games where movement makes a target harder to hit).
IIRC, RQ uses different hit location tables for ranged vs. melee combat.
Range may affect damage or armour penetration; in systems where the to-hit roll bonus affects damage, a range penalty to shoot often reduces damage indirectly (mainly modelling decreased accuracy; it could be argued that reduced velocity should have a separate effect). T2000/Cadillacs & Dinosaurs also has different armour penetration ratings for different ranges.
Something else I'll drop here is a reference to Phoenix Commands' to-hit table for firearms - see this thread (http://forum.rpg.net/showthread.php?690208-Phoenix-Command-Reverse-engineering-table-%202A-Odds-of-Hitting) which gives details of the highly complex equation used to generate the to-hit table.
"Imperial Assault", an FFG boardgame, apparently has custom dice with range as well as damage (with custom dice being better at various results) - bringing up the interesting idea of a roll generating [hit at range X] maybe separate to [dodge difficulty](attack roll) and [damage].
Weapons may have separate damage ratings for melee and thrown (e.g. TFT).
As with attack, extra rolls (beside the hit roll) might be required e.g. 'miss chance' (see Attack). T&T Deluxe requires a Luck check as well as DEX when using a sling with stones, noting they fly 'erratically'.
Dishonourable mentions: Fireborn has a shooting action for mechanical weapons which is confusingly called "Fire". ("Fire is also the name of a character attribute equivalent to Str, along with Water/Earth/Air.)

*Press the Attack: (DC Heroes) attacker beats up defender relentlessly. Gives +1 to hit; requires the attacker win initiative. (effectively just a combat modifier; it doesn't itself consume an action).
 
*Aim: at cost of an action gain to-hit bonus; more rarely aiming may delay initiative without costing an action. Using it may prevent movement, even where that is a free action normally. Aim may also give a damage bonus (or could give a bonus indirectly, if combined with a called shot or damage bonus from high hit roll). Bracing may be related to aiming, characters may be able to brace some weapons for extra bonuses (at cost of not moving). It may be terrain-dependent rather than an action i.e. you may need a low wall to set a weapon on. 5E D&D in the second or so playtest was interesting for having a 'precise shot' feat which reduced cover by a rolled amount [d6]- the bonus was capped at +2 maximum for partial cover or +5 for three quarters so that it sometimes negated cover bonus to AC but couldn't provide more bonus than that.
 
*Counterstrike/Simultaneous attack: counter-attacking at same time as attacker; usually both forfeit defense.
In Palladium "Simultaneous attack" lets a character hold initiative and attack as someone attacks them, so that neither can Parry. This is very useful for tough characters trying to hit very agile targets. The move synergizes with its two weapon fighting rules (paired weapon characters are the main characters that can defend vs. simultaneous attacks, by parrying with one weapon while striking with the other; a couple of weird Ninjas and Superspies martial arts may also have combined attack/parry special combat moves).  
HarnMaster has a 'counterstrike' option which can be chosen by the defender even if they're already attacked, but which favours the attacker. A hit deals more damage than if the target had tried to parry.
Some combat systems that don't use initiative treat all attacks as simultaneous by default e.g. Fighting Fantasy/Advanced Fighting Fantasy / Tunnels and Trolls (& Pendragon?), where both sides roll and winner inflicts hits.
T&T gives hits = difference in side totals, giving a few quirks; missile attacks aren't compared to melee totals so both sides instead deal incredible damage (with the missile resolved first).
Multiple attackers usually can roll to inflict damage, while the outnumbered character can only do damage once, if they win (Two Weapon fighters or monsters with multiple attacks may be an exception). Alternatively, multiple characters may just add their attacks together [e.g. Tunnels and Trolls]. Fighting Fantasy is more built around one-on-one combat, being a solo gamebook system.
 
*Free shot: make a special extra attack against a foe who can't fully defend themselves. For instance, 3E's "Attack of Opportunity" is triggered by an opponent exposing themself via movement, dismounting, casting a spell, reloading, etc. HarnMaster gives extra attacks for "tactical advantage" results when comparing attack/defense rolls.
Free shots are normally less powerful than a normal turn - in 3E D&D, a normal turn for a character abstracts a whole round of action ('full attack') and so usually includes several attacks, while an attack of opportunity is a single attack, making it less significant; in 4E a character gets only one attack per turn, but can't use special powers on opportunity attacks. ROAR normally made an opposed attack roll to represent abstractly a whole round of attacks; a 'free shot' could occur under special circumstances but did 1/5th normal damage since it represented a single blow. JAGS' interesting opposed action system let a character substitute any action with a shorter time in response to an opponent's action, if they paid its action point cost.
5E reactions are also sort of related - in 5E this is an action type which can be done once/rd (if triggered) and includes opportunity attacks, certain spells (e.g. Shield), or Hellish Rebuke) or other specific (mostly defensive) abilities. Streamlining to once/round gives a unified 'currency' to what would be individual limitations in 3E if any (letting someone do an AoO and a quickened spell, perhaps). This can require additional specifications - the Hydra in 5E gets multiple reactions equal to the number of extra heads 'which can only be used for opportunity attacks' for example; the 3E hydra gets bonus 'Combat Reflexes' (but number of attacks is special); anything in 4E can make one opportunity attack per turn.

*Unarmed attack: unarmed strike may just be a 'weapon', typically with poor damage, but there can be other elaborations including defense penalties (Palladium), free attacks to unarmed attackers going vs. armed foes (3E), automatic loss of initiative (2E). 2E AD&D gave unarmed strikes a descriptive table based on the raw d20 roll - with lower numbers unlocking repeats of stronger effects to reward higher skill bonuses - and also giving a % KO for each (a bit anomalous given that lethal bludgeoning attacks only stun on a deliberate Sap attempt). FATAL has different unarmed combat tables for different races specifying e.g. 'elbow vs. face' and a damage roll.
Unarmed damage is often partly or wholly nonlethal damage; a few systems also give characters increased 'soak' vs. unarmed damage (e.g. Storyteller) or extra rolls to resist damage (Palladium roll with punch for 1/2 damage).
Palladium has various specific kicks -in Ninjas & Superspies giving a problem in that there was little reason to not use the most damaging repeatedly (Systems Failure later added some elaborations to these, like the Roundhouse Kick or Axe Kick prohibit other kicks being used, while the Wheel Kick cannot come "right before or right after another kick".
Unarmed attack penalties sometimes inherit onto other related moves, such as unarmed trip or disarm attempts.
A fairly simple or abstract system (0D&D, FATE) an attack that deals not much damage (1 on d6, etc) might be described as an unarmed attack - a punch as the foes' lock swords - but complex unarmed systems tend to introduce extra rules like nonlethal damage or 'attacks of opportunity' etc. which prevent that sort of thing. (The more complex the combat option system, the more a description of a character action is likely to accidentally hit some sort of mechanical switch unintentionally, perhaps detrimentally).
The Way of the Tiger series of gamebooks included a number of specific punch, kick and throw moves the main character, a ninja, could use: specific moves sometimes had different special effects (such as a throw being foiled by an oiled-up foe). The battle at the climax of book 1 has a heavily scripted battle where virtually every move has specific effects (and ideally requires a specially learned "Kwon's Flail", unfamiliar to the BBEG, to beat him).


Attack+ Movement Actions
 
*Charge: may be only descriptive or may penalize defense for extra attack/damage. In 3.x charging commonly allows multiple attacks (for characters with the ‘Pounce’ special quality). A Flyby Attack/Hyperslam may be present in some games.
Dragon Warriors had no built in Charge action, although the game has rules for Minotaurs which treat their charge like a ray attack (match minotaur SPEED vs. EVASION, instead of the normal ATTACK vs. DEFENCE roll - i.e. it cannot be parried).
 
*Bull Rush (Pull/Push/Trip): manuever used to push foe backwards or move their location. Effect of roll may determine distance moved. Shield Rush may be a variant of this.
Pushback: in The Fantasy Trip a large (multi-hex) figure may move by 'pushing back' a number of one-hex figures, as long as its STR is greater than their combined STR; TFT damage is subtracted from STR so this uses current STR)..  (Mechanically, this works directly because of how abilities scale - e.g. the maths for this would work badly for Talislanta, where average abilities are based around 0, since a character with +1 Strength could push back an infinite number of 0-Str mooks). Other systems might do multi-pushback as a 'multiple actions' type affair with some more fuss

Knockback: There may be a separate knockback option for punching someone backward (without the attacker moving), or this may be a natural byproduct of punching someone in a supers game. HERO (5E) has a Breakfall skill to resist this.
 
*Pressing Forward (LegendQuest, Age of Heroes): in LegendQuest the attacker pushes foe back with repeated attacks, causing them a hit penalty if their resulting movement exceeds the allowed “free walk” allowance. Age of Heroes has 'Pressing Attacks' which force the target to move backward a hex or take a penalty to the parry roll.
 
*Trample/Overrun: running over things. 3.x D&D has this as a special attack with a Str-based save DC (trample), or giving free hoof attacks (Overrun); dragons get a 'crush' attack with a similar system to trample (but maintainable as a grapple). Simpler games like Tunnels and Trolls may just assume 'trample' is part of how a monster deals damage without needing specific natural weapon or combat manuever effects. Savage Worlds gives Gargantuan creatures a special squash damage of [Str + their Size - opponent size) vs. Toughness, a massive amount.
 
Multiple Actions:
 
*Multi Attack / Multiple Actions: the character takes a penalty to hit to attempt two actions. Found in various systems. Sometimes requires a roll to attempt, instead of needing a penalty (e.g. in Superbabes it requires a d20 roll under Dex and also costs fatigue points, as do all combat actions).
Another option is for several actions (swing on chandelier/attempt to stab) to require just a roll on the lowest-chance statistic - the logic being that if the dice favour you enough to succeed on the hardest part, then you also succeed on the rest.
Or, successes on the first roll may become bonus dice on a follow-up roll, as long as they're connected.
Shatterzone is interesting in that it handles gang-up bonuses as the inverse of multiple action penalties - multiple characters attempting an action together are spending multiple actions to get 1 action at a bonus, instead of 1 action to get multiple actions at a penalty. It does (wonkily) use this for group attacks as well i.e. several characters shooting at once, requiring extra rules to calculate number of hits and bonus damage.
Alternity 'multiattack' is a rank benefit of higher weapon skill; the character rolls a single 'control' d20 and then for each attack subtracts varying situation dice with extra attacks increasing step e.g. one might be -d4 and another -d8 [so a base 13 might get a -2 and -4 for rolls of 11,15). This gives slightly less dice rolling but more predictability.
Savage Worlds has a peculiar distinction in that when multiattacking some actions let PCs/wild cards roll their 'wild die' (e.g. using two weapons), and some don't (e.g. full auto fire, including Bolt spells with multiple bolts in Deluxe, Frenzy attacks).
T2000 2E/Cadillacs & Dinosaurs (the GDW 'House System') for guns includes penalties on successive bullets in a burst, based on recoil [the penalty is assessed based off # shots and character Str].
A specific 'multiple attacks' combat action isn't required if attacking is so abstract that one roll can hurt multiple targets. Tunnels and Trolls is one example of this (it uses multiple dice, but even trying to group individual dice rolls isn't meaningful since # dice is based off weapon size); a version closer to D&D is the 'Black Streams' solo AD&D adventure patch (mentioned in the 'damage' post) which lets a character destroy multiple opponents with one attack roll, provided all have that AC or worse.

*Last Ditch Effort:: another form of special 'multiple action' from Shatterzone, this is actually used for extended skill contests, which are normally divided into 4 steps (A,B,C and D) and have a time limit applied. A character hitting the time limit can hurry and use the multiple actions rules to complete all remaining steps with one action, but with an extra difficulty penalty. A character can attempt this at other times as well, but either way all steps of the extended skill check automatically fail if the last ditch effort fails.
 
*Full Attack: full round action found in 3E and Warhammer 2nd Ed; the character must give up their movement to attempt multiple attacks.
 
*Two Weapon Fighting (TWF):
A skill rating in 'offhand' or two-weapon fighting might determine chance to hit with offhand (Recon), # of actions with the offhand ("HDL" system), or size of offhand weapon (LegendQuest).
Two Weapon Fighting is sometimes designed to be balanced with other styles (i.e. using a shield, or great weapon), or occasionally is a 'higher level' combat ability e.g. in the Blood Sword gamebook series, its a legendary warrior ability (the only way to get 2 attacks), or in the related Dragon Warriors is a special ability of high rank Knights.

TWF is not always a form of multiple attacks - some systems use other options i.e. in 4E the basic 'Two Weapon Fighting' feat just adds +1 to damage, or in Tunnels and Trolls each character's combat roll represent a whole round of combat abstractly - TWF just adds extra dice (a 3-die shortsword in each hand lets a character roll 6 combat dice, same as a greatsword; ST and DEX requirements for both weapons are cumulative - an 'ambidexterity' special ability in TrollZine #3 lets a character use full DEX with each hand). Swords and Wizardry adds +1 to hit for using two weapons, dealing average damage. 'World of Dungeons' lets a character using a secondary weapon re-roll their damage roll with the offhand weapon's damage die, the 'Holmes companion (https://sites.google.com/site/meepodm/holmes.pdf?attredirects=0)' lets a TWF character roll twice for damage and take the best.
Another option (with no examples I can think of) would be for a particularly good attack roll (multiple successes, 5 over AC, whatever) let the offhand weapon hit also (presumably doing more damage than the usual 'extra success' result, if any) without a second attack roll. (maybe Fireborn)
However, TWF is usually represented by an additional attack with the offhand weapon, which is the best way to make damage/description of the offhand weapon relevant - whether you’re using a lit torch or a magic artifact sword in your offhand is irrelevant if an extra weapon just gives a flat +1 to damage (4E D&D). A system can also just let a character with multiple attacks already hold two weapons and divide their normal attacks between them, but in most cases this is at best a 'flavour' effect which likely just penalizes the character for using small weapons instead of a two-handed sword. [White Dwarf #19 Berserker class; similarly someone early in 4Es run once suggested re-skinning the Cleave power for fighters to represent dual wielding, before 'Tempest' options were added in its Martial Power accessory.] This rule probably implies that any character with 2+ attacks/round is ambidextrous. Similarly, a character with one attack might switch which attack they use from round to round - which could potentially be useful for a 4E character where different powers are more effective for different weapon 'keywords'. An example might be the 4E monster type 'bandit' which could switch between a more accurate dagger attack and a mace attack (offhand?) that missed more often, but also allows them to shift a square.
 
In the normal cases where TWF gives multiple actions - a game may treat TWF as just a normal use of a 'multiple actions at a penalty' rules (Savage Worlds, ORE perhaps?), or TWF may have specific rules which make it possible. This first option is more integrated with other subsystems, but note that TWF has intrinsic penalties (i.e. one-handed weapon / no shield) which make it inferior to attacking twice with one weapon, if that is also allowed. TWF itself may also count as a specific combat option e.g. the 4E 'Twin Strike' power (which actually does get two attack rolls unlike normal 4E TWF) or Feng Shui's "Double Tap" manuever) - this means that a TWF attack can only be used to deal damage, not extra parries or disarms or called shots or whatever. Alternatively TWF may just provide a bonus combat action which might be used for other actions - in this case a 'shield punch' may actually use the TWF rules, for instance, or an offhand action might be useable for a trip, disarm, or to pin an opponent's weapon (leaving them exposed to a hit from the main weapon).
 
Games with multiple attacks often limit TWF to a single extra attack - for instance 3.x limits TWF to a single extra attack unless multiple feats are taken, while SenZar allows an extra attack on only one Action Phase (characters start at one, but can get up to 5 or so phases per combat round at higher levels). AD&D 2E likewise limits characters to a single extra attack per round (a change from 1st edition, where higher fighter levels granted extra "attack routines" i.e. two weapons doubled attacks). "13th Age" lets a character using two weapons reroll a natural 2 on d20 (an extra attack is only 5% likely, slightly more if a character can modify die roll e.g. half-elves can subtract 1 once per combat) (as this only affects 5% of rolls, a +1 to hit would probably be better).
TWF often incurs some sort of to-hit penalty (like -2/-4 on d20 in D&D, or having to split a dice pool), with penalty sometimes reduced by an Ambidexterity ability, though depending on system this ability may be required to fight with two weapons at all.

TWF is often Dexterity intensive e.g AD&D reduces the to-hit penalty by Dexterity adjustment, while 3.x requires a high Dexterity to qualify for the appropriate Feat. It is also sometimes Strength intensive in systems that use Strength requirements for weapons are cumulative (e.g. Tunnels & Trolls - halflings here are bad at dual-wielding). In LegendQuest this also happens, and in LQ this also reduces the weapon's damage bonus from Str, calculated from the difference between total Str and Str-required.
In other games, TWF multiple attacks can often allow a character to leverage multiple uses of their STR bonus to damage, making it more appealing to stronger characters - this is sometimes balanced by reducing the damage bonus for offhand weapons (3E), reducing the damage bonus for light weapons, or prohibiting Str bonuses on TWF actions entirely (4E did this on most lower level TWF powers; 5E limits both weapons to being light barring a feat, and doesn't add a Str bonus to the offhand weapon unless the character has the "two weapon fighting" fighting style). If ability scores other than Str can apply to damage (4E, 5E) this still makes TWF very powerful, but incentivises TWF characters to at least not be especially musclebound.

Miscellaneous:
-Palladium has the interesting drawback for TWF that a character forfeits their normal Automatic Parry when using paired weapons. A significant balancing factor, it has the odd effect of making TWF particularly attractive to heavily armoured characters who can rely on armour in place of parrying (Ninja Turtles :) ). TWF in Palladium is inconsistent with its rules for multiple limbs - usually extra limbs adds +1 attack per round instead of extra attacks like that gained from paired weapons, as does 'ambidexterity' (from Heroes Unlimited mutation abnormality/Aliens Unlimited racial trait). Palladium usually treats 'paired weapons' as a martial arts power, though it can also be sold as a specific Weapon Proficiency e.g. TMNT. TMNT notes that you roll once and use the roll to hit for both weapons, which seems to be unique to it, rather than rolling twice.
Palladium (Heroes Unlimited) 2E also has an 'energy expulsion' power which can have its damage split with 2 separate attack rolls but as one attack, instead of the normal 'forfeit parry' rule which isn't particularly detrimental in ranged-vs.-ranged combat. Mystic China has a Triad Assassin gun-fu martial art which gives more attacks and specifies how many shots are with each hand; possibly redundant if the GM lets you use WP Paired with guns.
-An old D&D houserule was sometimes to roll a chance of for 'ambidexterity', before a character could use two weapons: one variant (White Dwarf #18) being to roll a dice for each hand (d6 for left, d12 for right for instance) with the higher roll determining handedness and equal rolls meaning ambidexterity. A sub-variant of that is to separate partial ambidexterity (can use either hand) from full dual wielding (can use both at once) i.e. full ambidexterity might only occur on a roll of 6/6 on d6/d12, with lower ties meaning the partial version. ROAR used various advantages, with 'coordinative' ambidexterity giving no hit penalty but making the off-hand not as strong.
Early Gamma World had a "Duality" mutation which made a character ambidextrous, in among various other mutations; it also let a character do a mental attack or other action (like pick a lock) at the same time. Other characters could only TWF if they had multiple limbs (arms).
-D&D (whatever edition) usually gives monsters with TWF the ability to do this basically for free. This was a drow ability in 1E which maybe via Drizzt became a ranger ability in 2E. 3E mariliths also got it for free (not needing any of the feats they got from all their HD). Phaerimm in 2E are an annoying instance in that they can use 4 scimitars to attack, despite having radial symmetry (i.e. half of these are at the back, unless it floats sideways); they probably should use multiple human-size weapons as the arms are relatively small (somewhat like Pathfinder centaurs), and actually probably do in 2E since the rules for L-size creatures are vague and probably don't let them use larger weapons. Mariliths are another race that typically used M weapons in 2E but got auto-sized up due to creature size in 3E (or 5E).
-Gangbusters (1E) Boxing skill is used to attack with both fists; the skill check if successful means a double hit with both fists, if it misses normal skill is rolled separately for a single hit. (This gives the same number of attack rolls as rolling twice for each weapon, but the second roll doesn't specify which weapon hits; it does let chance of a double hit be adjusted directly, instead of being determined by multiplying the individual probabilities together [rule of intersection]).
-deadEarth has a Moves score rolled on 2d6 which is basically action points a character has; 'paired weapon' skill reduces the action point cost of one-handed weapons by 1/2. (interacts oddly with the defend rules where a defender needs to spend the same # moves to defend, unless the GM houserules that).
-13th Age has a ranger at-will 'double melee attack' power where damage dice drops one size (d8 to d6), and a second attack can be made as a free action only if the first attack roll on d20 is a natural 'even' roll.
-TWF attacks may be staggered instead of all at once: LegendQuest deliberately rolls separate initiatives for each separately (a largely unfair advantage), while 2E D&D adds a weapon size adjustment that can make weapons land at slightly different times.
-Available off-hand weapons can be limited to smaller weapons based on size (e.g. 3E D&D 'light weapons'), specifically defined 'offhand' weapons (4E D&D)(benefits Small characters e.g. apparently gnome tempest with shortsword), or by weapons adding their Strength-required (Tunnels and Trolls). TFT has TWF limited to a 'main gauche' only, which has worse damage than a dagger (1d-1, rather than 1d+2).
-3E D&D has 'double weapons' which are two-handed but let a character make an attack with each end e.g. in core the quarterstaff, two-bladed sword, orc double-axe, dwarven urgrosh, gnome hooked hammer, and dire flail.
-5E D&D limits TWF to 1/round by costing a bonus action to use it (equivalent to a 'swift action' in 3E); meaning using two weapons can prevent use of some other abilities like fighter's 'healing surge' type power, or rogue free Disengage. It doesn't require giving up movement a la 3E/Pathfinder however. (An earlier version of TWF in the 5E playtest instead let a character attack twice, but with both dealing 1/2 damage - making the ability most useful against 'minion' type creatures).
-BESM 3E has a normal -3/-3 penalty to TWF (on a die roll to hit of 2d6), which increases to -6 if aimed at different targets. TWF ability [cheap at 2 points] reduces this one 'grade' to -1 or -3. On its own, this is a reasonable. HOWEVER, the game also has the option to strike two opponents with the same attack, at -3, meaning a TWF can attack two opponents with different swords at -6 to each, or stab two people with the same sword at only -3. (???)
-FGU games e.g. Aftermath often penalized offhand tasks by having an "offhand dexterity" attribute, generally lower than normal Dex but trainable. Original Recon as noted in Weapon Proficiencies had characters learn left-handed and right-handed weapon skills separately.
An 'ambidexterity' type ability obviously may affect non-combat use (writing a letter) as well as combat use. Potentially other sorts of multiple actions could be affected as well, e.g. casting a spell with one hand while attacking with the other.
-Fireborn with its attack 'sequences' system, lets a character do one move per success rolled; using a single weapon repeatedly requires one or more 'Ready' actions, while a character can use a second weapon without this i.e. a character would need 5 successes to use a Greatsword twice [Greatsword Strike+Ready+Ready+Ready+Greatsword Strike) but only two successes to [L. Weapon Strike + R. Weapon Strike].
-more simply, reportedly Shadowrun 5E lets characters with 2 weapons just split their attack dice pool between the two.
-Dragon Age lets characters 'stunt' if they roll any doubles on 3d6, getting stunt points equal to one of the dice (coloured differently). An extra attack is one option, which has discounted cost if a character has a TWF talent, but there's only an extra attack if character's get a stunt.  TWF characters may be indirectly more mobile since 'skirmish' (extra move) is a common low-cost stunt (if a character rolls well enough to TWF without the talent, they might however get to move too).
-'Atomic Highway' notes that TWF does basically nothing (is cosmetic) - the character can choose which weapon they can attack with and has a spare if disarmed. It also notes that with, say, two guns, ammo before reloading is effectively doubled (maybe an argument to balance that with an off-hand shot penalty).
-Gamma World has to deal with characters with extra arms fairly often; 4th edition ('92 Nesmith edition) gives an extra attack; the 7E (4E-D&D compatible) has a mutation card that lets a character with another arm make an extra basic attack as a minor action.
-WHFR 4E has a 'dual wielder' talent where one (percentile) attack roll is made, then the tens/units reversed to see if the second attack hits (so 34 for the first attack is a 43 for the second). The character also needs a separate Ambidexterity talent or suffers a -20 to their second weapon skill.
Notes:
See also Initiative for notes on combining TWF with high initiative rolls granting multiple attacks.
See also the post on Monsters for discussion of multiple natural weapons.
In games where # attacks is based off DEX, TWF could be treated as a bonus to DEX - though there could be problems with breakpoints where some characters get an extra attack dual-wielding and others with a higher score don't.
Defense action rules also interact with TWF - e.g. if each attack requires an action to block it can 'overwhelm' defense (cf. DeadEarth). T&T sort of models this as well.
In the common 'extra attack but both weapons have less damage' version, TWF characters will consider extra attacks or rerolls less valuable that 'great weapon characters', and suffer or benefit more from per-attack damage adjustments (damage reduction or vulnerability, if non-proportional, including armour if that works as damage reduction, as well as ability modifiers to damage and damage bonuses for a particular good attack roll).
External lists:
List of 3.5 D&D feats based off the 'Two Weapon Fighting' feat: http://alcyius.com/dndtools/feats/players-handbook-v35--6/two-weapon-fighting--2998/index.html (http://alcyius.com/dndtools/feats/players-handbook-v35--6/two-weapon-fighting--2998/index.html)
List of FATE stunts associated with two weapon fighting: http://evilhat.wikidot.com/two-weapon-fighting (http://evilhat.wikidot.com/two-weapon-fighting)
(Note that original FUDGE has no rules for TWF as such; the iconic character 'Groo the Wanderer' uses two swords, but this is just represented as a 'Superb' Sword skill).

*Multiple Opponents/Area attack: a single attack targets multiple opponents (e.g. with same roll). Sometimes found in supers games – using powers or with “Sweep Attacks” e.g rolling logs under several opponents. Legends of Anglerre has an "Unthinkable Attack" useable by certain epic creatures, which requires a turn to power up, burns a Fate point, and inflicts consequences on targets in a large area.
 
*Cleave/sweep: -e.g. fighters in AD&D could make a number of attacks equal to level vs. monsters of less than [1-1] HD (its been suggested how many are killed could be resolved quickly by rolling a 'dX' where X is the fighter's level. Replaced by the 'Cleave' feat in 3.x (bonus attack when an opponent is dropped) and then in 4E a cleave power which dealt [ability modifier] damage to an adjacent foe, slightly useful to kill "minions".
The ability actually dates all the way back to Chainmail, where a 'Hero' [=4th level fighter equivalent] was equivalent to 4 men and a 'Superhero' [=8th level fighter equivalent] was equal to 8. 0D&D apparently gave out this ability to monsters too (1 attack per HD, and bonuses to the HD applied to a single attack, e.g. a 6+3 HD troll would make six attacks, one of them getting +3...to damage?)

*Combination Move: ability to join two moves together as one action (Ninjas & Superspies) i.e. combination Parry/Entangle where parry also ties up opponent’s weapon.
 
*Full Auto:-gun option emptying clip to shoot more bullets, generally with less accuracy.
In Palladium, one attack with x10 damage IIRC; takes a full-round action in d20 modern.
nWoD reportedly has bonus dice for autofire but extra attacks from some powers for e.g. martial arts- ramping up damage for the latter potentially far faster... Some 'multiple attacks' in the earlier Aberrant had rules similar to a burst bonus: the 'Rapid Strike' mega-Dexterity enhancement added +Mega-Dex rating to punch/kick damage pool (a flurry of super-speed punches).
This may have accuracy penalties e.g.(As noted in dice pools - supplemental) the GDW House System (i.e. Cadillacs & Dinosaurs/Dark Conspiracy/Twilight 2000 2E), uses a d6 Dice Pool for autofire instead of its usual mechanic (d10 roll under) to handle lots of shots quickly. (check how TN adjustments for range?)
(For any 'spray' weapon - shotgun, railgun, or automatic weapon - the damage roll can represent how many of the projectiles hit the target, so less than Max Damage may mean describing more damage to the scenery. Credit to Novastar for this).
Warhammer 40K RPG rules e.g. Deathwatch represent 'full auto' by having a single attack (with a to-hit bonus of +20%) and degree of success giving multiple successful hits - one, plus one per 10% success margin. This is an elaboration on the normal system where attack rolls don't affect damage. As all the shots are from one "attack", a single successful Dodge negates all of them, unlike if they were rolled separately. Each has a separate damage roll - 'Righteous Fury' crits occur based on 10s on the damage roll + successful weapon skill check, so happen individually for each hit.
Dungeon World has a 'Volley' action which lets a player choose to burn extra abstract ammo units as a trade-off against extra damage, or choose to move into more danger as a trade-off. In DM, 'unlimited ammo' is largely a disadvantage, since ammo-loss tradeoffs can't be selected (though other GM tomfoolery including arrows would be thwarted as well).
Irregulars (http://www.therpgsite.com/showthread.php?t=33182) here [edit: dead link] has an interesting auto-fire rule; the normal game mechanic is dice pool (making multiple attacks messy), with autofire resolved by rolling an attack as normal and cross-referencing range to get a target number; a number of dice equal to number of shots is then rolled, giving two 'dice pool' checks instead of a roll of the 'dice pool' per shot. Its maybe slightly spoiled by having extra shots add a minor bonus to damage, so that the exact number of hits is sort of irrelevant. The minor damage add also makes it relatively more beneficial to spread fire against multiple targets.
Hero 5E potentially uses both options for autofire - it normally rolls damage separately for each hit but (in The Ultimate Skill) has an optional autofire skill [Deadly Sprayfire]which instead gives an Irregulars-type damage bonus [+1 damage class per extra attack that hits]; arguing this is more effective due to how HERO handles damage (subtractions from each damage roll/armour, chance of stun).
Autofire might or might not be allowed when using two weapons.
Palladium (Rifts) has rules for micromissile volleys as well as autofire: notably, a character cannot dodge volleys of 4+ missiles. Targets can shoot a missile, in which case there's a chance of nearby missiles being taken out when that missile explodes.
Fragged Empire normally uses 3d6+modifiers for virtually every game roll, except high Rate of Fire weapons which add ROF to the number of dice rolled. I believe that it doesn't affect damage directly, just gets extra damage via the attack roll (a 'strong hit' per 6 rolled). Cover specifically reduces damage for high ROF weapons.
Amazing Engine's Bughunters uses a Fitness (i.e. Str) check for autofire instead of Reflexes (recoil), with a -30% to hit per 45 degrees of arc. A character can make attacks in the area equal to 1/2 the ammo expended, as well as a free attack on anyone entering the zone; it lasts for a round starting on the characters' turn.
High Colonies rolls more dice if shooting multiple shots; 2 or more 1s give a 'jam' (3 is serious, 4+ weapon destroyed), guns can't jam in single-shot mode.

Ranged Burst: D&D 4E, and D&D 3E at least once (Epic feat "Storm of Throws") have an odd mechanic where a character using archaic melee weapons - e.g. axes or bows - make ranged attacks across an area, somewhat like if they were using autofire, instead of having a set number of attacks. Particularly egregious is the 4E rogue power 'Cloud of Steel' (7th level rogue, PHB I) - a close 'blast 5' power which lets a character shoot everyone in a 25' wide area as one action with a crossbow of all things, ignoring the normal reloading time. The mechanic is IMHO really a misapplication of one that makes more sense with explosions e.g. grenades or fireballs.

*Manyshot: 3.5 has a 'Manyshot' feat which lets a character with it shoot two arrows with a single attack roll, increasing to three or four as number attacks increase - this actually didn't increase how many arrows a character can fire normally, but is a 'standard action' so that characters could also move. Pathfinder instead gives two arrows on the first attack so that the feat synergizes with its prerequisite, Rapid Shot. Savage Worlds [Fantasy Companion/free fantasy web supplement] also has manyshot (as 'Double Arrow shot', IIRC) and keeps the basic mechanic (a single roll for two arrows at -2), but makes the edge elf-only.

(http://i1239.photobucket.com/albums/ff507/BSJ17/Robin_zps0cae3fcb.jpg)

*Multitasking: 3.0 D&D Savage Species has a 'Multitasking' feat letting characters with multiple arms perform a standard action per pair of arms as a full-round action.

*Vital Strike (Pathfinder) - including this w/ multiple actions mostly for reference. Vital Strike lets a character trade in multiple attacks to do a single attack with multiplied weapon base damage (as well as moving, normally prohibited with multiple attacks in pathfinder).

Movement

*Move: action type varies from system to system – anywhere between ‘counts as full turn’ and ‘free action up to x distance’. A character might be able to expend variable action points to get more or less movement, or different movement actions may be defined (e.g. Normal, Double Move, Run, 5’ step/Shift, Withdraw, Circling [JAGS], Intercept (Shadowrun)). In games where a character can opt to act twice with penalties, running may give penalties from this (e.g. Savage Worlds). Changing facing or standing up may also count as movement. 'Opening a door' counts as 10ft of movement in 3.0 D&D IIRC, while other systems may make this a separate (possibly free) action
(One game at least, MSF High (https://sites.google.com/site/joeysmsfhigh/home) has characters spend 'movement points' to do kick attacks).
A game posted in the design forum, Irregulars (http://www.therpgsite.com/showthread.php?t=33182), had multiple movement rates x various action lengths so a character could e.g. have a 'complex action' (full move), 'normal action' (2/3 move), simple action (1/3 move) or free action (1m) version of walk, jog, run or sprint. Moving didn't actually actually require an action but is assumed to be simultaneous with other actions up to that length, with faster movement meaning more penalties - e.g. you could walk+shoot, then break into a run with remaining movement).  
Movement can give various penalties to attack: e.g. in 3.x any movement (beyond a 5ft step) prevents a 'full attack'. In Savage Worlds movement is normally free up to allowance, although "Snapfire" weapons take a -2 penalty to attack if any movement is taken (before or after the shot i.e. this assumes the initial shot is done in less time if subsequent movement is taken).
5E D&D base a base move built in, then a character can "Dash" as an action (bonus action for level 2+ rogues). A houserule I'd seen on the internet to increase running movement was "Running: when you Dash you can Dash again as a bonus action".
Chill has movement penalties for firing, standing up, placing obstacle (moving a chair into a pursuer's path while running away), or watching behind.

*Giving Ground: parry combined with retreating backwards to give an extra bonus (LegendQuest, JAGS).
 
*Jump: specific movement type. Distance may require a roll on skill/attribute (e.g. 3.5 Jump/ Pathfinder Athletics) or be fixed i.e. 1ft per Str point (Synnibarr); or 1/4 normal movement rate (Attack of the Humans). A fixed distance might be "pushable" as an action (cf. DC Heroes). In combat there may be a “Leap Attack” that uses Jumping.
5E has a Str-based long-jump distance which is theoretically based on Str but practically more capped by movement rate (1ft of jump costs 1ft of move) unless a character uses a Dash action as well - see here (http://www.therpgsite.com/showthread.php?p=875478&highlight=funny#post875478)
(3E has a proviso that Jump uses movement as well, with excess movement potentially forcing an action to be spent on movement next round).

*Climb/Swim/etc – typically uses a skill roll (Str based). One game (RECON) uses a Perception check for Climbing.
 
Duck for cover
 
Change Facing - only for games which use facing (Superbabes, IIRC Gurps).

*Open Door- (movement). IIRC, 3.0 D&D counted this as equivalent to 10ft of movement if we care (though that is unusual). Perhaps less likely to occur in combat.

*Combat Driving: can include rules for vehicles, mounts, chariots, etc. Often controlling a vehicle consumes some sort of action (Palladium is noteworthy in that characters in robots add extra 'robot combat' actions to their normal hand-to-hand actions, getting more attacks). A number of standard actions (like bull rush) may apply to vehicles. Missile fire generally suffers movement penalties.

Defense
Note that games vary considerably as to whether defensive actions exist and must be declared, or are 'built in' to a default defense value.

*Parry: block opponent attack. Some systems assume certain amount of parrying, giving a “passive defense” rating or high defense value, while others assume an active parry must be made to factor in defensive skill; decisions like this determine how dangerous multiple (lower-level?) attackers are in a system. GURPS has a passive defense rating; Supernatural (Cortex) lets characters roll their attribute die on passive defense, or [attribute+skill] if using an action.
AD&D 2E has multiple types of parries (single attack or all opponent’s attacks). Parrying is normally adjusted by Dexterity or Agility, though in a couple of games Strength is used instead, including Conan D20 (Parry Defense is calculated with Strength, but with the proviso that penalties for low Dex are still added, and dextrous characters have low Parry but can just opt to Dodge instead), and AD&D where a character with a Strength to-hit bonus can spend their action parrying to subtract it from opponent attack (1E PHB, pg 104). Arduin Grimoire allows a Parry only if a character's DEX is higher than their opponent, possibly since it uses DEX-countdown initiative so that higher DEX is needed to go first/react faster.
In some cases parry may cost only a penalty to attack, rather than being an action (MSH). Some systems may allow a character to parry attacks vs. an ally (e.g. with a polearm; AD&D2E Complete Fighter); this may have separate rules as a ‘Guard’ action. Parries may apply a fixed or rolled penalty to an attacker, or be rolled as an opposed check; for example Palladium. Rolled parry systems of course have more dice rolls in combat, but also may handle situations where a character can't readily defend (i.e. when surprised or casting a spell) more intuitively. The choice of whether the defender gets an active roll can also be affected by luck point mechanics e.g. rerolls, which otherwise typically favour the attacker.
Hackmaster gives fumbled parries a 'free attack' to the attacker; also, for long combats/later combats in the day, a character rolling less than their Fatigue Number is fatigued.
 
Elaborations: The Stormbringer RPG has rolled parries, with the additional effect that a critical parry can break the attacker's weapon. HarnMaster, a critical Parry gives a DTA [Defender Tactical Advantage], i.e. a bonus attack to 'riposte' (IIRC this can be with their regular weapon, if parrying with shield). Honor + Intrigue (Barbarians of lemuria variant) reportedly does this as well - at least for some combat styles a buckler critical could be followed with a free sword attack.
Fireborn (see "actions") lets defenders script a sequence of moves in response to a similar attack sequence - a dice pool is rolled to see how many moves a character can pull off, with a 'defend' being needed to cancel each attack move, and potentially attacks included following a 'ready'. (As a house rule, heavy weapons could be made harder to riposte with due to requiring multiple 'ready' successes in defense, which is normally the case when making second attacks in Fireborn).
(Fireborn also has a proviso on the specific parry-equivalent manuever, "block", that a weapon has to be within a weight-category for a block to be possible. Larger targets can also "sweep" multiple foes who are unable to block).

Some systems give PCs a total of “defense points” to distribute as desired between opponents (making flanking rules largely unnecessary) e.g. Dragon Warriors, or the 'dodge pool' in 1E shadowrun.
5E D&D has a 'Parry' fighter manuever which burns a resource [manuever points] to reduce damage directly by manuever die (e.g. d8) + Dex mod, but doesn't alter hit difficulty. Atomic Highway lets characters do active defense rolls against a number of targets equal to Notice skill.
Games sometimes allow ranged attack (e.g. arrow) deflection as a separate special ability (e.g. D&D monk 'Deflect Arrows'). 5E D&D 'Deflect Arrows' works somewhat like fighter Parry, with damage reduced by [d10+Dex+monk level], and the monk can also catch the weapon if damage is reduced to 0.
I've seen a suggested house rule for 5E Parry (Opa Opa on this site) that lets a character do a 'parry' at the cost of a 'hit die', which is weird - doing super parry at cost of fatigue I think is the idea.
Tunnels & Trolls since it works by comparing attack totals and dealing the difference as damage, essentially builds a 'parry' into attacking (instead of having an AC). In it, doing anything else in combat, such as spellcasting or shooting an arrow, can be fatal since no defense total is generated.

Riposte: a parry followed by a quick counterattack. Sometimes a 'Riposte' may occur as a result of a good 'parry' e.g. HarnMaster gives a bonus attack for a critical parry, if opponent rolls poorly. Similarly Marvel Heroic lets a character spend a 'plot point' to gain an effect die from a reaction (defensive roll) - including dealing damage though this rule has probably wider applications.
Dragon #165 has a 'riposte' manuever for fighters, on top of a parry manuever (giving a penalty 1/round to an opponent's roll). The fighter delays their action, and if the parry works the delayed attack gets a +2 to hit. (the parry could actually work due to either the extra bonus or inherent AC, I think, and the riposte would still work.)
Palladium e.g. Ninjas & Superspies has a few similar combination manuevers e.g. 'Automatic Body Flip/Throw' where a character substitutes the manuever bonus for the normal Parry bonus (i.e. lower) and then flips the target on a win (the also lose the option of a 'roll with punch/fall').

*Spell Parry - [Age of Heroes] - Parry attempt but using a spell.

*Power Defense - - hazard studios' Supers! RPG lets nearly any power be used defensively (superstrength to punch a thrown car out the way, etc). The main limitation is that a power used for defense can't be used also to attack on the characters' turn. Specifically defensive powers (Armour, Mental Shield) can be used multiple times/round but with a -1d cumulative penalty.

*Block: by this I mean using a body location e.g. an arm to parry, taking damage to that location instead of the original location struck. This result may appear from a ‘partially successful’ Parry, rather than being defined as a separate manuever.

*Skill Defense: basically as Parry, except a couple of games e.g. Hollow Earth Expedition (HEX) gives characters a defense bonus from a skill in use, rather than just combat skill (i.e. you can defend with Photography while trying to photograph something, or Magic while casting a spell).
4E D&D has a "Reflexive Dodge" skill power, which uses a skill roll to calculate a damage reduction, rather than a defense number; "make an Acrobatics check and reduce the damage you take from the triggering attack by half the check result" (fairly high, but also limited to 1/encounter and level 16+); a similar power exists for Arcana skill vs. energy damage. (this sort of mechanic seems logical and thematic, though the 'function call' of the skill rules makes it potentially possible to stack on other modifiers from powers affecting skills; also, its slightly weird conceptually, since damage isn't modified by a check -making it asymmetric).
 
*Fend: similar to parry, but assumes defender is making attacks to hold the opponent at bay (like a lion tamer with a chair).
 
*Dodge/Tumble: used to avoid an attack or do something acrobatic, perhaps disengage from a dangerous area.
Dodge typically uses an opposed roll of some kind to activate (i.e. roll the same or better than the opponent); or there may be a flat chance of success. Some systems (SenZar, Talislanta) may add penalties to defense for an unsuccessful dodge attempt; which might result in a more likely hit (if the dodge had to be declared before the attack roll; otherwise this is moot unless degree of success adds to damage) or additional damage.
Dodge is sometimes not allowed vs. fast-moving attacks e.g. bullets. Dragon Warriors has an 'Evasion' which is matched against the Speed of the attack, instead of the attacker's skill.
Dodging may be automatic, count as one action (Palladium), impose a penalty to attack rolls if used (Marvel Super Heroes), or be free up to a certain limit. Some games demand dodge-type actions be declared in advance (3.x D&D Total Defense & Fighting Defensively) while others permit them as interrupts (often burning future actions).
Games where Dodge is normally rolled vs. an attack roll may sometimes also be rolled against a fixed target number - Palladium 'fireball' for instance has a fixed target number of 18, or a roll to avoid walking into a carnivorous plant in Rifts Dinosaur Swamp uses a 'passive dodge' of 16.
Star Wars D6 (2E, anyway) has a default fixed defense, but a character who Dodges replaces this with their roll even if its lower ("sometimes people accidentally leap into the line of fire or move right into someone's attack!").
Most editions of D&D are notable for having 'dodge' function with two alternate mechanics - attacker roll to-hit or defender roll to save - 5E 'Dodge' gives a character disadvantage to be hit on the attacker's roll, or advantage on a Dexterity save; 3E assumes a free Dodge against fireballs etc. and has no action giving a bonus to this.
Ninjas and Superspies (Palladium) distinguishes between regular Dodge and Multiple Dodge (lower bonuses but works against rear attacks). Automatic Dodge in N&SS costs one attack (and requires the character win initiative) unlike the later version for Juicers in Rifts; there are rules for characters dropping an Automatic Dodge to perform Multiple Dodge if targeted by rear attacks.
World of Synnibar has separate ratings for dodge vs. normal and 'wide beam' (20ft wide or more) blasts - should you fail other characters may be able to help with a 'heroic attempt' to pull you out the road, or you may get a God Roll as a final fallback should the blast be fatal.
Tunnels & Trolls has 'Dodge' as an option available only against (unfairly) large monsters like giants. A DEX save allows a character to deal their entire dice roll as damage, instead of having to compare it to their opponent's roll and probably be squashed by the difference [cf. Damage for a quick explanation of T&T combat]. One solo, Captif d'Yvoire, has a monster where you can do this but take damage to DEX and CON by the amount you fail the save, and also bases the SR level off its [current MR starting at 150/30]).
Exalted 'Full Dodge' gives a number of dodges equal to [Dex+Dodge+specialties] dice pool, but with a cumulative -1 to each roll.
Whether Dodge/Parry requires active declaration in advance, or can use a future action, is relatively important tactically . Notably in the case of multiple opponents: if 4 goblins engage a fighter and the one attacked can choose to dodge with a future action, they can raise defense substantially with only a 25% drop in offense, while all four need to defend otherwise (assuming the attacker can freely switch targets). The same principle applies the other way to PC 'boss fights'.
Mutazoids has a 'normal' and 'full' dodge; normal indicating a character is 'within the opponents' reach but dodging individual attacks' while full is 'staying out of reach and cannot attack'. This sort of parallels e.g. 3E D&Ds 'fighting defensively'/'full defense' split; these are interesting in that there are multiple manuevers which are separated by degree of split between attack and defense, instead of being defined by whether its a 'dodge' or a 'parry'.
High Colonies (which assumes most combat is gun combat) has a dice roll for defense based on what the target did on their initiative (stood still d6, walked/crawled 2d6, doubled 3d6, ran/charged 4d6, dodged 5d6).

*Make Saving Throw: usually this is a reactive event that doesn't take an action. Cf. Dodge (e.g. for the Palladium fireball). Some 3E or later stunlock spells (Hold Person) allow a reroll as a full-round action, basically so people feel like their turn may be doing something. In 3.5 this did have the problem of creating a perverse incentive for enemies to coup de grace Held PCs before they could re-enter the combat.

*Shield Wall: locking adjacent shields for extra bonus.
 
*Roll with punch/fall (e.g. Palladium): spend action where dodge etc. has already failed, to reduce damage by half. In game this I suppose reflects e.g. tensing up muscles against a punch.
The action does tend to have more bonuses than Dodge - presumably deliberately since unlike regular Parry the roll is made vs. a roll that is already successful (so has to be higher) and less abuseable in any case since it only halves damage rather than negating it fully. Roll with punch is slightly reminiscent of a "soak roll", though its more common for those to be an automatically occurring thing rather than an action.
Mutazoids has a 'rolling with an attack' action which reduces damage 1/2 and does not cost an action, but causes character to lose initiative next turn.
Sometimes treated as not an action but an automatic defense; for instance Mercenaries, Spies and Private Eyes has a 'Pugilism' skill which lets a character absorb 1 damage/skill level each combat round from unarmed attacks
 
*Maintain balance (Palladium - Systems Failure): negate successful knockdown attack with a skill roll (40%, or Acrobatics/Gymnastics %, instead of the usual d20 roll) at cost of one attack and instead of using a "roll with punch/fall".

*Tough it out (Hypothetical) - aka Con-based Intimidate, where a character takes an attack to show how tough they are.
(I've sort of done this myself in AD&D, but more with "player skill" than by any mechanical means).

*Heroic Attempt: mostly unique to Synnibarr; if one hero is about to be hit with an attack, another hero may attempt a ‘heroic attempt’ to interrupt it and interpose themselves, or pull the victim out of the way. Requires an unusual bonus initiative check to pull off. JAGS more or less allows this indirectly as well (it allows interrupts on any action, with a shorter action). Low Fantasy Gaming has a "Rescue" action, which requires a Dex check and also costs a Luck Point (regained after a long rest).
 
*Interpose: the character takes damage meant for someone else. e.g. Risus has rules for this which let characters take double damage (instead of rolling among team members to see who takes normal damage, since the system is quite abstract); the other characters also get extra dice nexd round to 'avenge' them, regardless of whether they were taken out entirely.

*Use Perfect Defense (Exalted) - really a form of magical power use, but bears mentioning. A 'perfect defense' in Exalted is a charm (power) that automatically blocks an opponent attack, e.g. by automatically giving [attacker's roll +1] defense successes. A character can only use one charm per round, which combined with the ability of character's to deal huge amounts of damage can leads to "paranoia combo" combat, where all characters use basic attacks only to leave them capable of putting up an emergency perfect defenses, very slowly depleting opponent's motes (power points) until an attack can get through.

*Act Under Fire /Defy Danger (Apocalypse World /Dungeon World): a very catch all 'move' for avoiding trouble but typically representing a dodge. DW balances the ubiquity of the move somewhat by allowing multiple possible stats to be used to modify it, depending on nature of the danger and how the character attempts to respond.

*Blank Mind: - e.g. the Invulnerable RPG includes this as a mental defense type action.

*Single Weapon Style: while not exactly a combat move, this is included by way of comparison with Two Weapons use. This is not infrequently just inferior to either two weapons or use of a two-handed weapon (which generally means more damage) or a shield.
Use of a single weapon might be encouraged by making it a classes' only option, or a default option in case of low Str/Dex (see 'weapon proficiencies and Str requirements'), or if other skills aren't also purchased. Games more rarely may provide a bonus to single-weapon users e.g. Complete Fighter for AD&D gave them an AC bonus - this sort of thing may be justified with the idea of a single-weapon fencing stance being more side-on and so presenting less frontage to an attacker. Being able to punch or grab an opponent may also be advantageous, and/or warrior-spellcasters may need a hand free if they want to cast spells occasionally. Low Fantasy Gaming encourages single weapon style by letting single weapon users switch weapons without an action, although this is slightly undermined by also letting characters switch melee/ranged for free also (e.g. someone with a greatsword can also switch to longbow for free and back).

Cooperative Actions
*Team Attack: two attackers attack simultaneously. May add damage for purposes of stunning (HERO), or add damage before armour subtraction to get more oomph vs. invulnerable foes (Superbabes).
 
*Aid Another: spend turn assisting an ally, adding bonus to their action. This might require a roll, or not (e.g. a character might fail to assist an ally, although this may make this quite bad as an action combat option - at the very least its possible the main character's action will still either fail, or would've succeeded regardless). The secondary character's bonus is usually 'scaled down' in some fashion rather than adding directly. Count-success systems handle 'critical fails' here fairly straightforwardly, in that -tve successes (a botch) may subtract successes from an ally.
In Savage Worlds, I have houseruled that a wild card helping an 'extra' NPC, could loan them their 'wild die' if they successfully make an appropriate check.

*Assist Spellcasting: [LegendQuest] allowing targets to assist a spell's working on them (e.g. some healing spells). In LQ, unconscious characters cannot assist.


*Create Advantage: (Fate, e.g. Fate Accelerated [FAE]): this creates an 'Aspect' and allows 1-2 free (without spending a fate point) uses of it; basically the same as 'aid another' but described in terms of Aspects. It has very broad use i.e. outside combat it can be used to represent various things, and most skills (not just Fighting) can be used to Create Advantage whether by noticing a useful detail or crafting a quality into an object.

*Beast Attack: ordering an animal companion to do something. 4E D&D has a range of animal powers, most of which replace the user's own attack however. 3E D&D has skills for 'pushing' or performing tricks with animals.

Using Cover: not exactly an action but a game may have rules for using cover (possibly including other characters!). Typically if an attack misses due to cover it will hit the cover (e.g. 3E D&D, Star Wars D6). Some systems may have rules for cover being broken - Star Wars use a 'Str roll' based on cover durability vs. damage to see how heavily damaged the cover is, while other games may just track HP of objects.

Initiative Actions
 
*Ready/Delay Attack: acting later in round. 3.x D&D distinguishes between ‘readying’ (a standard action interrupts foe) and delaying (a larger full round action can be performed, but after the opponent). IMHO if a 'ready' is used to interrupt, this ideally should use some sort of initiative-based mechanic so that (say) attacking people threatening hostages is risky. Covering someone may also be called out as a separate action (JAGS). LegendQuest lets characters using two weapons have separate initiatives for each weapon, hence a ready ("hold") can be used with one weapon while fending with the other.
Games may consider ready or delay to be an action e.g. in Fireborn 'delay' or 'interrupt' [='ready'] count as a characters mental action (characters get 1 mental and a number of physical actions, so a 'delay' will prevent e.g. aiming, defending, ambush or some other options). It lets an interrupting character whose trigger condition doesn't occur convert the action into a 'delay' however, compared to 3E where the action is just lost. Also for interrupt it specifically notes the interrupted target can change their action (e.g. if a sneaking PC successfully -with a quickness check - interrupts and shoots a troll which as they suspected is about to eat an orphan, the troll can change action and attack them instead).
 
*Shoot from hip (literally or not): penalty to hit to get bonus to initiative
 
*Set vs. Charge: hold action (esp. with reach weapon) dealing additional damage vs. charging opponents.
 
*Refocus: taking penalty to boost initiative roll next round. Redundant if actions are permitted to “hold over” between rounds.
 
*Re-roll initiative: Two-Fisted Tales has a 'reroll initiative' action which costs an action (they can't do anything else) but makes everyone reroll their initiative. [note its d10-d10 game mechanic makes a reroll less variable than say D20].

*Abort: for a system where an action is predeclared, dropping this action to do something else (HERO) e.g. ‘abort to defense’.
 
*Drawing a weapon: may be an action, apply an initiative penalty, or apply an attack roll penalty. If it counts as an action it might use up an attack or count as another action type e.g. an 'automatic action' or 'move action'; cost of an attack is worse if characters have only one attack/round (Dragon Warriors) than several (Palladium?).  It tends to have a more severe cost when combat rounds are defined as shorter.
Thrown weapons (knives, throwing axes) may require a “draw” action before each attack.
5E D&D has a more general "Use an Object" action that covers this (usually free as part of another action or movement, but otherwise costing a full action: this is perhaps too vaguely defined as its unclear whether some things, like drawing a shield, are 'free'. Drawing two weapons at once with one action seems to require a feat (?) whereas it could be done with a +1 BAB in 3E).
Note that being unarmed may just cause problems attacking (D&D), or might involve difficulties Parrying as well. In the latter case, being unarmed might be assumed as part of a surprised condition, even if characters normally draw for free on their turn.
Low Fantasy Gaming allows characters using one-handed weapons to switch between these without an action - as a deliberate decision to allow them more flexibility to balance them vs. shield users or large weapon users. Savage Worlds makes larger weapons harder to quick draw, requiring an Agility roll.
 
*Start/Complete Full Round Action: A 3E D&D action, a 'full round action' can be spread over two rounds, using a 'standard action' in each. Used when a character is forbidden a full round of actions, such as when surprised, magically slowed, or you're a zombie.
 
*Mitigate Surprise:(Hackmaster) - a character helps another character with a worse initiative, averaging their initiative scores.

 
Damage Modifying Moves

 *Gain Advantage: Twisting Tunnels has an abstract 'gain advantage' move wherein a character sets themselves up for a better attack - dealing 'major damage' instead of 'minor damage'. One example of this would be get into close combat with a light weapon. Other games with more complex tactical setups would instead add hit, damage or other specific situational modifiers. Also compare Fate's 'create advantage'.

*"Touch" - rules may be specified for just touching a target, usually as part of magical attacks. D&D 3E alters AC (having a 'touch AC'), while AD&D sometimes specifies that armour doesn't apply. 4E D&D has a "Reflex Defense" that is generally lower that AC and is used instead.
BESM adds a flat +3 bonus to attack rolls just to touch rather than deal damage, although it notes this may be cumulative with called shot penalty to hit a specific area for some things.  It also notes that prolonged contact generally means a 'grapple'. Note that normally BESM treats armour as 'damage reduction', so this is an extra rule to simulate D&Ds 'touch attacks' and is in a way being generated by DR (the touching-is-easier effect comes for free in games like 3E D&D, or AD&D, where the to-hit number is modified by armour and you can just ignore it to get the touch AC).

*Pull Punch: declared to reduce damage from an attack. Some systems distinguish between bashing/lethal (the equivalent action changes damage types). A roll may be required e.g. in Palladium (I've heard it suggested the Pull Punch roll in Palladium could also be needed for other tasks, such as a shapeshifted Dragon trying to shake a normal SDC creature's hand without damaging them).
One system (a supers freerpg, I forget the name) allows regulation of damage only in dice rather than exact points to build in some uncertainty (a character with punch damage 5d6 might roll 1d6,2d6,3d6,4d6 or 5d6 to try to get the right damage, but not roll the total and automatically reduce it to “just enough”).
'Pulling an attack' in Mutazoids is automatic and reduces damage by 1/2. Other systems can let a character opt to not add their Strength damage bonus, if any (5E D&D).
See also discussion on critical hits.
 
*Called Shot: attempt to hit a specific body location. May have different penalties depending on which location; might be useful against a specific monster with an “Achilles Heel” in a specific body location. May include “stapling people to walls” (thrown knife through clothing), cutting Z’s in opponent’s foreheads, or nerve strikes. May also include rules for breaking/severing limbs (usually involving damage > some threshold).
Variants: HarnMaster allows a character to choose “zone” (upper, normal or lower) at -10% to hit rather than fully calling a shot; the One Roll Engine’s “count matches” system may give a PC a couple of different hit locations possible off the same roll, at various #s of successes – building a sort of called shot into every attack.
Called shots for vital locations are potentially deadly in many systems; this may be somewhat mitigated by an active parry system (i.e. if the opponent has to take a penalty to hit, they become easier to parry).
Some weapons might have unusual effects on a called shot, e.g. in 2E Complete Fighter a bola can 'Pin/Trip' with a leg attack, entangle arms or make a "head" called shot to hit the neck and strangle an opponent (d3 damage per round).
Different approaches to called shots: 3E D&D generally avoids 'called shots', but characters can learn specific feats that allow similar effects e.g. 'Hamstring' (trade sneak attack for slowed movement).  That limits access to them a lot for most characters in most campaigns ('action points' in e.g. Eberron could give temporary access to feats in games that use them).
Exalted has no 'called shots', but a description involving a particular stab to something could well be part of a stunt, cf. Stunting below.
Called shots cause particular problems in systems that don't have them, since players will often want to try something like this in some special situation, which then becomes a precedent to always stab at the eyes or etc. Large monsters might allow this due to their size making it more feasible. This is something vaguely defined in e.g. Tunnels and Trolls 5E for missiles, which sets missile SRs by object size (Tiny including "eyes, coins or locks of chests"). It would rarely have a problem with ranged called shots being broken since even regular missile shots are incredibly lethal, at a risk of being pounded in return (defense of zero meaning huge damage if you miss, if no friends can help).

*Bypass Armour: called shot variant ignoring some armour worn at expense of a hit penalty (e.g. Shadowrun). (Only applicable where a system use armour variants other than “AC”/armour as target number). Bypassing armour also sometimes occurs as a critical result (Runequest criticals, Earthdawn "armour defeating hits"). Conan D20 has this apply by default for 'finesse fighters' who use Dex to hit.
A variant of this can also be to have a 'find hole in armour' action which is used before another attack. This works better with systems where armour makes a target harder to hit - the time cost replacing a hit penalty. deadEarth has an 'armour bypass' skill - characters with the skill can opt to bypass armour (skipping damage subtract) by adding their attack roll + armour penetration roll vs. 'Improbable' odds (actually not that difficult since since effectively 2x as many dice are rolled).
 
*Backstab: this is sometimes a specific move (AD&D, or may be an extra action that adds a 'sneak attack' bonus. AD&D requires a surprised opponent, while 3E requires an opponent be 'flanked' (have attackers on both sides) or flat-footed (losing Dex mod to AC from either surprise or immobility. 4E streamlined both of these into forms of 'combat advantage'. Backstab can require a specific class feature; it can also apply to anybody as a result of the combat engine - e.g. if to-hit roll success adds to damage, a character automatically does more damage to  enemies if their defense is lowered.  Backstab can require specific weapons i.e. small or 'finesse' weapons (5E D&D); it can give a flat bonus or work as a damage multiplier which favours using large weapons.

*Death Blow: special move to kill (or probably kill) opponent. Move may not exist or may be heavily controlled by a point cost, activation limitation (“Death Blow on a natural 20”), target level (can’t kill opponents greater than level N), or defender saving throw.
 
*Power Attack/Going for Broke: part of a combat action where a character takes a penalty to get a damage bonus; in 3.5 (Power Attack) requires a feat. 5E includes this as 'Great Weapon Master' for big weapons, or with 'Sharpshooter' for ranged. The 5E design essentially rolls together 'Power Attack' and 'Cleave' and is somewhat interesting in that both these effects operate in a complementary way to make sure the feat is largely equally useful in most situations: lots of small opponents bypasses the usefulness of 'extra damage' (if a normal hit would've taken out a foe anyway) but then activates the other 'take down another foe with a bonus action' ability.

In DC Heroes, anyone can use the same mechanic but ‘result points’ include varies forms of effect, not simply damage i.e. spell duration or degree of intimidation could be improved by taking a roll penalty. DC Heroes also the opposite (a plus to hit for less damage) called a “flailing attack”. 4E D&D generates this effect by multiple powers with slight to-hit or damage modifiers (i.e. careful attack for the opposite version). Freerpg Synchronicity uses the mechanic for 'swashbuckling moves' (though IIRC with the penalty applied to a separate roll for swashbuckling rather than the main roll). The same mechanic could possibly also potentially be used to represent e.g. Two Weapon Fighting, with extra damage from the second weapon applying a to-hit penalty.
Pathfinder 2E - in the playtest - apparently has a 'power attack' move where an extra 'action' (from a characters 3 actions/rd) is spent to get an extra damage die, but without any accuracy lost per se - at least, that is the case unless there's another action which could give a to-hit bonus. (The extra action could normally be used for an extra attack, but at a significant penalty).While called power attack still, this actually works very differently.
 
*Knockout/Sap: stuns opponent; effect level or damage may determine how long. This manuever may occasionally be seen designed for story use (capturing the PCs) –but if abusable could also lead to lots of NPCs being laid out and Coup de Grace’d. (also watch out for railroading). In some games may just be a “head” called shot effect.
Low Fantasy Gaming notes unarmed attacks take no extra penalty on knockouts. 2E D&D gave a KO% automatically will unarmed attacks (maybe too good).
 
*Coup de Grace: attack on downed foe. May be automatic or involve increased damage; in systems where damage is increased based on difference between attacker/defender rolls this move isn’t really required (a Defense of 0 automatically increases damage). A coup de grace might automatically kill an opponent, deal increased damage (e.g. in 3.x D&D, an automatic 'critical hit' with a saving throw then required to avoid death, with a badly-scaling damage-based DC), or in games with multiple HP tracks, deliver damage direct to a more critical variety of hit points (e.g. we've used "direct to HP" as a houserule in Palladium previously). A coup de grace might require helplessness, or merely grappling or even just surprise to deliver.
 
*Finishing Move: often a creature dropped to 0 hit points/the death negative threshold for the game may be described as killed in some gruesome way. This is typically just a descriptor, though videogames may hard code a separate manuever that does this (e.g. the Mortal Kombat series), and sometimes a game may include some mechanical benefit e.g. the 'Eviscerator' feat in 3E D&D means  the target is killed so gruesomely that surviving allies are shaken. Conversely a game may have the option to choose between stun/kill at 0 hp.
 
 
Special Attacks
 
*Trick Shot: attempt to do something tricky e.g. bounce an attack off another surface to avoid cover. May also include ‘ranged disarms’.
Apocalypse World has a separate damage rating for 'ricochets' [1-harm], but without much detail on how these are produced (deliberately or accidentally)
 
*Sunder: destroy held object/ other object. Problematic manuever for PCs since it breaks the treasure- still a good ability for monsters. Sometimes treated as a subset of called shot.
D&D 3.x generally allows a Str check to break objects, or can use damage - many other systems just allow damage (in, say, Savage Worlds, there's not a great deal of difference between damage and a Str check - its largely a Wound or nothing). Palladium for example just has SDC for objects (there is no "Strength check" mechanic).  (For comedy value: http://www.herogames.com/forums/topic/84713-granny-versus-a-burglar/ (http://www.herogames.com/forums/topic/84713-granny-versus-a-burglar/)
).
Sunder may be a specific weapon ability covering weapons like sword-breakers (e.g. Tunnels & Trolls 5E)
 
*Disarm: opponent drops a weapon/object held. Larger weapons tend to get a bonus to resist (in AD&D requires 2 successful attempts; 3.x gets +4 per size category different, unfortunately making the Greatsword far better than the rapier for disarming...and the polearm the best, since reach negates the Attack of Opportunity). Location it flies to may be determined randomly (scatter die?) or attacker may be permitted to grab; AD&D yses scatter table but Expert disarm variant lets attacker choose exact location. Sometimes permitted with ranged weapons.
Disarm sometimes occurs to an attacker as a result of a critical parry etc. Dungeon World's 'Class Warfare' has a weird 'Hand of Monkey' ability where an unarmoured character gets '2 armour' against hand-held weapons and if this reduces damage to 0, they are disarmed. This damage-based disarm is interesting in that disarm off gets weapon size or Str modifiers, which this system still preserves despite its simplicity. (also interestingly, there's a wielder 'Vorpal Blade: ignores armour' ability - making the weapon too sharp to be disarmed by the monk!)
Disarm with ranged weapons is most often disallowed, or requires some sort of special ability (cf. 'Trick Shot').

*Suppression Fire -included in e.g. Twilight 2000. 'Midnight at the Well of Souls' had (relatedly) "Opportunity Fire" as a separate action, perhaps in part due to having a move phase occuring before Ranged Fire was resolved - Opportunity Fire acted in the earlier section of the round prior to normal ranged attacks.
Shatterzone handles Suppression Fire as a combination 'interaction' attack (Intimidate roll to terrify targets from moving) + an attack (targets must make a manuever roll against the same number to avoid taking damage). Bughunters 'full auto' rule includes opportunity fire by default (a free attack on anyone moving across the area, see full auto).

*Toss: throwing sand in targets’ eyes or glove in their face, etc. May be application of a “dirty tricks” type skill.
 
*Grab: hold or wrestle a monster. At its simplest this may just be an opposed STR roll, but it can get complicated. (Palladium, not having a Str check rule, frequently has grabbing that has a fixed % chance of working - for example, a tentacle monster like a Vampire Intelligence might have a 40% chance of pinning, or Wrestling pins on an 18-20; both ignore the opponent's Str in resolving the grapple, while the creatures Str is vaguely considered in setting the % in the first case).

3.x D&D distinguishes between ‘grappling’ (struggling hand to hand up close) and ‘pinned’ (one side holds the other), and uses modified opposed attack rolls (based off STR with a special size bonus: monsters typically win due to getting more Str, attack bonus from HD up to twice CR, and the size bonus).
A good criticism here (http://thealexandrian.net/wordpress/1047/roleplaying-games/super-simple-grappling) is that the 3.x grapple system is complex due to inconsistency - some actions are impossible, some actions require a grapple check instead of the normal roll, some actions require a grapple check as well as the normal roll, some actions have specific limitations.
HERO has a grapple subsystem using STR damage rolls (sum of d6 per 5 points) instead of the usual 3d6 roll that's its default subsystem for attribute checks.
The City of Terrors solitaire for Tunnels and Trolls includes an arm wrestle that actually just uses the normal combat rules (both sides rolling unarmed dice + ST, DEX and LK adds -  T&T combat being an opposed roll in any case).
Other systems may include rules for martial art type joint locks/submission holds, or choke holds. Twilight 2000 uses a system of ‘controlling hits’ based off damage (hits equal to opponent Strength subdue them) while other games count successes or coloured results for effect. May include ‘hostage taking’ rules. Movement may be impossible, require a roll, or subtract opponent STR from movement rate (DC Heroes). Usually includes a “squeeze” type option to damage held target. Initiating the grab may deal damage.
Some weapons might also function-call the grapple rules e.g. mancatchers, armour spikes, nets or bolas.
Grabbing may also include rules for turning an opponent's weapon against them; this could also be indirectly referenced by e.g. telekinetic grab rules.
Grabbing can be a problematic mechanic since STR tends to scale very little with level for characters, even though in some cases how much damage a character needs to be killed increases dramatically. Consequently it can become easier to take out a character by grabbing them than by direct damage.
Grabs are generally a bad position for spellcasters, although 4E and 5E D&D both deliberately opt to make this not a problem; even Pathfinder slightly reduces Grapple effects compared to 3.5.
Some systems (3.x D&D, Lejendary Adventures [demon in quickstart adventure] may give monsters a free grab attack as part of a normal claw attack (or whatever) - "Improved Grab". This may be used to land a follow-up attack for free or with a to-hit bonus - the lion holds you down and then claws you. (3.x adds in various monster special abilities to do this since in it a grab doesn't give the attacker any to-hit advantage).
 
*Grab Item: this can be rolled into either Grabbing or Disarm, normally, or be a separate manuever. Dungeon World has a 'take control of an item' option on one move for using force. Faserip (MSH clone) has rules for this which however often end in item breakage (a normal success breaks an item if either parties' Str is higher than the object's material strength). An implication might be that someone could let go an item (give the attacker a free higher result level) rather than have it break, though AFAIK this isn't explicitly spelt out and so frequently the manuever just doesn't do what its supposed to.

*Choke: choking may be an option under the 'grab' manuever, or distinct. Choking may use subdual damage rules, have special effects, or apply fatigue damage (GURPS, IIRC). As with grapple it may be possible with a weapon (garote).
 
*Throw: Judo style throw; may require martial arts training.
 
*Lift/Throw Object:[/FONT]
Lifting things can happen in most any system, but actually throwing them at people tends to be particularly common as a combat option in superhero RPGs.
(http://i1239.photobucket.com/albums/ff507/BSJ17/kroww_zpsxovvbk29.jpg)
(pic from Superbabes RPG)
The 'lift' and 'throw' may be separate manuevers, or just one; DC Heroes as noted under 'shoot' has some of the more detailed rules for actually what you can pick up and how far it goes, although IIRC how the size of the object modifies damage is actually less defined than in Superbabes.

*Attack to off-balance (Superbabes): if successful, opponent is +3 to be hit next round.
 
*Pin Weapon (Clinch) – grab on opponents weapon to hold it in place; user may be able to punch foe with free hand. A two weapon fighter might be able to use this to pin an enemy’s shield in place as well. An Entangle (with a chain weapon) is usually basically the same thing. One old Sorcerer's Apprentice magazine mentions an old viking trick where using a crappy wooden shield lets an opponents' axe get stuck, holding their arm in position for a chop to the wrist- something like a weapon pin using a shield.
 
*Trip (/Unhorse) – knocks opponent to the ground or pulls rider of horse (Ride skill likely to help). May gain bonuses against unaware opponents. May include sweeping e.g. from staff.
Trip in 3E D&D is fairly unpleasant (being prone gives substantial penalties, and also standing up provokes attacks of opportunity) but a character gets a roll to avoid a trip. AD&D 2E includes a bonus to Dex roll if 'unmoving', presumably based on the action a character declared before initiative, whereas 3E has nothing equivalent since 'moving' occurs on an opponents turn rather than continuously, making the modifier largely redundant).
Dragon Age trips automatically with a successful stunt (unless the target is on horseback) but is a very minor debuff (+1 to be hit).
 
*Feint: distract opponent to land extra attack. May allow bonus damage or select hit location (e.g. cutting at head then rapidly at legs).
Zenobia has a particularly odd Feint mechanic:  after winning a combat round a character can opt to save some of their 'combat result' to the next round, where it's lost if the roll fails or becomes extra damage otherwise (damage is actually unchanged on a success as it equals the difference in combat rolls, but a result of 4+ lets a character deal a "Crippling Blow" as well).

*Twisting the blade: fairly Bad Guy trick; typically extra damage but to-hit penalty.
 
*Stand Still:: making an attack (often as an interrupt) to block another character's movement e.g. a 'clothesline' type manuever. Appears more abstractly in 4E D&D (Fighter's Challenge).
 
*Mark:: 4E D&D. Not exactly an attack, this occurs as a rider effect from attacks or other powers, which generally imposes a penalty on a character if they attack someone other than the one currently 'marking' them.

*Shield Push - cf. Bull Rush. A character may be able to push back an opponent using a shield. Shield size may modify the check, and the character might or might not have to move with the attack. May also have a chance of making the target fall over. 3.5 had a feat for this (Shield Slam, a charge effect), while 5E 'Shield Master' (feat) allows a bonus action attempt to shove a target back 5ft. 2E Complete Fighter also had shield push rules, including modifiers to the save based on if the target is moving (if that applied being difficult to work out: one interpretation being that this never applied - since the shield push occurs on the attacker's turn and the defender moves on their turn - although as 2E had a separate action declaration before initiative, the character might be considered 'moving' from the start of the round if that's what they were going to be doing).

Recovery Actions
*Second Wind: the character regains hit points or the like. 4E allows this once/encounter, while FantasyCraft charges action dice for a "Refresh".
 
*Recover – turn spent throwing off a condition. May require some sort of Con roll, etc. (source - JAGS). Treating this as an action may represent a stunlock on a character i.e. if the only action a character can attempt is to try to remove the condition. Savage Worlds lets a character remove a 'shaken' condition as a turn, but with a 'raise' (high roll) letting the character also act normally. (Savage Worlds uses shaken to represent damage as well as effects like intimidation, so 'recover' and 'second wind' are indistinguishable for SW).
"Recover" type actions can become more complicated when designed to remove conditions that reduce number of actions; the manuever has to be written so that a character who has no actions can still attempt it, rather than being locked up indefinitely. A (non-RPG) version of this would be the Ghostbusters boardgame; slimed characters suffer -1 action, a character can remove a 'slimed' token as long as they do no others that turn, but without it counting as an 'action', so that a character totally stunlocked by slime can deslime.

 
*Reload: replacing ammo in crossbow or firearm for additional use. Some systems e.g. Twilight 2000 distinguish reload types by weapons in considerable detail.
 
*Ready Weapon: an action may sometimes be needed to 'ready' a weapon after use (particularly for larger weapons). In 2E D&D (Complete Fighter), a disarm vs. a two-handed weapon caused the target to lose initiative as noted above; a character with multiple attacks could spend one to cancel the initiative penalty next round, or might be reduced to just attempting a punch with their other attack.
'Irregulars (http://www.therpgsite.com/showthread.php?t=33182)' has a 'controlling pause' simple action that cancels recoil penalties on a weapon for the next action. It notes this is 'not actually an action'; any other action (except shooting again with the same weapon) can be performed simultaneously, the important thing being that two shots/bursts not be fired in immediate succession to avoid recoil.
 
*Orientation Roll - MERP has rules for 'orientation rolls' following confusing actions such as a teleport, dive, fall or knockdown. This uses the Moving Manuever table and is modified for Perception, with the result determining how much action is allowed next round (% activity or any bonus reductions).

Standing Up could also perhaps be classed in this group, as well as in Movement.
 
Super Powers etc. type actions

*Use Power - character uses a power.  Individual powers may have different action times, etc.

*Power Stunt: by which I mean, using a power in an unorthodox fashion. Distinct from Pushing (where just the numerical value increases), a 'power stunt' is qualitatively different, an unusual use of a power. See notes under Powers. Games with rules for this include HERO (may cost XP, tricky due to being effects-based), Icons (requiring a power roll against its own rating), Marvel Super Heroes. Power stunts are pretty useful, particularly when used in rarely arising situations - like spiderman using his webs to save another falling character (which probably won't happen often), rather than just a damage-dealing use.

*Recharge Power: some powers may be 'on' without an additional action cost, but then need an action to use again in combat. An example of this would be the 3.5 soulknife's "Psychic Strike" power [move action to recover]. 3.5 psionics also often had powers that used 'psionic focus', recovery of which could be sped up with other character options.
 
*Deactivate Power: some powers don't need to be turned 'on', but it may be useful to turn them off in some circumstances. 3.x D&D for instance notes that it is a standard action to lower 'spell resistance', in order to receive a beneficial spell. Aberrant has a specific 'dormancy' background which lets a character turn off all a characters powers so they can pretend to be human; conversely powers can be made involuntarily continuous as a taint effect (at Taint 8).

*Cast a spell - using a spell may be a skill roll or could be an automatic class power.
Often casting a spell leaves a character's defense reduced during. (Hackmaster -later version - is interesting in having "spell fatigue" that reduces defense for several segments after the spell, too). See also 'magic' posts.
Using offensive spells often involves an attack roll, despite this spellcasting is usually a distinct action which has its own action time rules e.g. in 5E D&D, 'Extra Attack' wouldn't allow extra attacks with cantrips.
It would be fairly common for the design intention to be that a character make more weapon attacks than spell attacks in a round (some games would let a character make multiple attacks or only 1 spell). In the worst case where both cost '1 action' however, weapon attacks fairly often run into circumstantial problems that can make spells operate faster - drawing a weapon and/or moving might require an action.

*Cast half-action spell (i.e. 2 spells): A spellcaster might be a able to cast 2 spells if those are 'specific' spells. In Dragon Warriors, warlocks get a limited list of spells marked with an * that they can cast two of in the same round, letting them 'power up' faster than other professions, typically 'buff' type spells e.g. darkvision, ignore pain, stat enhancement (perhaps handy for warlocks since their spells have short durations - d20 spell expiry - meaning buffs are less likely to continue running between combats).
D&D 5E lets characters use a spell that's a 'bonus action' but if so, the other spell can only be a cantrip.

*Concentrate on spell - a 'move action' in 3E D&D, or minor action in 4th. In Savage Worlds IIRC concentrating provokes a multi-action penalty on further spellcasting rolls.


Player Actions
*Stunting bonus for description: WUSHU, Exalted. This covers many of the others but is designed from a different perspective. In these games doing difficult/cool things gives characters a description bonus, rather than a penalty; contrast to most systems where doing something tricky probably gives a penalty in exchange for doing something more cool when it succeeds, unless its a particularly appropriate situational thing that warrants a bonus. Stunting is a mechanic that encourages players to do wacky things, rather than a simulational mechanic. In a similar vein, Feng Shui gives characters +1 to hit with shot guns if they make a shotgun loading noise (ka-chick ?).
(cf. stunt as a bonus vs. older-school systems where a "stunt" is a player attempting an action that's mostly outside the known system, requiring DM judgment calls to function).
Stunting encourages players to imagine 'cool' ways they're doing things (which gets a bonus), but not to radically change what they're doing in ways that could change the mechanic being invoked and so accidentally give a penalty. It works better in fairly abstract systems with a few, broadly-defined combat moves.
 
*Use Safety Valve: this is usually not an action in-character as well, but sometimes is e.g. D&D 3.5 complete scoundrel, spending a “luck reroll” counts as an immediate action.
 
*Narrative Editing:
Could be thought of a sort of 'use safety valve' as generally some sort of resource cost is involved.
Cortex+ has 'create asset' as an action, requiring a plot point and adding an extra die. Picking up something to use as a club might count as a create action (if worth an extra die), or it could include having gadgets (related to a characters skills), contacts, etc.

*Argue with the GM: perhaps the slowest combat action of them all. I've included as a player action since if successful it does have an effect on the game, unlike most other IRL player actions (like eating pizza or telling Monty Python jokes).

*Soaking (Savage Worlds): soak in SW burns a "bennie" and so is a subset of using safety valve, really. The damage result changes, but there isn't particularly a clear way of explaining in-character why damage went down. In most systems with soaking, the soak roll is free and perhaps represents how tough the character is, although its unclear what the random factor the dice roll represents. It is also perhaps uncertain why Vigour is the stat used for the roll (since that already factors into Toughness), except that this 'steps up' the effect of the Vigour attribute which has only a slight effect on the [quite variable] damage roll. A roll is used because the designer's didn't like how in their preceding design for Deadlands, characters could automatically not be threatened by damage (from SW's design notes).
 
*Heroic Sacrifice (Icons): An Icons hero can opt to pass on using Determination (safety valve luck points) from a team pool to recover, choosing to remain defeated, which adds an additional Determination point to the pool by "inspiring the rest of the team with his or her sacrifice".

Miscellaneous
 
*Presence Attack/Intimidate/Taunt – turn used to overawe, intimidate or distract foe; may gain initiative, apply attack penalty to foe.
 
*Talk!: (Edited in 6/11/2014, and I can't believe I've missed adding this one as long as I have).  Generally talking is something that isn't covered much by the rules. 3.5 D&D specifies that its a free action that can be performed even when its not your turn (an addition from 3.0) and also mentions it may be disallowed when surprised (so players can kill sentries and such). Excessive talking aka Diplomacy is a full-round action (if done at a -10 penalty)..oddly a character can't move while using Diplomacy by RAW. (Meanwhile, Charm Person is a standard action).
Talking rules may be covered by more complex 'social combat' systems. Dr Who: Adventures in Time and Space has social combat occur in a phase before the physical combat phase (to encourage diplomacy winning the day as in the source material). Exalted has various social charms which however can, reportedly, often be thwarted by just entering combat (encouraging "do not listen to the witch, she lies!" type occurences. Dogs in the Vineyard is designed to begin with talking, then escalate into physical violence (the same combat but adding a bucket more dice into the conflict). [/FONT]

*Spot: roll to notice something untoward – may have separate rules for deliberate spotting vs. reactive.
 
*"Grope": (HarnMaster) this action in HM covers situations like recovering a dropped weapon while attacked or perhaps pulling an impaled weapon out of a foe; uses a Dex check.
 
*Pushing: attempt to briefly increase an attribute -or a super power rating - for a specific effect, such as lifting a weight or running or flying faster/jumping further than normal. Rarely found (usually in supers games e.g. DC Heroes). It often applies to generally diceless actions, and generally use of it implies some sort of attribute-based 'effect' system, a follow-up roll boosted by the pushed score (incompatible with pushing giving a multi-tasking penalty), or at least an ad-hoc ability threshold to perform some action (e.g. 'you need Str 13+ to wield a bastard sword). May require dice roll and/or expenditure of luck points or fatigue points. Uses an Athletics check in FantasyCraft. A variant is also seen in Masterbook.
'Pushing' mechanics could also be used as an umbrella that can cover a number of other situations/combat moves, if the rules are sufficiently integrated. For example, it could be used to handle using a too-heavy weapon (multiaction penalties then apply to weapon use, or a character just has fewer attacks due to action costs), to initiative i.e. going faster then giving a to-hit penalty (if initiative uses the same mechanic as other actions), to movement (i.e. running might be simply a result of spending an action to Push movement).
DC Heroes, while one of few games with this, had particular problems with it due to the logarithmic nature of character stats - the 2E DC Heroes review in Dragon #165 reported that a good die roll in 1E would let Batman lift a DC-9 airplane, though this was fixed.
"Safety valve" mechanics, such as Willpower expenditure in Storyteller, can sometimes fill a similar role.
If pushing requires a roll it is perhaps opposite to 'taking 10', with more effect in exchange for a chance of failure.

*Instinctive Attack: [Runequest] this is a roll by the target under [Con x 1%], to determine if they can continue fighting 'instinctively' after a head shot that should knock them out. (Perhaps not a true 'manuever' but I don't know where else to put this).
 
*Use Casual STR (HERO): the character can use their STR at 1/2 value quickly (zero phase action).
Other attributes are also occasionally used 'casually' e.g. to represent passive use.

*Perform Automatic Action: carry out a minor task that doesn't require a dice roll. In some circumstances automatic actions might become 'dice' actions; Shadowrun 1E for instance gives +1 to Target Numbers if a character is in combat (per opponent), with automatic actions now requiring Quickness rolls against TN 4.
Automatic actions may or may not be 'free' depending on system.
(DC Heroes is one of the more defined systems here, giving one automatic action + one dice action each round).
Perhaps this is a category of actions rather than a specific action.
Automatic actions might belong to a fixed list of 'minor' actions, or what's automatic might vary from character-to-character (e.g. compare 3E D&D's "Take 10" rules; see the "cutting down excess rolling" post).

*Drink Potion: a typical D&D action. The potion drinking may also need to be paired with an action to retrieve the object (e.g. in 3E D&D, which also has 'potion belts' in Forgotten Realms at least, to get rid of the retrieve action).
Time required to drink a potion is sometimes noted to increase e.g. for dying characters (full round action to administer without them choking) or in weightless conditions (Dragon #71 notes it takes 1-4 rounds on the Astral Plane).

*Rage - getting angry for combat bonuses. D&D treats this as a barbarian class feature with a fiddly list of bonuses, useable several times/day at player discretion (with the understanding you 'rage' anytime you want your bonuses). Dragon Warriors likewise has a barbarian class feature, letting characters shift points from Defense into Attack.Gamma World 4E has combat modifiers for rage, but applied at GM discretion when appropriate for the character to be angry. In Star Wars D6 a character may be able to get angrier permanently (Dark side points) in exchange for force points. In oWoD Werewolf all characters have Rage points, operating as a secondary safety valve.

*Situational special stunts ["Improvise Action"]: many systems let characters improvise special moves based on situation, whether swinging on chandeliers or throwing sand in eyes or whatnot (whether something is improvised depends a lot on what options are already covered in the system).  Interesting things here are the stunt systems in D&D 4E ("page 42" in the DMG and its list of guidelines, giving options generally comparable to use of an at-will power) or Feng Shui (which similarly sets penalties based on game mechanics, distinct from in-world description - see page 3 post on effect). This option tends to be poorer for higher-level characters, whose normal fighting, spellcasting, etc. functions are all powered up to heck -4E's system being a good start here (auto-scaled damage at least) but still not enough, and with the idea of special stunts working at cross-purposes to the general design where single rolls are not deadly and most defenses/bonuses scale automatically. Improvise action is less discouraged if increased abilities happen to synergise with whatever the insane plan happens to be.
If other combat actions aren't detailed in depth (old school games), this could end up as a pretty commonly-used maneuver, encompassing e.g. grabs or disarms. Games with incomplete/nontransparent rules could incentivize improvising by making how well it works largely unknown to be player (perhaps even obscuring normal attack's effectiveness as much as possible - AC, monster special abilities, etc.). This option also starts looking particularly good in combat after several rounds of getting nowhere the conventional way.

'Low Fantasy Gaming' is another game that has an action like this - there's a generic "Exploit" action that lets a character do more or less anything - grabs, blinding with a cut over an eye, throwing sand, disarming - with an extra ability check to see if this works. A 'minor' exploit suffers no hit penalties etc. and does normal damage, but once an exploit is failed no further attempts can be made against a target.

Dungeon World has a "Pull a Stunt" manuever that is also similar - options e.g. putting yourself in a position, negate opponent's advantage, taking control of something. Compare to: 'Create Advantage' (FATE, under Cooperative Actions), 'Gain Advantage' (Twisting Tunnels, under Damage Modifying), and "Stunting Bonus for Description" (Exalted, this post).

*Don/Remove armour [components] - usually requires multiple rounds. Time required may vary by armour, or be modifiable by assistance (2E) or item add-ons (3E 'quick release straps', or the Calling magic enhancement).

*Find A Thing:: (doesn't exactly belong in combat but IDK where else to put it). Action to "pull out" a useful objects. Dragonlance Adventures has a 'kender pockets' table, where a kender can attempt to pull out a random object (off a table maintained by the GM for that purpose, starting based off a generic list in the book). Night's Black Agent's reportedly has a "Preparedness" skill, which at higher levels allows a character to declare (retroactively) that they have something useful for the situation; (my Complete 2E AD&D rebuild (http://www.therpgsite.com/showthread.php?t=33014) has something similar as a kit ability for the 'Scavenger', giving them kender pockets but resolved with a Foraging NWP check). (This is also mentioned in the later 'abstraction' post).

*"Mental Default" - Fireborn allows various mental actions (1 per round) as well as various physical. Skipping any other 'mental' action lets a character get a free reroll on a physical action.

*Distract [Chill]- Chill lets' player characters attempt to 'distract' monsters, which lets them make a surprise check; however, this makes characters lose a Luck point permanently which can't be recovered and what they're doing has to be described and allowed by the GM.

*Other minor: A few other misc. very specific manuevers include hammering the opponent into the ground like a nail (Superbabes), pulling an opponent into a punch (combination grab/punch dealing two-handed damage/double damage?(Superbabes), the fastball special (character A throws character B at an opponent; HERO), mount (getting atop grabbed opponent; JAGS), breakfall (Ninjas & Superspies), Beat/Expulsion (briefly slam opponent weapon out of the way; Riddle of Steel – one variant here is attacker and the other defender), half-sword (grasp blade to reduce weapon length; Riddle of Steel; Stop Short - stopping movement quickly to trick opponent (Riddle of Steel), Finesse Throw (LegendQuest- throw using Dex but without adding Str mod to damage, and range halved). A thread here (http://forum.rpg.net/showthread.php?688393-ACKS-B-X-Shields-and-cloaks) discusses a 'grab shield' manuever (spinning a strapped shield with the resulting force breaking the defender's arm). Shadowrun also has a few matrix-combat related combat actions.

recent edits: improvised action section expanded

This last post for combat (unless I think of anything else) is just a grab bag of things I've not yet mentioned. If there's anything ppl feel I've neglected, feel free to make suggestions.

Poison: may inflict either damage, ability damage, or some weird effect. Traditional D&D had poison nearly always causing death (with a save to negate). Tunnels and Trolls gives poisons a damage multiplier (on weapon damage) rather than fixed damage i.e. curare x2, dragon’s venom x4 (which can generate huge amounts of damage; older T&T added in poison before comparing sides' attack totals so it could also help to hit). Dungeon Worlds' 'class warfare' has a 'Serpents' Tears' poison that lets damage be rolled twice (take highest) though this makes less sense (a scratch should deliver less poison). Freerpg "Dark Passages" by David Johansen gives poison damage 'per level' (to offset D&D-style hit points), and also doesn't give a level bonus to saves, so its equally deadly regardless of level.
Poison may be just an item that's purchaseable, or be a class feature or skill.
Most systems categorize poison as Ingested/Injected/Contact/Inhaled (or something like that). RPGs often have unrealistic onset times for convenience's sake. Elaborations: LegendQuest has a dosage table which lists # doses require to coat a weapon of a given size (from 1 unit for a arrow head, to 3 for a knife, 4 for a ballista bolt or hand axe or 8 for a long sword); extra doses increase the # hits that are effectively poisoned as well i.e. the longsword is poisoned for the next 8 swings.
Many systems allow for a chance of self-poisoning e.g. on weapons fumbles. Some fantasy settings inflict social controls on use of poison (e.g. the death penalty in 1e AD&D, as well as class and alignment restrictions on their use).
Where poisons are all-or-nothing (e.g. auto-death or save-or-die) then defenses against them likewise are usually complete - if you get a resistance to poison its usually "total immunity". Poison that's more complex mechanically has more scope for target number modifiers, damage reductions, etc.


Mass Combat: a few systems include a mass combat system for quickly resolving large numbers of enemies e.g. Basic D&D’s War Machine rules, or the system in “Under the Moons of Zoon”.
If abstract such games may give an army damage based off its size (# troops) and perhaps a random variable with a leader strategy modifier and resolve over a number of rounds, or a really abstract method might just be a few random rolls on tables to determine victory/defeat (e.g. in the Central Casting character background generator books). At the very detailed level, figures may represent “squads” and be played out with something like 3.0 D&D’s Complete Miniatures’ Handbook rules, or the wargame of your choice.  
People have also suggested using the Swarm rules for things like e.g. Orcs in 3.x/4E D&D.
Savage Worlds again is designed for handling large numbers of creatures as part of its regular combat system (monsters are “up, down [shaken], or off the table”), and multiple checks for large numbers of NPCs can be rolled easily e.g. 10 guys shooting arrows might have Shooting d6 each, and so 10d6 can be rolled to find hits – handy for something like pirate ship battles). SW does have the slight problem that as damage is compared against a threshold each time, instead of being subtracted, each damage roll has to be made individually.

Tunnels and Trolls or (I believe) “Forward – to Adventure!” use side-by-side battle systems and so also can resolve large combats fairly quickly.

Using the normal combat procedures for some games, multiple rolls of e.g. d20 can theoretically be streamlined using tables: Dragon Magazine #113 includes a fast-rolling table for D&D hit rolls/saves, where a single d100 roll generates the equivalent number of hits/misses as rolling 20d20 at a given target number. However, this can’t easily determine # of crits/fumbles, only hits/misses.

Other Alternative Combat Systems: a couple of games have optional 'advanced combat' systems which are used for major fights, as well as standard combat rules.
GURPS has various optional books which the GM can use as necessary.
Riddle of Steel has separate Duelling rules IIRC. 2nd Ed. AD&D also had optional 'duelling' rules in a sourcebook, as well as the GM being able to switch between side-based and individual initiative as desired.
Other games may have the option to use miniatures or not, although minis are something more likely to be useful in large-scale battles (lots of mooks), meaning they're not necessarily useful in 'climactic' encounters (not vs. single BBEGs, unless they also have lots of mooks).

Combat Event Rolls: this was an obscure mechanic from Combat & Tactics in 2nd Ed. D&D. The GM would roll on a table each round, which would generate a number of unusual combat results including the battle moving a number of squares in a given
direction, an armour strap breaking, or a weapon getting stuck in a fallen opponent (if applicable).


Surprise: World of Synnibarr has tables for surprise with multiple types of surprise (AA,A,B, C - invisible ambush, invisible, ambush, and sucker punch). Shatterzone has 'partial surprise' (where a character can make defensive actions only) and full surprise (character is useless).
The Fantasy Trip either gives a full free turn or for 'lesser surprise' just gives an automatic win of initiative (for somewhat alert targets).
AD&D allows an attack for each segment of surprise (assuming every blow counts, unlike in its usual minute-long round).

Arenas : "Red Box Hack" has an interesting method of categorizing areas - different "arenas" give a bonus to different weapons or actions e.g. Hazardous (reach weapons), Open (ranged weapons), Tight (light weapons), Dense (heavy weapons) or Neutral (no bonus).

Character capabilities determine whether terrain hazards are a significant threat. These abilities can include: direction finding, ability to forage/hunt food, ability to carry equipment, resistance to environmental extremes (heat or cold), disease or other problems. (Of course, its not necessary for terrain to be a major hassle, particularly in a high powered game).
Spells and specific character abilities that negate terrain as a game challenge include: Teleport (bypasses hazards), flight (same), energy resistance (heat or cold), not needing to eat/drink (e.g. spells such as create water were nerfed on Dark Sun for this reason), unlimited carrying capacity (via bags of holding or vehicles), and skills preventing characters getting lost, and even ability to produce fire magically. Note also:
 
*Fantasy or SF games may have racial options which give more-or-less immunity to some hazards (and/or susceptibility to others); something to think about when balancing these.
 
*Environmental damage is less significant where characters have large reserves of HPs; occasionally systems with level-based HPs have ended up assigning damage to hot/cold conditions that should result in massive depopulation of certain zones. (IIRC, 3.x D&D cold rules would kill most of the population of Finland fairly quickly). Difficulty of rolls to avoid damage or find food will vary depending on the core mechanics of the system (again in 3.x, it may be easy to take-10 and find food or water easily, largely regardless of terrain conditions).
 
*Energy resistance as “damage reduction” is particularly powerful dealing with heat/cold effects. This may be acceptable, but if the effect is excessive note that frostburn treated as a large lump sum of damage infrequently (say, each 10 minutes or hourly) is less affected by this sort of energy resistance than small amounts of round-by-round damage (unless there’s some sort of “minimum successful damage is at least 1” rule). As with armour, energy resistance may also be treated as a chance of resisting an attack/armour bypass, albeit that this has odd effects in other parts of the game (e.g. fire resistance 75% seen in at least one game I can think of [World of Synnibarr]: “3 of those missiles did nothing, but that fourth one was a bitch”!), or even a proportional energy resistance (mechanically annoying, unless you’re doing this by varying target numbers on a dice pool i.e. reducing damage by 70% would mean rolling d10 for each point of base damage, a 4+ negating it ; though if soaking also applies separately, that will operate synergistically and breaks the proportionality).
'Dark Fantasy' gives fires an 'ignition class' determining damage per round, then sets damage from hits and chance of catching fire to 1/4 due to briefness of contact. [something it doesn't consider but that's perhaps raised as a question, is that this is true for e.g. a flaming swords, but a flaming arrow would remain embedded].

*Foraging systems tend to be more detailed in systems where characters are actually likely to starve to death (Interestingly for D&D, while Ranger is popular as a class choice in later 3.x/4E D&D, the wilderness aspect of the concept becomes less important across editions). HarnMaster has extremely detailed Fishing charts (including exact Fish species caught for either fresh or salt water!), as well as foraging rules; it cross-references skill result by expected conditions on a table to determine food found rather than just applying a bonus/penalty to the check, thus reducing food found more severely for harsh terrain; Cadillacs and Dinosaurs lists food availability by terrain type (including heavy seasonal adjustments) as well as detailing the exact amount of meat provided by deceased dinosaurs in their monster descriptions.
 
*In games where characters use vehicles alot (whether modern or SF) miring, mechanical breakdowns, fuel concerns and the like for those can also be critical, as well as the usual food/environment concerns. Of course, certain terrain types may be impassable to some mounts or vehicles e.g. mountains or heavy jungle; others may just slow movement rate.
Cadillacs & Dinosaurs again is one of the better treatments of vehicle-based hex crawling of this sort I have seen , including lists of random encounters based on hex type (jungle, mountains, etc) which directly plug in both monster encounters, NPC encounters and terrain hazards that are detailed e.g. rock slides, volcanic eruptions, earth tremors, earthquakes, subterranean gas, and storms (for those boating adventurers). While alot of other games have rules for similar hazards it succeeded fairly well (IMHO) at bringing those rules forward and making them a focus of the game.
 
*a number of SF games detail various interesting environments (Traveller?GURPS probably has a few sourcebooks for this too...) – dangerous conditions in such games could include more severe temperatures, high/low gravity, toxic or corrosive atmospheres (or suffocants e.g. Argon in StarCluster supplement Sweet Chariot) , atmospheric pressure/vacuum, radiation, and microbes, as well as the usual hostile organisms. Note some games (e.g. Aberrant) give characters massive freezing damage for exposure to space, incorrect as vacuum is actually an excellent insulator, (cf. thermos flasks). http://tvtropes.org/pmwiki/pmwiki.php/Main/SpaceIsCold (http://tvtropes.org/pmwiki/pmwiki.php/Main/SpaceIsCold)

Quote from: Bloody Stupid Johnson;498457
*a number of SF games detail various interesting environments (Traveller?GURPS probably has a few sourcebooks for this too...) – dangerous conditions in such games could include more severe temperatures, high/low gravity, toxic or corrosive atmospheres (or suffocants e.g. Argon in StarCluster supplement Sweet Chariot) , atmospheric pressure/vacuum, radiation, and microbes, as well as the usual hostile organisms. Note some games (e.g. Aberrant) give characters massive freezing damage for exposure to space, incorrect as vacuum is actually an excellent insulator, (cf. thermos flasks). http://tvtropes.org/pmwiki/pmwiki.php/Main/SpaceIsCold (http://tvtropes.org/pmwiki/pmwiki.php/Main/SpaceIsCold)

Actually, argon is not a suffocant on Chariot, any more than nitrogen is in Earth's atmosphere. It's a noble gas, and non-reactive, but under high pressure becomes an intoxicant and a poison, like nitrogen - cf. rapture of the deep, nitrogen narcosis - the victim gets both drunk and poisoned. That pressure (4 atmospheres) is reached at approximately 2 kilometers above sea level on Chariot, so normal mammal life is only found at higher elevations.

Also, Sweet Chariot is not a supplement for StarCluster 2, but a full game, using the StarPool dice pool mechanic rather than the percentiles used in StarCluster 2. :D

-clash

Quote from: flyingmice;498479Actually, argon is not a suffocant on Chariot, any more than nitrogen is in Earth's atmosphere. It's a noble gas, and non-reactive, but under high pressure becomes an intoxicant and a poison, like nitrogen - cf. rapture of the deep, nitrogen narcosis - the victim gets both drunk and poisoned. That pressure (4 atmospheres) is reached at approximately 2 kilometers above sea level on Chariot, so normal mammal life is only found at higher elevations.
 
Also, Sweet Chariot is not a supplement for StarCluster 2, but a full game, using the StarPool dice pool mechanic rather than the percentiles used in StarCluster 2. :D
 
-clash

Whoops! OK, thanks Clash, cheers.

Quote from: Bloody Stupid Johnson;498630Whoops! OK, thanks Clash, cheers.

No problemo! You're doing a great job so far! :D

-clash

Sweet Chariot came about because of random tables. Unlike StarCluster 3, first and second edition came with a setting. I generated that setting using tables I created for the purpose then threw away - I created entirely new ones for SC 3. Chariot was the first world in the first system I created, and for years the specter of how a billion people lived on a planet with poisonous atmosphere and too much solar radiation with only steam-level technology bothered the HELL out of me. Sweet Chariot was the result of Albert Bailey and I brainstorming some workable way for that to have happened, and what it all entailed. In the process it became a very fun - and risky - place to game.

-clash

Thanks Clash :)
 
Thought it warranted a mention as one of the more interesting SF planets I've seen. I hadn't known the background, more proof of what they say about how randomly-rolled things that seem contradictory can be the most awesome I guess.

Quote from: Bloody Stupid Johnson;498722Thanks Clash :)
 
Thought it warranted a mention as one of the more interesting SF planets I've seen. I hadn't known the background, more proof of what they say about how randomly-rolled things that seem contradictory can be the most awesome I guess.

Thank you very much for mentioning it! :D

-clash

NP...anyway on to vehicles...
 
(http://i1239.photobucket.com/albums/ff507/BSJ17/smallboat-1.jpg)
 
Above: Cadillacs & Dinosaurs vehicle card
 
 
 
Vehicles rules are critical in SF games where PCs are going to do battle in spaceships, and very handy in shipboard games. Mecha battle games (MechWarrior, Junk, Mekton Zeta, Robotech) have particularly detailed vehicle rules as well.
Other game rules that interlock with the Vehicles rules include Size, Gadgetry, movement rules/chase rules, cover (to passengers), and hit location (ships frequently get their own malfunction tables to determine e.g. if the bridge catches on fire or the crew on C Deck goes and sucks space – often even in games without hit location systems for characters). Important combat manuevers include Trample/Overrun and ramming.
 
Approaches to Vehicles: Vehicles rules at the simple level can include just a few sample vehicles with a cost for each and maybe some very basic data (the GM may be left to wing it on the details, as often as not); More complex rulesets may attempt to actually give rules to let players create their own vehicles, much more ambitious. Cost for vehicles is sometimes in game cash (credits or gold pieces) – though sometimes a vehicle instead has some sort of associated “character point cost” /counts as an advantage etc.
Some examples here to consider the sort of different approaches:
 
*Teenage Mutant Ninja Turtles has a perhaps surprisingly detailed DIY vehicle systems: these tend to be added to across sourcebooks with specifics added as appropriate (one has road vehicles, others space travel or time travel, etc). There are large price lists for common features, with prices arrived at by the designer either using real world costs or in an ad hoc fashion (a mixture, but I’m not entirely sure which). Here for example a PC might pay the price of a basic car or motorcycle (which gives them basic stats), then a cost to upgrade the electrics and add armour, weapons, radios, etc.
 
*the infamous GURPS Vehicles (we’ve all seen the motivational poster (http://i1239.photobucket.com/albums/ff507/BSJ17/gurpsvehicles.jpg)?) Calculus isn’t actually required, but it does go as far as using cubes/cube roots of volumes in some places. The entire design process is an abstraction of an engineering task, where a vehicle is built from scratch (instead of starting with a car or motorcycle or boat, as in TMNT you buy everything individually including wings, wheels, hulls, and turrets). “subassemblies” and other components are selected, volumes and weights are determined, and so on. (as in the real world, the cash cost of everything is determined near the end, where you go back and figure out you can’t afford to build the thing in the first place). Size modifiers and hit points are determined at the end from the total volume. It is a more flexible approach than TMNT, but more involved; the system is also very detailed e.g. gives you the costs of everything you might want from electrified rails to “contra-gravity generators”. The degree of detail in costing is a little odd given that Wealth level itself is quite abstractly determined by spending points, but this sort of cost system does perhaps help with setting questions like “how many aircraft carriers can Government X afford?”
 
*a power-based approach, as in DC Heroes or HERO. In these a vehicle is just an example of the gadgetry rules, which themselves use the powers systems. An item has a cost in character points, and is sort of built like a character (though it won't have the full range of attributes). In DC Heroes, every gadget at least has the Body (hit points) attribute, and a vehicle will also have either a DEX or some sort of propulsion Power, such as Flight or Running; custom items will cost points either paid initially to get the Gadget advantage, or by the creator during the building process if built during a game. Hit points and exact abilities are determined by specific advantages/disadvantages given to powers and how they are “skinned” as regards fluff.
 
Impact on Character Generation: In many games, characters may have the option to get driving/piloting skills of some sort – depending on how much focus of the game is on this, Pilot may itself be viable as a major archetype/class, or a few skills of this kind may just round out a character who is already something else in concept, like a super-spy or warrior. Shadowrun 1E has ‘ Rigger’ as a separate archetype but (realizing that what they do tends to occur separately to other PCs or be downplayed) eventually merged it with Decker. D&D 3.5 has various “charioteering” feats – which were not really worth picking up for PCs, but were possibly of interest to the GM if they wanted Gladiator-style drive-by scythings in their D&D arena game. The old Robotech game by Palladium, being largely about giant robots blowing up other giant robots, has specific classes for different vehicles, e.g. Veritech pilot or Destroid Pilot.
 
Other Notes
*Attribute sets for vehicles: Marvel Super Heroes limited vehicles to three stats: Control, Speed, and Body. DC Heroes builds as noted lets characters build whatever attributes or powers they feel like into Gadgets. Mecha games may provide a bonus or multiplier to the user’s own STR, or have an intrinsic STR score. Some games may have a percentage or other value for ‘reliability’ as a unique vehicle trait e.g. 2nd Ed. AD&D gives ships a “seaworthiness” rating, rolled to avoid sinking. Star Wars SAGA, IIRC, gives vehicles the same attributes as characters including e.g. Strength, Dex and Con.
 
*Damage and Scale: vehicles may use a larger scale of hit points than characters. Spelljammer (AD&D 2nd Ed) has “ship points” (1 SP = 10 HPs), while Palladium has Mega Damage (1 MDC = 100 SDC). West End Games Star Wars had, IIRC, 3 different scales for damage, IIRC, from personal to small vehicles to larger ships like the kilometres-long Super Star Destroyers. Metascape: Guild Space uses several scales. Savage Worlds has "heavy armour" - a heavily armoured thing (with this tag) can only be damaged by a "heavy weapon";  heavy weapons don't inherently do any extra damage to other objects though most will be rated fairly highly. The tag just prevents tanks being accidentally obliterated by crazy damage roll-ups from handguns or the like.
 
*Mounts in FRPGs are somewhat similar to vehicles in some ways, though they have statistics more like those of monsters, and may even level up automatically with characters to stay relevant.
 
Interesting ideas from other systems: Ork vehicles in the Warhammer 40K wargame used miniature vehicles for combats. In the older rules unlike other factions as many extra ork figures could be piled on as the player wanted, but any figures falling off were killed.

Falling: one of the more interesting methods for this is to base damage on the falling person or objects size; handy since big things usually have lots of HPs (you probably want a crashing shuttle to actually be totalled rather than scratched by 20d6 damage). While I'd normally feel damage proportional to size to be fine at least in a fantasy game, IRL the square-cube law (double the height = 8x the mass) means larger objects actually suffer worse from falling; compare effects of a 10ft fall on a flea and an elephant. ‘The Mutant Epoch’ was a recent game that allowed for this. Mechanics around this sort of thing typically become easier with a “Size score” for characters/objects, though Epoch used a table.
SF games may need to allow for differences in falling damage based on planet gravity. Detailed systems sometimes add modifiers for landing surface e.g “deep water” or “mud”, “snow” etc. (HarnMaster). Rolemaster used a table to determine falling damage, in keeping with how weapon damage also requires a table (RM falling damage is relatively dangerous due to speed with which bonus increased and inability to add most defensive bonuses).
Characters may sometimes have options to reduce falling damage: Palladium has a 'roll with Punch/Fall' combat move, while other games e.g. 3.x D&D let characters make Jump checks to mitigate damage.

Interesting note on increasing falling damage in Pathfinder 2.0 (PF having similar falling damage 2E/3E, but more hit points) and dungeon design:

QuoteBulmahn:- "I messed that up in the podcast, having misread the sentence in the rulebook. To be clear here folks, we are not going for super realistic physics here. This is an RPG after all, but it would be nice not to have to have pits in dungeons that are 50 feet deep just to deal reasonable damage to a character (it always messed up dungeon floor plans.. where are those pits going down into the level below).

Lifting Objects: depending on system this may be a totally fixed roll (i.e. STR x 10), a base from STR increased by some sort of Willpower roll (Storyteller adds Willpower successes, or possibly a STR check modified by another STR check (mostly I find this weird, though I suppose it makes a Strength scale slightly more exponential, or something). Depending on outcome a roll may be an effect-type roll (roll anytime you lift something, roll determines amount lifted; compare that to the weight) or in simpler systems weight determines check modifiers to a simple check e.g. HarnMaster will make a character roll under from [End x 1] to [End x 5] depending on how heavy a load is.
Some systems may apply separate adjustments for base Strength and Size to lifting objects e.g. 3.x D&D; Shadowrun 4E has an automatic base lift of [STRx15] then rolls [Str+Body] dice for extra successes (worth 15 kg each), giving a weird result that the variable only is affected by Body.
Skills rarely improve lifting (the Trinity and Aberrant games by White Wolf, for example, uses a dice pool of [Strength+ Might skill]; this replaced a more complicated system in e.g. Werewolf IIRC where base STR + Willpower successes were used on a table, complicated by Willpower having a 1-10 rather than 1-5 range but needing a lower weighting than STR. In the Str+Might system, Willpower could still influence this but only indirectly (as on all rolls), by spending a Willpower point.
 
Note that lifting capacity is proportional to muscle cross-section and roughly increases as the square of height, though realistically using this, giants aren’t going to be able to stand up (weight increases at the cube of height).
Another designer friend of mine who was once something of a body building enthusiast, once built a complex derived system for Strength; a character determined a final Strength using a base value from the square of their height, a Muscle score which reflected how much working out they had done (never rolled against directly, aside from 'bodybuilding contests'), and a separately purchased 'build' multiplier, which were all multiplied together to get a final strength.
 
Older D&D sometimes used a combined Strength total to shift an object ('30 or more to move the slab') which was unfortunately out of kilter with the exponential scaling of the attribute, and meant a titan (Str 25) couldn't move objects 3 ordinary humans could (see for instance 'Wall of Iron'). A more precise system was HERO's adding together of pound values to get total lift, which could then be mapped back to a STR score.
(Another 'ad hoc' system seen in one GM's Palladium game was to give a PC extra d30 rolls under Strength when NPCs helped move levers etc.- d30 being needed because of Palladium's stat scale, and the NPCs having lower and maybe not exactly known Strength).

Also see thread here for a not-completely-serious extended discussion on rock lifting in various systems:  Characters-from-Different-RPG-Systems-Try-To-Lift-A-Rock (http://forum.rpg.net/showthread.php?611707-Characters-from-Different-RPG-Systems-Try-To-Lift-A-Rock/page1)

Off-topic, another instance where multiple AD&D characters added together their Strength was the 2E Tome of Magic 'Champion's Strength' spell - this let several priests donate their strength damage modifiers to one target. So, a completely different ad-hoc mechanic to any other sort of Str assist; this one had the problem most characters have a +0 damage modifier, or this could give a damage bonus that's normally impossible from just Str (six titans could cast it for a +72 damage bonus).

Encumbrance: somewhat relatedly, systems may use exact encumberance in pounds; Basic D&D instead measured it in “cn” for coins, at the rather heavy 10 cn = 1 lb. A few systems (Swordbearer, reputedly; Dragon Warriors) also use just an “object limit” e.g. 10 objects, plus/minus possible Str modifiers. Of course games often handwave the details of encumbrance, particularly when PCs have horses/vehicles/bags of holding.
deadEarth uses weight but gives containers such as backpacks or hiking packs a negative weight (e.g. military backpack:-15 lbs), to reflect their ability to increase carrying capacity.
 
Fire: fire damage works particularly well for systems where its possible to calculate a probability or DC of something catching alight off a number of points of damage - though very few systems actually do this (see discussion of Marvel Super Hereos above under Combat – Damage). Fire (or sunlight for vampires, say) might also be surface area based, as below.
 
Immersion Damage (in something bad e.g. acid, lava): damage for this is logically based off amount of surface area exposed, as a proportion. The easiest way to handle proportions in game is in count success systems, by setting the target number i.e. if "Boiled in Acid" is 10 dice of damage, complete immersion would be TN 0 (= 10 damage) and half submerged would be TN 6 (average 5 points of damage).
 
Some systems have tried to have surface-area based calculations to deal damage - this only works well if a creature's HPs (or other attacked attribute) are at least proportional to its surface area. For example, the 5th level druid spell Slimewave in 3.0 D&D hits a creature with a patch of green slime for each 5ft of area it has, each of which deals d4 Con damage a round; an Orc (medium size) might survive for three or four rounds (one slime patch), while the spell dissolves Colossal creatures (like most great wyrm dragons; 40ft facing or 8 slime patches) within the round.
(While it was for weapons) Larger-than-man-size damage in AD&D (2nd Ed.) could cause similar less drastic problems for monster PCs: PCs belonging to races that normally had multiple monster HD got a bonus of only +1 HP per monster HD to a PCs normal class-based HP, making them relatively squishy. (a 1st PC fighter-ogre would have d10+4 (for 4 HD) + Con bonus HP (or 5-18), vs. a real ogre's 4d8 (4-32), but still take d12 longsword rather than d8, or 2d8 from a bastard sword).  
 
Luck Rolls: some games have a 'Fate roll' or 'Luck roll' that is a mostly unmodified, to use ad hoc to determine if something happens - examples include the fixed 5d10 roll of original Storyteller, and the (albeit unnecessarily complicated) d100-roll-under-another-d100 'Fate roll' in World of Synnibarr.
This is basically just a streamlining of how most other systems would ad-hoc assign percentages of whatever event happening ("there's a 40% chance the goblin storeroom has the iron spikes you need") that the DM opts not to decide just via fiat, though it also puts it into the context of the games' general resolution system and so gives an output (i.e. Number of Successes for Storyteller) which might be useful for game purposes in some way.
Additionally, using a single system lets the resolution chances be modified by other defined modifiers, such as how 'luck rolls' in Storyteller can be modified by the Charmed Existence merit (ignore a single "1" on any roll).
Sometimes this can give PCs a way to leverage greater-than-expected chances of success, if they can burn rerolls or Luck points or something on checks.

T&T luck rolls and BRP luck rolls are sort of similar too, though using a Luck attribute. For T&T this likewise can be used to get game-mechanically-useful effect, though it also means the Luck attribute either modifies everything (or is ignored perhaps inconsistently - a number of places in the solos use some other [unmodified] die roll instead - for instance having a character survive if they can roll doubles).
Whether something ends up as a 'luck roll' or a standard skill or attribute test depends a bit on the areas defined by other attributes in the system (attributes, resources ratings, popularity scores, etc.)- this mechanic gets used just for things where existing values don't really apply. A luck roll could also be used if another value which does cover the conceptual space is not really mechanically testable due to lack of a useful scale or a missing method for testing that value in the relevant situation (e.g. damage in many games, attributes in Palladium which doesn't have attribute checks per se), in which case its a minor break in the system.
4E D&Ds 'skill challenges' might also be used to resolve some tasks that otherwise need a 'luck roll' - sometimes useful, though potentially leading to shoehorning of skills into situations where they weren't really that applicable to.

Luck rolls might need to be in addition to a normal random determination, to avoid absurd results (e.g. discussed here (http://www.therpgsite.com/showthread.php?p=868104#post868104) in passing) - if a character with 25% luck is choosing one of three boxes at random, an unmodified Luck roll would give a 1-in-4 chance of the correct box. Consequently, game mechanically, you have the option of either a) making a luck roll an extra - if you pass the Luck roll, the correct box is automatically chosen, otherwise there's a 1-in-3 chance.  If every character by default has a Luck rating, this could generate too high a chance of the right box, however. Another approach is to modify the Luck check for the # boxes such that a normal 'luck' character has a 1-in-3 chance, a particularly unlucky character less and an unusually lucky character more.

A "luck" attribute can be used to do "saving rolls" as well as random event determination. Tunnels and Trolls often works that way; Low Fantasy Gaming has a Luck which works like a stat but allows level-increase (Lk = 10+1/2 level), with some checks also getting attribute modifiers e.g. Dex to dodge a Lightning bolt, and with the score reduced by 1 when a check is made. Characters also get a 'reroll pool' equal to level.

Cf. post #60 Event Generation
Making a 'luck roll' be an attribute test on a character's Luck attribute can also be thought to favour PCs, who usually have higher-than-normal attributes. As an example, Chill gives characters who are swimming more than 24 hours a Luck roll (on their d% Luck attribute) to find floating debris, or drown - having a game system for this gives a generous result, though at least it uses a game mechanic in such a way that a character's chances are fair.

Saving throws: older games tend to have fairly idiosyncratic systems for saves, with later systems streamlined them for easier identification of what does what e.g. Fortitude/Reflex/Will in 3.x D&D. Modifers may be class-based, or racially-based (e.g. in Battlelords of the 23rd Century). Some systems may just use skill checks or attribute checks for the equivalent of saves; RQ2 uses skills but with an optional rule for some of the equivalent skills e.g. Resilience that they be capped at [stat * 5], Tunnels & Trolls just uses attribute checks (older editions have no other numbers). There is a bit of a design advantage in separating "saving throws" as a distinct category in that it makes it easier to design effects that don't harm saves - for instance the "poisoned" effect in 5E disadvantages skills but not saves, so a character isn't hampered if they need to make a save to end the ongoing effect of the poison.

AD&D 2E was somewhat weird in that a save-like situation might use either an ability check (roll under d20) or save (roll over d20) which gave very very different results - the 1st level thief with an 18 Dex would be 90% likely to pass a Dex roll to not be crushed by a falling boulder, but would probably fail the equivalent save to dodge (i.e. a save vs. Breath Weapon of 16+, w/ +4 defensive adjustment from Dex).
 
A trend in design discussion recently seems to be toward rolled saves with standardized “defense” numbers like “Fortitude Defense”, an integrated system with armour class or the like. This isn't really a new idea: Hero for example has attack/defense values for both physical and mental combat, as does the 1992 Edition of Gamma World which used rolls of d20 + mutation modifier vs. “Mental Defense” (the mental equivalent of armour class). Dragon Warriors is similar, with hostile effects occurring if a roll is made under the attackers’ Magical Attack (just as a sword blow hits if it rolls under a warrior’s Attack).
 
This does make the system more consistent, and can be used to more easily reset an attack from one defense to another, but keep in mind the following, IMHO:
 
*Feel: an “attack” that lets the GM announce a “death” result feels less fair than getting a save to negate Death, even where the probability is identical. Dragon Warriors is particularly an offender here, since save or dies (SoDs) requiring a Magical Attack rolls are frequent – the actual text example of a Magical Attack is for a gorgon rolling to petrify a PC
 
*Area of Effect/multiple checks: a GM may be able to roll several saves for monsters faster than a player can roll several attacks, as they know the target number i.e. the GM quickly calculates he needs a 15+ on d20 to save vs the fireball and just rolls a bunch of dice, counting how many are crispied). This can however go either way, depending on whether its the players or the monsters that dish out the most AoE effects.
 
*Who rolls what can have interactions with other rules, like whether a character gets to spend luck points to reroll. An amalgamated defense system sometimes gives other odd effects, like invisibility giving a wizard +2 to hit with their sleep spell (4E D&D).
 
*Conflation: in a defense system there is a tendency that a secondary roll to resist gets streamlined out; instead of an attack vs. AC that deals X damage and then requires a roll vs. being moved, only one roll is made. That is, two effects that should be resisted separately (by different factors) end up conflated - ‘I hit the Gargantuan monster’ and ‘I push the Gargantuan monster’ are different things, but a single roll often seems to do both, ignoring most of a critter’s modifiers against half the effect.
 
An interesting compromise between rolled saves and standardized defences can be reached here using the idea of a ‘Passive Defense’ vs. ‘Active Defense’. For example in Talislanta or GURPS, a character receives a passive defense vs. physical attacks they’re normally aware of, but can opt to spend an action to make a full “active defense” against them (a dice roll) to raise the difficulty to hit them.

Final Note on Saves: Possibly more effort goes into designing saving throw systems in games where characters are expected to probably last a whole campaign - parallel scaling of attacker/defender adjustments, character abilities giving rerolls, carefully balanced effects, rerolls each round, etc.
T&T spells often don't allow even an ability check to resist; Gamma World characters don't exactly have a saving throw system - in most editions a 'Health check' system works against a handful of effects and 'mental defense' against some others, but things may also frequently end up outside those fairly limited subsystems - e.g. AoE damage is automatic although a character can 'duck for cover' for 1/2 damage with a Dex check at -5. GW characters normally convert to D&D (1E DMG, or Dragon #187) as not receiving saving throws vs. spells, also.

Insanity and Horror: Games noted for rules around these sorts of things include Call of Cthulhu (Sanity rating as a percentage, game lists various things causing SAN loss and loss of a number of SAN points will roll for random insanity), and Palladium (various random tables with type of roll indicated based on the trauma, as well as having "horror factor" rolls for supernatural creatures; characters receive just a save vs. insanity [adjusted for Mental Endurance] rather than tracking individual SAN points as in CoC). Kult also has insanity rules - based off insane characters being right and so giving powers to character with significant numbers of insanity points.

Starvation and Thirst: Games sometimes have rules for these depending on likelihood of this coming up. A Survival skill may be used to find food for X people for Y days. Starvation may deal fatigue damage or Str loss, or just damage; thirst may likewise cause fatigue or damage or CON loss. Dark Sun for 2E AD&D had thirst rules dealing around d6 Con damage/damage if a minimum ingestion amount (based on race) was not met, as well as having rules for "Severe Desperation" which could cause a character to become chaotic evil to obtain water if they failed a saving throw. CON damage from dehydration was a bad way to go in that it notes specifically a 0 Con character had only a 25% resurrection survival percentage, i.e. they use the 0 Con rather than their normal Con for resurrection. This was somewhat WTF in that a character who was a bit desiccated would be probably irrecoverable, while a character killed with an axe to the face and then over time reduced to a clean-picked skeleton would roll for resurrection at no penalty.

Item breakage, miscellaneous wear and tear and consequences : games vary in how much they want to handle 'gritty' realism in the 'Fantasy Vietnam' style. Games can have assorted rules for item breakage, item saving throws, and miscellaneous consequences. Early generation games generally work through a detailed, procedurally-generated system where lots of specific rules are invoked - a saving throw fail vs. fireball may trigger a bunch of secondary item saving throws, a spell mishap may involve a roll on the spell mishaps table, arrows are tracked individually, a shield might have a number of hit points that are being crossed off as its used. OTOH, in more recent games gritty realism could be handled more abstractly - Dungeon World for example builds in assorted losses as consequences of failed 'moves' where rather than having a separate roll, a limited success on a save/attack/whatever can generate item losses, running out of arrows or whatever.
On the plus side, this saves a lot of detailed book keeping. It does introduce possibly more GM fiat into results, and players may have less leverage to avoid potential negative consequences. If a partial success lets the GM do a dick move, then a player strategy to avoid something most likely means they get a different negative consequence rather than avoiding it entirely - chaining your sword to you to prevent it being disarmed prevents a 'drop weapon' being narratively feasible, so some sort of fumble might break it instead. Or a donkey loaded with bonus arrows might just prevent someone choosing the 'runs out of arrows' partial success Volley option, rather than being an advantage.

(http://i1239.photobucket.com/albums/ff507/BSJ17/parkinson-rifts2.jpg)
Above: the Blind Warrior Women are OK with Rifts not having Spot checks.
 
Noticing things in games typically uses a mix of player-driven description and rolls to notice things for tricky /in doubt situations. Perception scores may be rolled or function as some sort of target number (“Passive perception”). This is already touched on a bit in the earlier post on cutting down excessive dice rolling.
Passive perception may also be desirable in that the player is not called on to 'make a Spot check', and hence isn't provided ooc information that there is something there. Some GMs may roll player rolls unknown to them in secret, ask for a dice roll without saying which modifier applies. It would also be possible for a game with a 'wild die' /die pool /multiple checks to have the GM roll some of the dice, giving the player only partial information on how successful a roll was. A particularly cruel approach I've seen suggested is to have 'botches' stored by the GM - they can use it for the event its rolled for, or they can keep it and spoil another roll later with misinformation - meaning that no roll results are entirely knowable.

AD&D is interesting here in that while some specific situations such as “Hear noise” or finding secret doors are individually defined, it typically uses player described searching (“I look in the pocket of the cloak”, “I see if I can lift up the bottom of the chest”, etc). No general perception attribute though specific checks could cover for it when appropriate e.g. ability checks. Palladium is similar to this as well, though one game (Nightbane, aka Nightspawn) adds Perception rules.
 
Other games may have Perception attributes (/skills/derived attributes), though this can in rare cases cause more confusion than not having them; while additive systems may just use an opposed roll, roll-under mechanics can struggle with this. Jonathan Tweet discusses this in his notes on how Runequest influenced the structure of the d20 system here; http://www.jonathantweet.com/jotgamerunequest.html (http://www.jonathantweet.com/jotgamerunequest.html)
(Anecdotally, I’ve found this myself not too long ago. In Cadillacs & Dinosaurs, a d10 roll-under system, we had a situation where the Observation skill had a default of zero for untrained characters regardless of attribute – a rule that easy tasks get a x2 skill multiplier wasn’t helping); this was particularly odd when someone else failed a Stealth check, requiring some pondering - requiring a roll by PCs to notice hiding NPCs means the PCs probably fail to notice them; requiring a roll by NPCs to sneak means the NPCs probably fail to sneak.).
 
Dirk Remmeke here (http://www.therpgsite.com/showthread.php?35607-Skill-Based-RPGs-Problematic-Skills&p=934476&highlight=ambush#post934476) discusses the idea of not having a specific perception skill (or attribute) with the relevant skill instead being highly situation-depended

Other perception related rules:
HERO has detailed rules that distinguish between “targeting” and “non-targeting” senses; characters can have senses beyond the usual few that count as ‘targeting’ (equal to vision) and upgrade a “non-targeting” sense to “targeting” (i.e. Daredevil radar hearing).
Some games have multiple vision types:
*AD&D has “infravision” –allowing characters to see using heat radiation – and more rarely “ultravision” which used ultraviolet radiation assumed to be common in the underdark (?), and provided vision similar to normal vision, rather than Predatorvision.
*Palladium had “night vision” (seeing in low light conditions); D&D 3.x distinguishes between “low light” vision which works as long as some light is present, and “darkvision” which just breaks the rules of physics, as well as defining "blindsight" and "blindsense".
*5E D&D makes darkvision more generally available than 3E (replacing low-light) but it is somewhat weaker than 3E darkvision and includes some of aspects of low-light vision; instead of the only limitation being that colour discrimination is lost, 5E darkvision gives vision equivalent to 'dim light' in total darkness, i.e. lightly obscured, i.e. disadvantage to perception checks/-5 to passive perception, and full vision in dim light.
*Shadowrun has both Low-Light and Thermographic vision.
*Dragon Warriors distinguishes four types of sight: normal vision, darkvision, gloomsight, elfsight, and panoptical vision. Creatures with darkvision (orcs for example) could see perfectly well in utter darkness but were blinded by bright daylight (the same penalty humans had in the dark). Creatures with gloomsight, such as dwarves, preferred shadowy places and had a lesser penalty in either daylight or total darkness. Creatures with elfsight preferred light but had lower penalties in low-light conditions, while creatures with Panoptical vision were comfortable with any level of illumination (no bonus or penalty, which in DW still gave them lower perception that a day creature in bright light, which had a bonus).
I reverse-engineered DW-type vision back into a powers system for one of my games based off Marvel Super Heroes/FASERIP, which I'd dubbed Unearthly Heroes.  It had a darkvision system which was an extension of the basic powers system. Powers and attributes both used the same universal rating system - 0 (nonexistent), 2 (feeble), 5 (poor), 10 (typical), 15 (good), 20 (excellent), etc. The "Enhance" power added its rating to another power or attribute, up to x2 base unless the 'unlimited assist' advantage was added to it. Light was also given a rating (as the 'Light Generation' power) with 10 (typical) being dim light, 15 good and 20 full daylight, and penalties for very bright light (30/remarkable or better). Darkvision simply worked as Enhance operating on the environment's "light generation" rating. 'Unlimited Assist' was needed to see in pitch blackness (light 0); and the 'Always On' disadvantage could make already bright light blinding, i.e. as seen for drow or other light-sensitive creatures.
*Recon has a table of light condition x precipitation level to determine maximum effective range, with another line on the chart setting maximum for heavy/light vegetation). See below:
(http://i1239.photobucket.com/albums/ff507/BSJ17/recon_pertable_zps09qrsozh.jpg)
(note the die roll for precipitation level. Could also be an example of 'grid rolling' if the GM rolls lunar phase too.)

Lessons in Hiding
Some further notes on stealth.
AD&D: is interesting in having scores for both 'hide in shadows' and 'move silently'. Description of how these worked had some vagueness - notably some GMs might rule both checks required and necessary (making stealth nearly impossible at low levels) while others used 'hide' as a second save when 'move silently' failed - for ducking for cover. There is also some debate on how to run 'untrained' checks (one interesting solution being to use 'surprise' to represent an opportunity not just to get free attacks but to sneak past).
Savage Worlds: gives two checks in most cases - normal guards move to high-alert after one roll is failed, and notice targets after two failures.
Burning Wheel: stealth is particularly called out for its 'Let It Ride' rule, where multiple checks aren't required unless circumstances change.
(Miniatures-based) The Fantasy Trip suggests removing invisible creatures from the board while they're hidden.

Overall: stealth varies between games along two axes: how difficult it is to hide and how much advantage an 'alpha strike' provides (this last depending on average hit points, bonus damage for sneak attacks, etc).

Finding items: this is not an RPG as such but a boardgame, but "Dark Darker Darkest" has a search system where characters roll dice = # characters, with successes indicating number of items found. Once successfully searched a room can't be searched again, meaning that a 5-person search party might find 5 things, while a single person finds only one thing and then 'exhausts' the room.

A few systems don't have any sort of crafting system. Others have skills for this, but without much development of how these are used – it remains up to GM discretion.
The normal ‘default’ system is probably making a simple skill check to construct an item, with roll determining final quality, using time and cost guidelines depending on the sort of item. Fumbles or bad results may generate a setback or ruin a product completely.
 
Interesting crafting systems include:
*The D&D 3.x system uses a generalized Craft system; there are many Craft skills (as many as you care to invent) which share a single generic item-building system; this was an attempt to compress what were dozens of Non Weapon Proficiencies in 2nd Ed. D&D into a single skill. Instead of detailed tables of items with time to craft, difficulty, and cost, the system derives crafting time from item cost; the base cost of an item is 1/3 the final cost in raw materials, and a Craft check generates progress in silver pieces per week; this may work for estimating a craftsman’s income, but crafting an item may require a number of checks. Math is fairly cumbersome here since progress on an item in silver pieces is calculated as [DC x roll]; item quality is fixed (a character can fail to make a thingy in the allotted time, but can’t turn out a crude item or a masterwork item accidentally. The generic time means that some items take a long time to craft and makes e.g. goldsmithing much lengthier process than iron working.
 
*Warhammer 2nd ed has skills for crafting but doesn’t explain how they work; they are rolled together even more than D&D3, with craft and “profession” type skills both grouped into the skill “Trade”.
 
*Shadowrun; in 1st edition a Craft check determines how long a task takes; divide the base time by the # successes. Time required to build an item is based off cost but with divisor varying by type of item. By 4th edition, Build/Repair evolved into an extended test (rolling and accumulating successes across several rolls).
 
*Alternity uses simple checks for Juryrig (temporary repair), but complex skill checks (Bill Slavicsek’s first attempt at Skill Challenges) for the Repair skill or to build items. Characters can score multiple “successes” for good rolls, up to 3 per attempt (a d20 roll under their full skill score is worth 1 success, under half score is worth 2, and one-quarter of the score is worth three successes; 3 failures or 1 critical failure botches the challenge) and up to 10+ may be needed depending on repair complexity.
 
*In most systems each die roll for Crafting (success or failure) takes a certain amount of time, but Burning Wheel varies this. It uses a count-successes system; proportion of necessary successes determines what happens:
0% - an apparently magnificent work [125% usual time required to create] that crumbles to junk when first used;
Under 50% - junk produced, in half the base time (throw it away)
50%: junk produced, in quarter of the base time (throw it away).
One less than needed: item that looks serviceable but fails “dramatically” at some point.
 
*HarnMaster crafts have a weird effect system, mostly demonstrating an interesting workaround to limitations of the core mechanic. Harn has some difficulty determining how well a character succeeds at a task; it does not use "margin of success" to determine how well a character succeeds, instead speeding up results in combat, etc. by having any roll ending in an 0 or 5 (an 05,10,15,20, etc...) be a critical success or critical failure.
Crafting uses the same system, but to go back and generate more detailed results for Crafting (i.e. higher quality items for more skilled craftspeople), it uses a "Value Enhancement table" and a "Product Quality table" which cross-reference a Skill Index (the 10s place of character skill) with a Critical Success, Normal Success, Normal Fail or Critical Fail result to give a final value or product quality. This gives slightly odd results in that (for example) a character with 60% skill (SI 6) can generate either a x4.0 (Critical Success), x2.0 (Marginal Success) or x1.0 (Marginal Failure) value enhancement, but not a 3.0.
The product quality table is similarly quirky; range of modifiers makes it quite difficult to forge a product of average (+0) quality.
 
*Gamma World 4th Ed (1992) has very few skills – despite my describing it as a ‘derived attribute game, each class has 3-5 unique skills - but technical skills are strongly represented, with one of only 4 classes, the Examiner dealing with ancient artifacts and getting separate skills in Jury-Rig (=building items from scrap) and Repair Artifact. The warrior class, Enforcer, also has a “Makeshift Weapons/Armour’ skill (one of their three skills). All characters also have a “Use Artifacts” derived attribute; this is used on a trippy flowchart with random rolls to determine if a character can determine what an item does, or ends up eventually at results including ‘Dangerous Event’, ‘False Function’, ‘Falls Apart’, ‘Assumed Useless’ and ‘Assumed Broken’)..
 
*GURPS is noteworthy for usually having a number of separate variants of a Craft skill, by Tech Level.
(Palladium tends to do something similar but less systematically - it would just ad hoc define separate e.g. blacksmithing, flint chipping etc. - Transdimensional TMNT has a number of such 'historical' skills). DC Heroes assumes modern tech and 'gadgets' are built using that tech level, except that a "Genius" advantage lets characters construct more advanced items (robots, force fields, etc.) (perhaps an example of something that would be better off as a skill modifier adjusting skill 'factor cost').
 
Exotic materials: Talislanta has weird materials including various colours of Adamant (alloys of steel and diamond of the appropriate colour); D&D has adamantine and mithril, as well as dragonhide, chitin, ironwood and obdurium; Shadowrun has orichalcum. One of the lengthier lists (I’ve seen anyway) is the exotic materials list of SenZar; each has its own special abilities, as well as an affinity for particular magics which reduce cost to enchant them (e.g. Supremium can receive the Bifurcation enchantment – x3 damage, deathblow cuts foe in half - at 10% of the normal cost).
 
Below: list of exotic weapon and armour materials and their properties from the SenZar RPG. (Arrangement of these into a periodic table is just me dicking around, not actual SenZar rules).
 
(http://i1239.photobucket.com/albums/ff507/BSJ17/SenzarPeriodictable.jpg)

A variant of rolling a Craft roll every so often (such as 1/day) might be to roll one Craft check to see how long it takes to build something. Making it a time roll probably gets rid of the chance of a 'raw materials broken' result, unless that happens on a critical failure: another option would be to add a per-day cost such that a low roll does cost more (abstractly representing the likelihood that a long time in Crafting will involve starting again with more raw materials). This works a bit differently in that the worst-case Craft result could be set at [cost = over the counter cost] such that a low skill point investment in Craft is still useful instead of being worse than no Craft skill.

“In the land of Mordor, in the fires of Mount Doom, the Dark Lord Sauron forged in secret a master ring, to control all others. And into this Ring, he poured his cruelty, his malice and his will to dominate all life.”
 
I was initially going to separate Crafting into just magical/non-magical, but while thinking this over realized that since some games have technological item building rules I should mention as well, so this would be something of a misgnomer.
 
Complex crafting may use similar rules to regular crafting, though class-based systems often relegate magic item building to particular classes rather than using skills.
 
Some interesting systems, in no particular order:
 
*1e/2e AD&D magical item construction is performed by wizards, and requires the GM to determine a list of fantastical ingredients – monster body parts and the like – which the wizard must quest for, hire adventurers to get, or buy through contacts (if available). Construction requires steps including the Enchant Item spell (6th level), a saving throw for the target item, casting of other spells (possibly requiring spell research), a Permanentcy spell (8th level, 5% chance of Constitution loss), and finally a percentage roll to see if the item works properly or is cursed. The wizard earns XP for constructing the item. Costs and processes for making an item are wholly DM-determined (though the monster manual often notes certain monsters are useful for certain things); magical items should be very rare (probably much rarer than they actually end up being in D&D games).
2E has a system of 'impossible ingredients' where a character might need to find/interpret what to get to serve as 'the breath of a mountain' or 'the shadow of a cloud' (based on Viking sagas?)- the Complete Wizard Handbook has a random table to generate these.
 
*Palladium Fantasy has most items constructed by NPCs called Alchemists. This again requires fantastic ingredients, but both items and ingredients have defined costs, and are bought/traded freely.
 
*D&D 3.x requires large gold expenditure to make an item (what this buys is undefined), as well as XP (representing “life force” of the caster). Items are in theory costed based on either [bonus-squared] or a spell level of an equivalent spell [e.g. spell level x caster level x 2000 GP], though standard items rarely follow the equation, and just have a listed construction cost and spells needed to create them. The right Feat and a minimum caster level is required to create items. Items require 1 day per 1000 GP to construct.
Broken magic items can be reforged at 1/2 cost, in a nod to fantasy literature.
 
*GURPS Magic uses estimated wages of mages to calculate GP value of magical items: a wizard can generate a point of magic per day and earns $700 a month (22 working days), so items cost $33 per point after factoring in about a 5% error rate.

*DC Heroes (3e): both technological and magical items are constructed by making checks of Gadgetry or Occultism skill vs. the number of points of the desired superpower to install this into an item. Characters must make a Resources check to buy parts, then someone (any other concerned party will do, not necessarily the builder) must spend Hero Points to actually construct an item, with a cost based on the strength of the power. Characters may get bonuses on the design by having Plans of devices (reduces task difficulty) – an interesting possible adventure hook.
DC Heroes gadgetry has been described as “resembling a Pentagon procurement scandal” (http://www.allenvarney.com/rev_02.html (http://www.allenvarney.com/rev_02.html) ); though note that (in 3rd ed. at least) Hero Point cost to build a device is much lower (perhaps a fifth or so) of adding equivalent Powers innately from Character Growth. Taking the Gadgetry advantage to initially own a Gadget is however a bad idea (same cost as just buying the powers built in, initially) unless the character has the Intensive Training advantage, which raises the cost to buy powers but cheapens skills.
 
*HERO purchases devices in character points, handwaving any construction or acquisition process; points are paid by the user of an item, rather than the builder (unlike in DC, you can’t beat up Batman and just use all his stuff without paying the points). Items use standard power costs, discounted by the Focus limitation to account for the possibility to removing them, and possibly other appropriate Limitations.
Savage Worlds is similar in approach to this – a character with “Weird Science” gets a new Gadget by taking the “New Power” Edge (using an item requires a “Weird Science” roll, but I’m otherwise unclear on whether you can beat up mad scientists and take their stuff).
 
 
*Tinker gnomes (1st ed. AD&D Dragonlance Adventures): a table of effects gives a base “Complexity” of an item; this also equals its base Size, except points can be exchanged between the two (i.e. making it larger makes it less complex). Exact component lists are provided including pulleys, gears, bellows, tuning forks, etc, though are mostly flavour; an item has components equal to its complexity, and base cost for each is multiplied x item Size. Build time uses a table and is based on [Size x Complexity]. Complexity score is compared to character level to see what penalty the device has to operate (to hit and damage if applicable; also, to a roll on a chart to see if it functions when used), while Size just makes the things unwieldy – gnomish inventions are often the size of a wagon and possibly as large as a mountain. A table of malfunctions is included for when an “unpredictable effect” is rolled.
The system is fairly workable (some specific effects are unbalanced) with enough flavour for the GM to make ad hoc judgments if needed.
 
*For magic items, GURPS has some sort of system of “energy points” and skill checks. Wizards can churn out lots of magical items given enough time, and occasionally can build items on the spot (I did like this feature - again something I've seen before in fantasy literature).
SenZar is similar to GURPs (but probably more broken); magic items have a Power Point cost and require time to make and Power rolls, but have only minor GP cost. A market value is given for finished items.
 
*2nd Ed AD&D psionics allowed for psionic item creation using the Empower metapsionic power; using this to create an intelligent psionic item requires only an freshly made item worth 250% to 500% of a normal item’s cost, and to pass a few power checks/spend power points, though the power takes days to use, usually fails (roll under Wis-12), and is expensive in terms of power points. The power did have a prerequisite level of 10th, and knowing it required power choices be spent to access the discipline, buy the power and prerequisite powers); still, this power lets you create intelligent warhammers that can disintegrate people for a cost of 10 GP. Items can also be given multiple powers.
 
*Ars Magica: interesting in that it has a currency for magic other than gold or character points, a form of magical energy called vis which is expended when constructing an item. Making an item requires a season in the lab; however, extended downtime is quite expected in Ars Magica.

*New Khazan (a sort of spelljammer for Tunnels and Trolls) has a sort-of-interesting magitech based around the spell points in 7E T&T ("Kremm" energy).

*I'm not overly familiar with Shadowrun 5E, but comments on one review I'd seen mentioned that it has rules for creating foci/items that make it difficult to make low-powered items - the creator's dice are limited by item Force (e.g. 1), rolled against 4-7 dice or so based on what the item does and needing a success for the item to be created.

Edit: adding this link to a quite interesting homebrew 'Magitech' system - spellcasting system designed to be heavily abuseable out of combat
http://www.giantitp.com/forums/showthread.php?t=252794 (http://www.giantitp.com/forums/showthread.php?t=252794)

Lovin' this thread. That is all.

(Okay, not quite. I'm shocked, shocked I tells ya, that Torg's Drama Deck isn't even mentioned in the cards section. The omission is criminal, criminal I tells ya.)

oops yeah that is a pretty glaring omission ...have gone back and added some notes and a link to more detail.
 
Thanks Jasyn!



General - Events
Apart from 'random encounters' focussed on monsters, or terrain-based hexmap rules, or treasure generation,games may have various forms of event randomization.

The most developed system for this may be the Mythic RPG designed as a GM 'emulator'; this has a system where a GM is replaced by common-sense question resolution tables- players choose specific questions, assign a probability, and roll. Any roll has a chance to trigger a random event (base system is d100, and doubles less than the 'chaos factor' trigger i.e. chaos factor 3 = 11,22, or 33 will trigger).
In other systems, 'Everway' cards can be used as an idea generator for the GM.
Outside RPGs, the boardgame Tales of the Arabian Nights is slightly interesting too - this uses a huge 'choose your own adventure' type book to generate events rather than using GM fiat (or player fiat as in Mythic).
Magic fumbles ('wild surges' in 2E, or original Advanced Fighting Fantasy's Oops! table, or in Arduin) are also event generators of a sort, although very specific. Most use fixed tables of results (some wild surges have results dependent on the original spell, such as reversed effect or changed target).

The Daredevils RPG has a "Doctrinal Progress" table, which can be rolled on by the GM when an adventure 'has bogged down': an NPC reaction roll is used (abstractly rather than necessarily being NPC reaction) and gives either a 'debacle', setback, or obstacle (...i.e. something happens at least, albeit bad), no progress, chance of data (ie. clue), or advancement/breakthrough.

Adventures/Events may also hinge on NPC organizations.
Justin Alexander has this note here (http://www.therpgsite.com/showthread.php?p=843589#post843589) on a "Push Pyramid" for managing NPC organizations:

QuoteBlowback is a lesser known game by Elizabeth Sampat, but it created the Push Pyramid for managing the responses of large NPC organizations to PC activity. Kenneth Hite took this idea and turned it into the Vampyramid for Night's Black Agents, added the Conspyramid for running NPC conspiracies, and then laced in a ton of really cool and innovative mechanics by which the PCs can navigate through these structures.

(http://i1239.photobucket.com/albums/ff507/BSJ17/jennifer-connelly-and-david-bowie-in-labyrinth-1986-movie-image-21_zpseb91d8e1.jpg)
 
By default, most games have a single attribute for social interaction (Charisma or Appearance or similar), that skills are based off. Games may allow social skills to affect NPCs and not PCs, or PCs may be wholly player controlled.
Social rolls may usually be opposed by a target’s own Charisma, by the game’s Willpower statistic, or may have a set target number (e.g. for 3.x D&D Diplomacy checks, which tended to break since check bonuses could escalate infinitely against the set difficulties by target attitude).
 
 
Games Without Charisma
In other cases, games lack a Charisma but roll functions of it into another attribute (perhaps avoiding having a Cha so player’s can’t dump it):
 
*GURPS bases social skills off Intelligence (which also includes perception and willpower), and may modify the score with advantages/disadvantages.
 
*Savage Worlds bases Persuasion off Spirit (the willpower attribute) though it also has a derived attribute called Charisma which is the sum of persuasion modifiers due to Edges or Hindrances (default 0).
 
*Cortex uses Willpower (e.g. in Supernatural). As well as their Willpower + Persuasion roll (both rated d2 to d12), especially pretty characters may add an 'allure' advantage die (rated from d2 to d6).
 
*Marvel Super Heroes has a Popularity rating which is used for social interactions with NPCs (not a true attribute), which for bad guys is negative (e.g. Galactus, who eats planets, has a popularity of -1000; good for intimidating people but bad for getting dates). This may rise/fall as a result of a character’s actions, or bad press (Spiderman). Being narrowly defined, this was somewhat less prone to abuse compared to the Charismas of other games. (The idea of “negative Charisma” also appears for monsters in Tunnels and Trolls). Villains and Vigilantes still has a Charisma attribute, but it may be increased by donations to charity or good deeds.
 
*World of Synnibarr has a reaction modifier determined by Ego (Int+Wisdom), plus a randomly-rolled personality modifier (rerolled every few levels) and appearance modifier. It also applies a modifier based on differences in alignment (aura colour).
 
 
Games Without Social Checks
In some cases, games may not use mechanical testing of Charisma or social skills – it may be up to the player to talk through any and all situations. Here playing a stinky dwarf with 8 Charisma places a roleplaying hindrance on a character (similar to playing a low Intelligence), rather than providing a penalty to dice rolls. E.g.
 
*older D&D leans towards this approach; though reaction rolls/Charisma checks may sometimes be used, it tends to be less common. The “Etiquette” skill of 2nd Ed. provides knowledge of customs/forms of address to assist in roleplaying, but has no direct effect.
 
* Dragon Warriors has a Looks attribute only (no mechanics are given to test this);
 
*Palladium deliberately eschews social skills. A character has Mental Affinity and Physical Beauty attributes which largely just provide only a guideline on how to roleplay the character; if quite high (>15) a rating gives a “%trust/intimidate” or “% charm/impress” value. (For some further discussion on social skill overuse and Palladium see the RPGPundit thread here: http://www.therpgsite.com/showthread.php?t=20381 (http://www.therpgsite.com/showthread.php?t=20381) )
This can get 'weird'. The "Wu Shu T'Sung" martial art in Ninjas and Superspies for example has a display kata which 'doubles the number of attacks per round, but can't be used in combat' and is 'often enough to intimidate opponents into retreating'. [No mechanics given - an NPC has to be assumed to not know its useless in combat].

 
*Possibly Amber also falls into this category (?)
 
(There's some discussion here (http://www.therpgsite.com/showpost.php?p=422002&postcount=210) by Arminius regarding some of why social checks differ from other checks, that may be of interest. There are also argument's that mechanical testing of charisma is good because this allows characters to have essentially different abilities to the player, if you want to have a character that is persuasive when you're not a used car salesman yourself. Gamers are somewhat split between feeling that use of player skill here is unfair - and that it is the game.)
 
Games With Multiple Social Attributes
*a number of games have separate physical appearance and mental Charisma stats (Palladium, Kult). The Storyteller system has separate scores for Appearance, Charisma and Manipulation, each used in different circumstances, presumably since the game is intended for social interactions to be front and centre such that a single attribute would be overpowered.
 
*Amazing Engine has separate attributes for Charm and Position (social status). "Position" can be checked game mechanically, but seems to convert from 1-100 to a real rank pretty badly; for instance, Bughunters uses a roll of [d100+Pos] to determine a character's background, then that can apply ad hoc modifiers to how character is treated, as well as giving a bonus to a characters chance of a 'job opening' for a given 'class', then with Pos score + a huge bonus by class determining military rank (Position modifies actual rank only slightly since its 1-100 and class can add +0 or +200 etc.).


 
*DC Heroes has three stats, used simultaneously for social rolls. Influence determines how high a roll is needed to affect a target, Aura determines how much effect a character gets if they do succeed (in result points), and target Spirit resists. A few special social interactions use other stats e.g. Force (Str), Weardown (Will) and Bluff (Int).
 
*Harnmaster has various very specific stats including separate Comeliness and Voice attributes and a spiritual “Aura”; social skills (on d%) are each modified for 3 different stats e.g. Acting = Voice/Agility/Intelligence, Languages and Rhetoric are Voice/Int/Will, and Singing is Voice/Voice/Hearing.
 
*The Demonspawn gamebooks have separate scores for Charm or same-sex charisma, and Attraction, or appeal to the opposite sex (the weird thing about those stats in the books were that both attributes added to Life Points i.e. helped absorb damage; Life Points equalled the total of all the characters 8 or so more-or-less percentile [2d6x8] attributes, giving PCs hundreds of LPs).
 
 
Other elaborations
 
*Dying Earth has no attributes, but Persuasion and Rebuff appear as (mandatory) skills. Each of these has a default “Style” which may be rolled (for bonus points) or just selected: Persuade styles are Glib, Eloquent, Obfuscatory, Forthright, Charming, and Intimidating, while Rebuff styles are Obtuse, Wary, Penetrating, Lawyerly, Contrary and Pure-Hearted. Each style is “trumped” by one opposing style, giving it a penalty e.g. Obtuse trumps Glib (they can’t follow what’s being said) but is trumped by Intimidating, or Eloquent trumps Contrary but is trumped by Wary. (see quick start rules: http://www.dyingearth.com/downloads.htm (http://www.dyingearth.com/downloads.htm) )
 
*Indie game Dogs In The Vineyard is a system designed primarily around a social conflict mechanic. Combats escalate from social to physical; dice are rolled initially then act as a resource during a conflict; a character puts forward dice, with the opponent having to match the roll. A character failing social conflict can “escalate” the conflict, rolling extra dice for weapons/physical stats to continue the exchange; the social layer happening first will always (IIRC) add its resources to the physical combat. Character relationships are worth extra dice.
 
*Exalted has a fairly detailed social combat system including various “Charms” with social effects – many of these very strong. Existence of these may give PCs an incentive to avoiding talking to NPCs, to prevent them being owned immediately.
 
*there's some discussion here (http://forum.rpg.net/showthread.php?553532-FATE-3-0-Social-quot-weapons-quot-and-quot-armour-quot) on social 'weapons' and 'armour' for FATE, mirroring normal weapons' role but in social combat e.g. a bad reputation inflicting more 'harm', or 'unpopular in particular area' being a social 'consequence' taken rather than 'stress'.

* The Soothsayer RPG has a single Personality (i.e. Cha) rating which also determines points to spend across five personality ratings scored 1-10 (Conscience, Culture, Humanity, Spirit, and Temperament).
 
*Pendragon has a system of Passions (personality traits) rated 1-20 which influence character behaviour. Potentially these model a character’s behaviour and thus their resistance to certain social attacks much more accurately than would a simple Willpower roll or the like e.g. Seduction might actually involve a check against Chaste/Lustful, or Intimidation a check vs. Valorous/Cowardly.

*Supers! (Hazard Studios') treats "Rage" (the disadvantage, e.g. for sample villain 'Ares') as a susceptibility to social combat, suffering "double normal Composure damage from insult-based Presence attacks", berserking at 0.

*HERO is unusual in that "presence attacks" use a mechanic similar to damage rolls (d6 per 5 PRE points as a pool) instead of the default mechanic for success/failure attribute checks (3d6 roll under 9, +1 per 5 stat points)

*Apocalypse World has a weird 'Hx' (History) system where characters have +0 to +3 or so ratings for every other player character, describing the strength of their relationship. These go up and down, modified by use of class-specific sex powers (!) and other events. These are also used in character advancement.
Dungeon World has (at least, in sourcebooks e.g. Class Warfare's) abilities ("Heart of Gold") which if used on PCs cause them to get awarded ('Mark') xp.

*Maelstrom has a slightly interesting trading system. Character stats are rated as percentages; a Trader (only) can make a Persuasion save to sell goods. Each attempt to sell costs d6 time units, with the day of trading having time units equal to the Speed percentage (i.e. Speed as well as running and the like also lets them socialize/sell faster).
It has Preaching rules that distinguish between subjects that have no opinion (successful roll-under preaching ability will do) and actively hostile listeners (who also get a roll under Will to resist).

Existence of social systems (do we roll dice, RP this out, or both?) is something that's fairly divisive among gamers, with their being a tendency for people to run a game in their preferred mode (if possible) regardless of the actual rules. In some cases this leads to a social attribute or skill investment becomes wasted points, when it would've been better for an official rule change removing the options at the outset. This problem happens to not occur somewhat in more abstract games, where it is difficult to separate 'social' tasks from other tasks, due to skills or personality traits or aspects all being useful for whatever (e.g. Marvel Heroic ? perhaps Apocalypse World) - perhaps corresponding to 'intent-based' rather than 'task-based' resolution.

Edit note: I've had some recent interesting offline discussion on social skills, with it being proposed that to use game mechanics, but keep roleplaying, that a player rolls and then has to roleplay the success or failure. I could see talking in character as being something that could possibly end up being skipped as it doesn't affect the roll, but it could be encouraged if the player is rewarded with XP for good roleplaying (i.e. that's accurate to their character).

Different interaction scenarios may just have different rules, or may be defined separately in such a way different resources are involved to purchase them - Storyteller's Appearance vs. Manipulation attributes, 3E D&D's "Diplomacy" and "Bluff" skills. In that case a character may be very good at one thing and poor at another. Dungeon World is interesting in that it has one especially generic manuever for talking - "Parley" can include either and just requires "leverage" over an NPC, which could be a positive incentive (I give you this thing) or negative (Intimidate).

Equipment is purchased in two or three main ways:
 
*Defined currency and expenses: e.g. you get 10 gold pieces; at the inn you spend 3 gold pieces, leaving you with 7 gold pieces. Even in these systems, minor expenses are sometimes assumed to be part of general living expenses, with a character’s living standard deducting a certain number of gold pieces.
 
*Abstract Resource ratings e.g. you have a Resources of two dots, which gives you a OK house/car/etc and an approximate salary. Some games like this rely on fiat to function, while others may list appropriate items for a given resource level, or a check may be made to purchase an item; a character may have a limited # of checks allowed per week or month. Storyteller, DC Heroes, Marvel Super Heroes all have various Resources/Wealth systems that work like this; Call of Cthulhu includes a “credit rating” skill.
The abstract method cuts down on book keeping, but works best where a characters income is generated off-camera i.e. where characters work in a secret identity or have investment funds. It is nonideal for games where a primary objective of adventuring is to earn cash/treasure, e.g. D&D or Cyberpunk.
While it simplifies bookkeeping, systems such as this are also more prone to theoretical breakage e.g. D20 modern's system lets you buy and sell items to potentially increase your Wealth rating, as well as providing potentially unlimited supplies of useful mundane items (such as medikits in Gamma World 5th edition).
 
*Some games are almost a hybrid of these two; characters may have a Resources rating which gives characters an income that they spend to purchase items (GURPS ?). i.e. no resources check system governs what is purchasable, so that conversion to a cash value is necessary anyway.
 
*Character Points: Also as mentioned earlier, some games primarily use character points to purchase important equipment, based on utility. The old joke goes that for Hero a towel might count as power, built as ...
Towel : Transform 1d6 minor (10) wet object to dry, OAF (-1), Extra Time/ Full Phase (-1/2), 2 Recoverable Charges (before towel gets soaked, recover by wringing, -1), No Range (-1/2); Real Cost: 2 points
(Note that Hero does include a disclaimer that very basic equipment should not be assessed a point cost).
 
Elaborations/Variants
*As well as cost, items may have other limiting factors, e.g. “Availability codes” determining if they are legal/illegal. Other games may define regional availability i.e. % availability in a small village vs. a city or castle (Dragon Warriors does this as a percentage; 3.x D&D handles it via a “gold piece limit” by community size)
 
*In Ninjas & Superspies or StarCluster, available equipment depends on the sponsoring organization, possibly built by the GM and/or players using points
 
*Deadlands has rules for "el cheapo" gear; characters with the Miserly flaw have to buy only 'el cheapo' things. Small items/clothes tend to be only socially awkward, while skill-critical items (saddles) get a 'malfunction number' which is rolled on d20, adding an extra die roll on top of the normal die pool.

*some games reset character wealth between adventures (Barbarians of Lemuria ? ) – emulation of the genre where Conan wins a small fortune then spends it on wenching and debauchery before the next adventure. BoL eschews an equipment costs system in favour of encouraging the GM to let players have whatever equipment they want. "What use is a palace in Patanga, when you are lost in the Jungles of Chush armed with only a sword in your tired fist?"
 
 
*In powers-based systems, resources rating could potentially be modified using power advantages/disadvantage rules, to give an interesting range of effects (characters who must pass a skill check each month to earn their income, who have a variable income month-to-month, are paid in random items by the black market, and so on.
 
 
*D&D 3.x treats cash as a “stock” rather than a “flow” – it is assumed characters will stockpile all their treasure from killing monsters and convert it to magic items, with only small amounts used on consumables. A given number of encounters are required to gain a level, and approximate cash value is known for each encounter, making it possible to estimate the expected wealth of a character of a given level. The model does not however take into account the likely sales of randomly-found treasures to get other more suitable treasure; this would result in replacement characters having up to double the number of items of characters actually played from 1st level, if anyone particularly followed the wealth-by-level guidelines. Additionally, NPCs are much poorer than PCs (their treasure is fudged up to 3x that of a normal single encounter of their level).
Others here (http://www.tgdmb.com/viewtopic.php?t=54457&start=425) have pointed out that the quadratic costing of items (i.e. cost proportional to bonus squared) in 3.5 has fundamental problems because of the curve - going from +1 to +2 quadruples cost, while going from +4 to +5 is a cost increase of only 56%. This curve doesn't discourage either selling off extra items to purchase improvements, or loading up on +1 items (the 'Christmas Tree effect').
 
3E or Pathfinder have items limited to particular 'slots' (e.g. one amulet, one hat, two rings, etc.); 5E D&D instead has 'attunement' which limits a character to having 3 attuned items, which also prevents characters trading items between each other (e.g. hats of disguise). 3E number of slots is potentially modifyable with feats (an epic feat or a monstrous feat for creatures with extra heads, arms or whatever), or dodged around with items built to be 'slotless', have multiple functions or occupy weird slots.

*Some games have certain equipment limited by merits/flaws or archetypes. This sort of idea can work in a short-lived/ 1-shot game, but in longer games causes problems because other characters may gain these items without point expenditure. The Ars Magica character with the merit “superior equipment of faerie iron” may be outdated by another character finding this, or they may just die accidentally and their items end up owned by another PC. In some SF games, complications arise due to even super powers (Synnibarr) or skills (e.g. Cyberpunk skill chips) being purchaseable with cash.
Similar problems also occur with characters whose main ability is being rich (e.g. the slug-like Quan Nobles in Talislanta).
 
Characters sometimes purchase wealth/equipment with “background” points (Storyteller) which may be used for various things such as Resources, Mentors, Allies and equipment; this sort of system is relatively fair since any of these backgrounds are equally mutable and could be gained or lost through roleplaying, rather than using the same pool of “character points” as other character abilities.
 
*some games may have very strange economies where currency is limitedly applicable. A Stone Age game might just use the barter system, if there’s anything worth buying – an assuming characters don’t just take what they want; the “Sufficiently Advanced” RPG assumes a post-scarcity society where information is the only currency. The Slaine d20 supplement (IIRC) uses a traditional Celtic economy which establishes prices in terms of female slaves and cows.
 
*a few games or supplements may have gone beyond basic equipment and into trying to design a detailed economy e.g. Board Enterprises’ supplements on their worlds’ currency (Coins of Fletnern, a free supplement at drivethrurpg – very detailed) and economy (Grain into Gold, which I haven’t read).

Couple of things not mentioned that might deserve a comment

i) James Bond uses a skill system where the score is out of 30 and there is a dificulty modifier to get a target numbr which you roll against on %d. The roll them yeilds a quality number from 1-4 (based roughly on quartiles but actually read from a universal table). The quality rating then determines the level of success ammount of damage etc. as well as generating hero points.
You should also mention the James Bond chase system in vehicals someplace and the method of getting special equipment by spending XP on it.

ii) The Old FGU system games (Daredevil, Aftermath et al) have attributes and talents. Talents are stuff like Combative, Esthetic, Mechanical etc. Talents are generated with a dice roll agaisnt a table to yield a score from -4 to +4 (if memory serves) and then you get a pool to add to them. They are separate from your attributes which are the usual Str, Dex, Int. Talents can get you special advantages and add to your skills so Skills are made up of talent + Attribute + skill points. I only mention it becuase FGU stuff was reasonably influential back in the day and didn't get a mention I could see in your notes so far.

iii) Bunnies and Burrows deserves a mention as well. It had a unique stat system (so you could compare rabbits with , dogs, horses and men) with a 2 number system with the fisrt number giving you a category and the second number a score. It was another FGU game and considering it was published just after D&D in the late 70s it was very advanced being the first game to have a skill system, martial arts rules and putting emphasis on Role play and cunning over kill everything and take their stuff.

Much obliged Jibba-Jibba - I'm not as familiar with some of these but do have James Bond here, and I think have enough detail in your comments to add notes on the others.  Thank you, will fix tomorrow.

Just a quick clarification on StarCluster (3+) - your company supplies equipment it thinks you need to do your job, but it may not supply the best equipment or the kind you prefer. You can get other equipment via a personal wealth system. This maintains a certain base of standard equipment, so even very poor characters have what is necessary.

I don't think it's necessary to change your description, I just wanted to point that out to those who didn't know.

-clash

Hi Clash...yep looking back I can see it could be misread...thanks!

(Also, sorry, this probably belongs earlier in the thread but oh well).
 
The range of attribute scores depends mainly on the core mechanic of the system. Attribute scores are normally designed with the player characters in mind – scores are largely used to differentiate between the PCs and equivalent foes, so typically operate at a human scale.
It is possible that a game will include a wider variety of opponents – much stronger or weaker than the PCs – or that a game may be written as a “Physics engine”, in which case the game is designed to accommodate not just human battles but other cases. Depending on gaming style, this sort of thing may rarely come up and be determined by GM fiat or similar when it does (flip a coin or assign a percentage to determine which rooster wins in the cock fight, or which god wins in the God War), but edge cases may appear where something is critical, or a game setting will make such comparisons necessary.
Occasionally systems don’t quite manage to deal with all the things they probably should: Cadillacs & Dinosaurs for instance has a 1-10 STR scale for humans (inherited from military game Twilight:2000) but doesn’t assign Str to any of the larger dinosaurs, since humans can’t grapple tyrannosaurs. As a consequence, dinosaur-vs-dinosaur (or dinosaur-vs-vehicle) grappling isn’t covered by the rules; this sort of thing is wholly up to GM fiat.
Games that do give everything stats, may not always work quite as hoped. Dice Pool systems in particular scale badly since the pools become unwieldy, hit point vs. damage may not always work at the lower end of the scale (D&D housecat vs. wizard), or Strength modifier may be out of whack with lifting capacity, giving tiny creatures a suspiciously high chance to perform some feat of strength.
 
The range of a normal ability score needs to consider both reasonable dice roll modifiers as well as other game effects based off attributes. For instance if a system limits weapon use by STR, then STR needs to normally fall in a range where a normal human can't dual wield greatswords easily, or extra rules are required to limit this.
Ability damage or reductions are another factor to consider: The Mutant Epoch for instance has a system where attributes average about a 25 but can go up to 100 or so for starting characters. Individual mutations have an APP (Appearance) penalty, but a character with an upside-down face (-4d6 APP) can still be three times as pretty as an average human if they have a good initial APP roll.

Approaches to having a system work at different scales include:
 
*Attribute categories: Bunnies and Burrows (the Watership Down RPG which has PC rabbits) has stats with not just a number but also a category for different creatures (e.g. rabbits, horses and humans all belong to different categories for Str). FUDGE (written by the author of the GURPS adaptation of Bunnies & Burrows) includes a concept of “Scale” which is similar; this has multiple categories, and allows comparison of numbers across different categories.
 
In similar approaches, Savage Worlds gives animals intelligence ('Smarts') rated the same as humans i.e. d4 to d10 or more, with the note that this is [Animal] intelligence; this both prevents animals dropping below the d4 minimum that works in the system, and makes animals reasonably good at resisting Smarts 'tricks' in combat; it requires some interpretation by the GM as to what the limitations of animal intelligence are, but avoids complex patchfixing like 3Es bluff penalties vs. animals, and lets Notice be Smarts based without animals becoming incompetent at perception checks.
 
*Ranks: sort of relatedly, a system can use numbers for normal scores and descriptive ranks outside this. Amber uses a numerical scale for Amberites, who are superhuman, but rank descriptions for weaker characters (who may be “Chaos Rank” or the pitiful “Human Rank”). A similar idea might be applied in reverse for huge attributes, e.g. dinosaurs could have various ranks of Super-Strength instead of a numerical score like humans.
 
*Moderating scores (e.g. using divisors): JAGS and Forgotten Futures are two examples; both use roll-under, but in an opposing contest if both values are very high, they are divided to get a value with a chance of failure. JAGS uses a table for determining the divisor (i.e. if both are 21+, divide by 2) ; there are significant shifts whenever the divisor changes; Forgotten Futures is arbitrary (the GM sets whatever divisor he feels is appropriate to reduce both scores back to 12 or less (2d6 roll under system).
GURPS has "contests of ST for Very Weak/Strong creatures" rules; if both targets have Str <6 or >20, the weaker value is set to 10 and the higher value is scaled proportionally (x 10/lower ST) e.g. a contest between Str 50 and Str 60 is resolved as 10 vs. 12. This is fairly good, though again note breakpoints.
 
*Open-ended attribute scale: A core mechanic may be designed expressly so that most things fit on the single attribute scale; a game can use an additive system where scores have an ever-increasing (logarithmic) value, a table for comparing massive linear values that has built in diminishing returns (Marvel Super Heroes), a ‘floating die’ system or a multiplicative system (e.g. see post #25 in this thread).
 
*Miscellenous special abilities may be used represent a being that goes beyond the normal scale. Dragon Warriors has creatures that get +3 bonuses to damage from Strength (such as golems), even though a 19+ score is normally maxed out at +2 bonus to damage; AD&D has a ceiling of 25 Strength but notes some deities and the like have extraordinary lifting capacity and etc. beyond the usual limits (in Deities and Demigods, Atlas and Magni have strength of 25 [special] and can lift anything; Thor has a strength of 25 [special] and gets a damage modifier of +16 from Strength instead of the usual +14).

Mayor: Er, Master Betty, what is the Evil Councils' plan?
Master Betty: Nyah. Haha. It is EVIL, it is so EVIL. It is a bad, bad plan, which will hurt many... people... who are good. I think its great that its so bad.
-Kung Pow; Enter The Fist[/I]
 
Many game systems may some attempt to control (or at least describe) the moral behaviour of PCs.
These may be just good or evil – either a description or a number which quantifies this more precisely – or characters may have more complex restrictions/motivations. Games may also have specific alignment rewards/punishments hard-coded into the rules (e.g. Marvel Super Heroes).
 
 
Categorical Alignments
The traditional alignment system as seen in D&D gives a method categorizing characters depending on whether they're the good guys or the bad guys. The alignments give a loose description of NPC behaviour, and limit PC behaviour by threatening them with an experience point penalty if they do not conform ("You can't do that, you're lawful good"). In some respects this can be seen as preventing characters from behaving inconsistently, but in other circumstances, this may be punishing characters for actual character development. Alignment is also subject to alot of interpretation as to what constitutes "good" vs. "evil" and when characters crossed the line, as well as generating simplistic conflicts (the paladin is forced to choose between Law and Good). Interpreted overly rigidly, it can create characters that are caricatures of their alignment (e.g. evil creatures with no human relationships or feelings).
Different versions of D&D have had a nine-alignment system (an "ethical" axis of Lawful/Chaotic and a "moral" axis of Good/Evil), a three-alignment system (Lawful, Neutral, Chaotic), or a five alignment system (4E D&D; Lawful, Good, Unaligned, Evil, Chaotic Evil); Warhammer also has similar alignments.
 
Variant rules within D&D included:
*the Dragonlance system - 1st ed. Dragonlance for D&D used a detailed alignment tracking system which had 10 "steps" between alignments, with moving to the midpoints causing confusion and hence penalties (I sort of adopted this in a 3E campaign and gave characters "evil points" for awhile for tracking purposes, until I realized it just encouraged them).
*Severe Desperation- Dark Sun is often seen as being the least compatible with the original alignments, and contained the "Severe Desperation" optional rule where a character at risk of death had to pass a check or become Chaotic Evil with respect to saving themselves (Some aspects of Dark Sun, such as Preservers being able to defile occasionally with the risk of becoming corrupted and becoming Defilers, could definitely have used some sort of number for tracking their progress toward the dark side)
*Planescape retained "alignment", but most planar characters had an outlook probably more heavily coloured by their Faction, which had particular philosophical beliefs and powers. Factions included the Fated, who believed in individual destiny and could never accept or give help to others, the Doomguard who saw it as their role to further entrophy, the Harmonium who believed in spreading law throughout the planes, the Athar working to undermine the deities, and the Free League who refused to believe they were a faction.
Older D&Ds (Basic, AD&D) included rules for "alignment languages", which all characters of an alignment could speak; this probably gave rise to some specific languages like Celestial and Infernal in 3E and later.

Closely related to D&D, Palladium uses an alignment variant which removes neutrals and defines exactly how characters behave (i.e. will/wont betray a friend, kill, steal, or attack an unarmed foe); which at least cuts down on arguments over whether paladins killing baby orcs is good or not. The Palladium alignments included Principled (LG), Scrupulous (CG), Unprincipled (N ?), Anarchist (CN), Miscreant (NE), Aberrant (LE), and Diabolic (CE). Mystic China also includes a "Taoist" alignment.
 
A couple of other games also included descriptive alignment systems e.g. DC Heroes defined a list of "Motivations" for characters which described a sort of personality seed for a character and how they would act in most circumstances. These included Upholding the Good (Superman), Seeking Justice (Batman), Responsibility of Power (Green Lantern), Unwanted Power (Cyborg), Thrill of Adventure (Changeling) , and for bad guys Mercenary, Nihilist, Power Lust, Psychopath (the Joker), and Thrill Seeker.
Omnifray has a "spiritual status" system that describes souls as being either Primordial (pagan), Redeemed (belonging to the angels), Excommunicated (cast out from redeemed status), Fallen (spirit belongs to lower powers) and Unbidden (mystical).
 
 
Numerical (Quantitative) Alignment ("Idiom")
As well as the description-based alignment systems, a number of games use use numbers to define how good/evil characters are: In Kirk's analysis of RPG design work linked earlier, these are described as the "Idiom" pattern. This gives a number that's rollable against for some sort of check, and can be adjusted up/down more easily for PC behaviour. These systems may be less descriptive of NPC behaviour.
 
*West End Games' Star Wars gives characters "Dark Side Points" for committing evil acts. Force-sensitive characters are more susceptible to the Dark Side and so walk a much finer line as regards gaining dark side points. A roll less than current Dark Side points on d6 results in the character becoming (at least temporarily) an NPC. SAGA reportedly has a rule where dark side points automatically add to Use the Force checks.
 
*HarnMaster rolls a "Morality" score which determines a character's behavioural code, and which deities they may worship.
 
*Vampire gives characters a "Humanity" score, which is eroded by inhuman acts unless the character can pass a Conscience roll. The lower the score, the more horrific the acts that could force a check for humanity loss. Later supplements added the idea of "Paths" which characters could switch to instead of Humanity, giving those vampires a different set of limitations.
 
*Indie games may have personality traits which go beyond just regulating character behaviour (as with Vampire) to provide extensive bonuses/penalties to a character on non-alignment-related checks – a not-so-subtle incentive to the player to behave in line with game expectations. Humanity in Sorceror for example determining if a character can bind demons (if low) or dismiss demons (if high).
 
 
Inescapable Alignment
By this I mean that a particular set of morals is actually hard-coded into the game - all PCs behave or suffer penalties, almost as if everyone has to play e.g. Lawful Good.
For instance, Marvel Super Heroes mandates a specific code of conduct for all heroes, in accordance with Silver Age comic book codes; characters suffered loss of "Karma points" for behaving unheroically e.g. killing people rather than subduing them. Villains had a different code of conduct which gave them karma for upholding genre conventions e.g. leaving PCs in death traps with one inept guard. This in effect gave a two-alignment system, though players were always "Good guys"; rough types such as Wolverine or the Punisher just had to live with less points than other characters.[/FONT]
 
 
More Complex Systems & Other Elaborations
*GURPS and the like may handle alignment-related issues via Merits and Flaws which control character behaviour to an extent (e.g. Heroes may get extra points for Compulsive Honesty or Self-Sacrifice). These are more complex than a simple Good/Evil switch; they tend to limit character development greatly (it requires lots of points to remove the flaw) but at least attempt to reward characters proportionally with their role-playing handicaps, and give more potential to customize a character's behavioural limitations to their culture.
 
*Central Casting (a series of generic supplements for any RPG for determining character background) determined a character's "Alignment" with respect to good/evil by rolling their personality traits and determining how many Lightside traits were present vs. Darkside traits. A character's background was rolled on the tables with some events giving lightside, darkside, or random traits.
 
* Dragon #173 had a fairly weird Priority system for D&D which had characters defining an order of importance between aspects such as Deity, Sovereign, Homeland, Comrades (the adventuring party), Race, Family, and Self. Lawfuls ranked all of these, while Neutrals ranked only three or four of these and Chaotics consider them all equally important (or unimportant). Evil characters ranked Self at the top of their hierarchy. In this system characters also had to choose behaviour linked to their traits (e.g. the dwarf honours Family by feasting with his clan when in town); Chaotics received odd superstitions to balance their relative freedom.
 
*Pendragon uses numbers to define personality traits, but with 13 or so different traits rather than a single good/evil axis.
 
*Dying Earth has a sort of anti-alignment system in which characters are vulnerable (unless they buy Resistances) to various temptations such as arrogance, greed, food, sex, laziness, and nitpicking , designed to create amoral characters which make shmucks of themselves as in the original Dying Earth books.
 
*Runequest Cults have come up in discussion of alignment before; RQ e.g. Cults of Prax includes lengthy descriptions of given cultures/religion including beliefs, likes/dislikes, and behaviour restrictions for various levels of involvement in the cult. Touched on here:
http://www.therpgsite.com/showthread.php?t=19345 (http://www.therpgsite.com/showthread.php?t=19345)

*DungeonWorld has "alignments" which are a single behavioural trait that earns XP, named 'Good', or 'Neutral' or 'Chaotic', etc. - what the trait demands varies by character class. Arguably these could be considered to be mostly just personality traits rather than a true alignment system, though the general descriptions also prompt assumptions on how characters should behave.

The following is a bit out of order again, sorry...
D&D and simple class-based classes may just have binary weapon proficiencies - different classes being proficient with, or allowed to choose, different weapons. (Very rarely in 2E a weapon might cost multiple 'slots' to learn, e.g. the assassin kit could learn a non-thief weapon for 2 slots, or Masque of the Red Death (1890s-themed) characters could learn 'rare' medieval weapons for 2 slots).
AD&D also had a 'weapon specialization' which cost multiple 'slots'. 2E, not having a 'feat' or special power system, sometimes gave specific weapons unusual benefits for specialization e.g. special Dark Sun weapons in Dragon #185.

Skill-based games: these may have a single "Melee" or "Fighting" type skill for all melee weapons, or different skills for multiple weapons (Doing the latter removes the ability of the high-level D&D fighter to just pick up a lead pipe and beat anyone to death with it, though).

HarnMaster "opens" new weapon skills at a higher default (multiple of the skill base) for experienced characters, but this is still a fairly limited benefit. LegendQuest as noted earlier in skills, has variable-breadth skills which let a character buy either general "melee" skill levels, or specific weapon skills.
Even games with a single "Melee" type skill may allow "skill specializations" or the like with specific weapons; these may be a specific form of skill or purchaseable as an advantage/disadvantage.
Recon has separate skills for primary and off-hand weapon use, for each weapon, while other games sometimes make 'ambidexterity' a weapon proficiency e.g. 2nd Ed. D&D.
FantasyCraft has weapon tricks for various weapons, as well as short feat trees: some feats let characters apply weapon tricks for other weapons, like performing club tricks with your flail, hammer tricks with greatsword, polearm and staff tricks with spear, etc.
 
Weapon proficiencies & magical weapons
Fantasy RPGs usually have magical weapons which appear, which might be randomly generated or placed as fits the GMs conception of their world. Weapon proficiency systems are one factor to consider when determining how available magic items are; if the two aren't compatible you may get either of the following
a) a magical sword etc. goes to the character (/party), but is considered by them to be trash because they can't use it.
b) a magical sword etc. goes to a character which is a benefit to them, but which prevents a character using a number of their abilities (feats, etc).
 
Ability to create magical weapons can prevent proficiency/weapon mismatches. However ability to e.g. produce a +3 bastard sword from nowhere is of limited use if one was going to appear in game anyway.
 
Skill based games with multiple combat skills may have a "use it and it improves" diminishing returns improvement system (e.g. Runequest); therefore unlike some level-based or point-based games characters aren't permanently behind in the long term if they change weapons due to a new item dropping.
 
Feats: D&D 3.x's "feat" system means optimal use of a weapon may requires not just proficiency but also one or more feats; any ranged attacks require Point blank Shot/Precise Shot, reach weapons improve in usefulness with Combat Reflexes, greatswords require Power Attack, quarterstaffs or the various "double" weapons require Two Weapon Fighting, multiple thrown attacks requires Quick Draw, and so on. A warriors' feat choices lock him in to one or a few weapons even though they are theoretically proficient in all martial weapons, even without a character having taken wholly weapon-specific feats such as Weapon Focus, Weapon Specialization, or Improved Critical.
A character has set resources based on their level, so a character who changes weapons (i.e. who takes Weapon Focus: longword, then gets a magic scimitar thats better) is permanently behind an appropriately equipped/constructed character. Consequently, the system is designed to allow PCs to dump awesome magic trash at the item mart for conversion into something useful.
Compare this with say 2nd edition (where a character could pick up a new weapon proficiency every 3 levels or so and so learn to use new items), or SenZar (where characters but can learn a new weapon in just days of training, with no xp cost/feat cost). However even a complex feat system could support characters who know multiple weapons; this just requires characters get enough feats to allow a range of weapons, feats designed to work with various weapons, and splat bloat to not continually expand lists of add-on abilities for particular weapons that encourage specialized builds.
 
Weapon proficiency may be modified by race e.g. races getting particular weapon proficiencies/free ranks in weapon skills for free.
Star Wars' Saga edition is interesting in that many races hail from primitive worlds (e.g. Gamorreans or Ewoks); primitive races generally didn't receive weapon proficiencies in e.g. blasters normally given by class, as a racial disadvantage. This generated a slight perverse incentive for such creatures to be Jedi, since Jedi in any case come with no blaster proficiency (so not suffering any handicap). This sort of ability wouldn't need to be a codified racial feature at all in a skill-based system, where the GM could limit skill selection based on background and potentially have 'civilized' ewoks if that made sense for a given background.

 
Calculating weapon proficiency bonuses:
*In some systems, different weapons may have different skills. Skills may also have varying breadth e.g. LegendQuest, so that a character might have some general "melee" levels (more expensive) and some weapon-specific skill levels.
 
*in some systems different weapons may have differing controlling attributes - particularly in systems with lots of attributes (ROAR used different averages of about 3 attributes per weapon). This can be used to implement different racial weapon preferences as an emergent property (as races have different attribute raises). Done clumsily this can cause oddities; consider how in 4E D&D, player's handbook dwarves gain bonuses to Con which improves their warhammer abilities (via fighter powers) and potentially crossbow skills [Steady Shot]; however half-elves likewise have Con modifiers... and so are good with warhammers and crossbows.
3E D&D defaults melee weapons to Str, with 'light' and some other weapons being able to instead use Dex to hit if a character takes the "Weapon Finesse" feat; 5E D&D separates 'light' from 'finesse' so some light (offhand) weapons can't be finessed and also lets finesse add Dex to damage (possible foobah: hand crossbows are described as 'light' but TWF, the only thing that keys off the 'light' property, only work with melee or thrown weapons). Thrown weapons can use Str to hit. 4E D&D applies different modifiers to both hit and damage depending on power used (e.g. paladins generally do +Cha mod when hitting things with weapons, and need to take a 'Divine Might' power if they want to occasionally deal +Str mod to damage). Marvel super heroes used Fighting to hit, Str for grappling, and Endurance (the basis for movement) for charging, as well as sometimes using separately rolled power ratings in place of stats. HarnMaster (d%) modifies ranged attacks for PER as well as double-DEX.
 
*Level based games usually have a level-based attack, plus either proficiency bonus or non-proficiency penalty; older D&D versions (3E and before) applied a penalty for non-proficiency, while 4E applies a bonus to hit for being proficient (+2 or +3). Older D&Ds gave a variable penalty (-2 to warriors, up to -5 for wizards; half if a related weapon was known) while 3E gave a flat -4 penalty (though warriors were proficient by default in all weapons). Kyle Aaron has pointed out that players are more likely to "forget" penalties, but the penalty does remove an extra addition step from attack rolls; also bonuses also don't change between different weapons, and PCs will generally only rarely use non-proficient weapons anyway.
4Es defense system does simplify (and balance) 'touch attacks' compared to 3Es system, but not particularly better than most alternative armour methods (i.e. armour as damage reduction, or a separate bypass roll). As implemented it results in martial powers - which add weapon proficiency bonus - having quite high chance to hit against non-armour defense.
 
Other elaborations:
*Palladium's Ninjas & Superspies lets some characters learn multiple Martial Art Forms, each of which has their own separate base # of attacks, bonuses and allowed manuevers - flavourful ("My Snake Style will overpower your Crane Style!"), but requiring separate sets of combat info for each Form known.

Strength Minimums
*a little off topic (but this doesn't really deserve a full topic of its own) some systems have Strength minimums for different weapons -
Tunnels & Trolls, GURPS, and Savage Worlds are examples (and T&T also has DEX requirements). Savage Worlds lets characters use weapons with damage dice larger than their Strength die, but with damage capped. Tunnels & Trolls (which has 2-minute combat rounds) assigns minimum requirements ad hoc, and gives characters damage to their Strength equal to the differential between current ST and ST-required of the weapon, so characters using weapons that are too large tire faster and faster, eventually taking excess damage to CON.
T&T Deluxe replaces this with a Saving Roll to avoid dropping a weapon outright on Str or Dex (L1 for 1 pt short, L2 for 2 pts, L4 for 3 pts, L8 for 4 pts, an insane L16 for 5 points - the design problem here being that the save is on the deficient attribute so by rolling the same stat and increasing the level, is essentially 'double dipping' a penalty and guaranteeing its impossible e.g. a character with Str 10 using a Str 15 weapon has to make a Level-16 Str roll, i.e. has to roll 85 on 2 six-sided dice (doubles roll up). About the only thing that could modify the base would be a talent (skill), created with GM approval.
D&D 3E imposes Str minimums for purchasing some particular weapon proficiencies (i.e Bastard Sword and Dwarven Waraxe) although characters can use these two-handed as 'martial' weapons. It also has 'composite longbows' which have varying minimum Strength, although the modifier varies only how much of a character's normal Str-modifier applies to damage; 4E dropped this when it adjusted bows to add DEX mod rather than STR mod to damage (despite bows with different 'pulls' being a thing in reality). T&T actually rates bows of different 'pulls' as different weapon types - Extra-heavy, Heavy, Medium, Light and Very Light bows are different weapons with different base damage dice, DEX required and range; arguably T&T wizards should be able to use 'very light' bows (as 2d weapons)- though nothing larger. It also allows bows to be 'built' or 'backed' [composite] for extra range/damage adds, at extra cost.
Potentially bows with different 'pull' could have different rates of fire, as well.
 
Strength minimums can be annoying in that they limit character's available weapon proficiencies; if a character can increase their STR via levelling up or magic, they also end up changing optimum weapons, possibly making previous weapon proficiencies or magical items redundant. (T&T does this deliberately - some weapons are deliberately out of reach of lower-level characters due to their STR or DEX being too low, or excessive GP cost - but at least as there are no weapon skills, points can't be wasted). T&T also has the issue of characters being 'double hosed' by poor ST and/or DEX, with low scores both limiting characters to poor weapons and also giving additional penalties; the Beta playtest of the Deluxe edition of T&T removed attack penalties for low scores for that reason. The overall design where some weapons are clearly 'better' than others, is a fairly different paradigm to D&D where for the most part it aims for a 'level playing field' where you can pick any 'martial' weapon and have it be equivalent to any other. However T&Ts approach is perhaps inevitable, given its simple combat system where everyone on one side rolls their dice and adds them together, losing side taking the difference as damage. The 4d+1 weapon is distinctly better than the 4d weapon, without it being possible for hit penalties, speed factors, or other variations, so its Str- and Dex- required system that creates winning and losing weapons but limits access to the winning weapons, is maybe the only alternative to just having all weapons be exactly the same.
 
Related to this:
*Lord Vreeg's Celtricia game has separate STR/DEX requirements depending on whether a weapon is one-handed or two-handed.
 
*A Strength minimum system might replace 1-handed or 2-handed weapon rules, or awkward weapon sizing rules: a character can use whatever weapons their total Strength permits, though this requires Strength follow an appropriate range (i.e. haflings actually have to be substantially weaker than humans, and it has to be difficult to reach a Str such that using a greatsword in each hand is possible!). Damage directly proportional to Strength-required can also balance two-handed weapons vs. two-weapon-fighting i.e. the Strength 15 character might be able to use a Strength required 15 weapon (a greatsword) in two hands for 3d6 damage, or a Str-required 10 longsword (2d6 damage) + a Str-required 5 shortsword (d6 damage). (I first saw something like this proposed as a houserule for Tunnels & Trolls). This might not work well for characters with > 2 arms, however.
Note that T&T normally lets a character use two weapons if they can meet the combined STR/DEX requirement, but some weapons are also explicitly called out as two-handed.

*The Fantasy Trip has larger weapons having higher STR-required, and this replaces a Str damage bonus (there's no benefit for using a smaller weapon). It does however adjust unarmed damage for Str.

*Cadillacs & Dinosaurs has a Str-based recoil system for firearms where a character multiples [recoil factor of weapon x number of bursts fired] and, if this exceeds their Strength, the amount over reduces to-hit target numbers (or total dice rolled for automatic weapons fire - cf. autofire notes in combat moves). So, its interesting in that Str-required isn't exactly set, but instead increases as you opt to take more attacks with a weapon.
-similar to that, Nexus: the Infinite City (precursor to Feng Shui), a 'burst' is treated as giving a bonus to-hit rather than an extra attack, but likewise increases Str-required.
-slightly similar to the basic rule, Amazing Engine's "Bughunters" game has Str-requirements for recoil by dividing weapons into "light, medium or heavy" recoil categories; these effectively just translate to a 30, 45 or 60 Str ["Fitness"]-requirement with an extra step. Penalty to hit is -5% per 10% Fitness under the minimum.
-Shadowrun 5E has a recoil # calculated at [1 + 1/3 Str round up] + any 'recoil compensation' bonuses; bullets fired subtract from that and any remainder is the dice pool penalty. It could be more realistic in some circumstances (troll using handgun vs. mage using same handgun), but if characters are assumed to be using 'size appropriate weapons to start, it gives stronger characters an improper advantage, maybe; larger guns should generate more recoil per bullet and the old 'flat' system with no Str adjustment would model it better.

*some rules I was experimenting with let characters 'Push' their Strength as an action to meet Str minimums for weapons, which would therefore apply a multi-tasking penalty (for making 2 actions, the Push and the attack) to an attack roll made the same round.

Either Strength minimums, class-based weapon proficiencies, or complex sets of weapon effects can all serve to ensure that most of a weapon list is useful (depending on what character is being played). Otherwise just picking the biggest damage weapon ends up the best choice (for instance in Unisystem's Army of Darkness, you'd be crazy to use a gladius [Str x 3] since an axe is [Str x 5] with no other drawbacks, and uses the same skill).


Weapons Design
The following doesn't exactly fit here, but in absence of a better place here's a discussion of weapons keywords.

An example of how multiple, somewhat abstract keywords can be slightly complex:
e.g. in 5E the hand x-bow has the 'light', 'loading' and 'ammunition' keywords; as a ranged weapon the light is irrelevant to most purposes to which that normally applies. The Crossbow Expert lets someone ignore the loading property (so can use as many times as they have attacks; but still requires a free hand to reload (the ammunition property). The net result is that its impossible for a (2-handed) character to dual wield hand crossbows firing as a bonus action, but can fire with 1 hand crossbow twice easily. (a character can't benefit from both TWF and Crossbow Expert as both use up bonus actions).

https://www.reddit.com/r/DnD/comments/376m7u/dualwielding_hand_crossbows_the_final_word/ (https://www.reddit.com/r/DnD/comments/376m7u/dualwielding_hand_crossbows_the_final_word/)


recent edits: T&T weapons design

(http://i1239.photobucket.com/albums/ff507/BSJ17/cyclops4.jpg)
 

Quote from: InkyHat(From here (http://forum.rpg.net/showthread.php?549239-I-m-tired-of-effects-based-power-amp-magic-systems/page5)) I thought Mutants and Masterminds and other effects based powers systems were awesome.
And then I tried to play M&M.

"I slam the door in his face"
"Roll Environmental Manipulation to close the door, and Stun to see if it stops him."
"I was using my hands... and I don't have either of those..."
"Oh, then spend two Hero points to acquire them for the scene."
-Does So-
"Okay, you succeed, he's surprised that you slammed the door in his face."
"I yell to my friends in the other room that the bad guy just showed up."
"Roll Super-Ventriloquism."
"You're shitting me right?"
"Yeah."

This use of the term 'effect-based' is a term first used by Champions/ Hero System to describe how an underlying system can be re-skinned to provide a variety of effects. Note that 'effect' in this context is entirely different to I normally mean by 'effect' e.g. around page 4, i.e. a term from DC Heroes for the amount of damage or other outcome from an action.

This is the first of a few posts on super powers/character power types; this should end up including psionics, magic (divine or arcane), mutation-based super powers and possibly “Chi” martial abilities.
 
This post deals with generic "super powers" e.g. of the comic book variety, which I'm calling the "mutation" power type. This is the sort of abilities seen in e.g. mutants like the X-men; Gamma World type mutant characters function IMHO similarly.
 
 
Defining Characteristics
A mutant (or superhero), in contrast to other power types (particularly magic) generally has only a few abilities, but these can be very powerful. Depending on system, mutant powers may have a limited number of “power points” or may be unlimited use. Power points can tie into an attribute used by normal people if imagined as being ‘fatigue’ (e.g. Hero System’s Endurance, Villains & Vigilantes Power) or may use some alternative pool of “super power energy” that is zero for non-mutant characters (e.g. Aberrants’ ‘quantum pool’, calculated from their Quantum attribute; Savage Worlds' power points). Characters may sometimes be allowed to burn Hit Points or Con Points for extra power points.
Mutant powers may improve with experience, either with all powers having level-based effects (Palladium), or with individual powers having ratings that can be raised by spending XP - either their own specific ratings or potentially some sort of 'power use' skill. Powers may require some sort of activation roll, or function automatically – usually powers are automatic. Mutant abilities can include super attributes, particularly super-strength.
 
Note that whether a power requires an activation roll to use is a separate issue to whether or not the power is binary (yes/no) - the two approaches go together most easily, but a power can also work automatically and have an effect that's variable, or have a fixed % chance of working despite being binary (Golden Open Gaming for d20 needed an 11+ d20 roll to activate a super feat, for example). An activation roll may make buying more of a power useful despite a fixed-effect.
Note that even if a power theoretically functions without a separate roll, it may sometimes have separate failure chances dictated by its design and other game rules, e.g. a defensive power might need a successful Initiative roll to pull off in time.




In a few games, super powers may be the only power type: this includes mutant heavy games such as Gamma World, or Aberrant where a default super type are "novas", evolved humans.
 
In other games a single super powers system may be used for various other power types beyond mutations, potentially including e.g. gadgetry, psionics, or even magic; systems with this setup include Savage Worlds, Hero, and Mutants & Masterminds. In some cases there may still be distinct limitations/advantages for a power being e.g. psionic or magical in nature (e.g. Savage Worlds’ multiple Arcane, Divine, Weird Science and “Super Power” background edges), while in others this is purely flavour (Mutants & Masterminds), at least barring other characters having powers designed to tag from that (e.g. someone else selecting a disadvantage with a 'not against psionics'-type limitation).
The Invulnerable RPG has various 'origins' which set power source e.g. mutant - biological, battle suit - tech, etc. Characters can split their points between multiple origins and so have multiple power types (creating e.g. Wolverine type characters); additionally it makes 'tech' powers more common since a character can take the 'Implement' power modifier to make another power due to a super-device.
Effect-based games may be quite good for converting characters between systems, since a mechanical framework can be chosen that somewhat matches the original system, whatever it was.
An effect-based approach is somewhat incompatible with a 'class' system for characters (why would you separate powers into two piles -one for each class- when the underlying basis for both sets is identical? How can you make the classes different if they are?) though they may have archetypes.

 
A system may sometimes be designed around one power type mainly, with this 'reskinned' for rare or obscure cases - making a sort of bolt-on effect based approach. For example, mutations in Gamma World 5E (the "d20 system" based version) are generally just for mutants, but there's a "Feral Machine" robot type, which rolls a number of "pseudo-mutations", based on these machines having wearing down of various parts or jury-rigged extra parts.

 
Rating Powers
Methods for determining how strong powers are include:
 
a) Fixed effects depending on character level (Palladium).
 
b) Individually defined power ratings (e.g. Marvel Super Heroes; 2nd and 4th edition (1992) Gamma World). MSH randomly rolls power ratings on the same scale as attribute scores, which is often convenient as a basis for other game functions; Powers range from Feeble (2) to Unearthly (100) and beyond; Savage Worlds’ “Super Power” arcane background edge lets characters buy a power as a skill (which in SW have the same scale as attributes). The 1st ed. of Mutants & Masterminds bought powers as skills as well (level-based ratings) though probably an attribute-based model for powers would be better.
Power ratings sometimes directly determine damage (e.g. in MSH, an Incredible (40) rated power does 40 damage basically regardless of which power it is), while in other systems damage is assigned based on the power, with power rating perhaps adding a bonus e.g. in Gamma World 4E "Hands of Power" might do 3d6+ mutation modifier damage, while "Thorns" deals 2d6+modifier and "Quills" is d6 with no power score. Having power rating directly determine damage does generate a huge incentive to buy one attack up to maximum and spam it continuously.
Probably the best example/argument for power ratings was DC Heroes; its AP system lets the same power set work for both 'street level' and 'cosmic level' games, and exactly defines a powers' range, damage, duration etc. in real-world terms.
Most 'successful' designs using power ratings on this scale use random-roll power rating determination, since point-buy will lead to potential abuse (and unlike attributes, number of powers may vary meaning a purchase system has to give reasonable numbers whether a single power is bought, or several).
Gamma World 4E power ratings also made it possible to add level-advancement to powers e.g. Espers and Enforcers gain +1 per level to mental and physical mutation power scores respectively. Some powers are random but don't have a 'power rating' e.g. multiple arms being just +d4 arms. Potentially, these powers could be instead designed to be power-rating-based (i.e. a power rating of 5 = 1 extra arm, 10 = 2 extra, 15 = 3 extra, etc.) which would give more of a 'curve' to results than d4 and/or be more consistent - but would actually lead to problems with Enforcers growing more arms as they went up in level. Consistent ratings are useful for the purpose of purchasing powers and perhaps other manipulations of the score, like 'damage' to ratings from 'power nullification' type powers, though ad hoc costs without a consistent power score are possible just more complex (HERO).
One workaround for the issue that point-buy powers are incentivizes to spam a higher-rated power continuously is seen in JAGS special abilities book (free from the jagsrpg site); extra attack powers cost 1/3 the cost of the main attack power. Players can also be incentivized to have multiple attack forms if resistances to particular damage types, etc. are reasonably cheap or effective (in the same way multi-classing can be more valuable if a single-class character can end up fighting a monster immune to their main shtick).

Powers bought from a point budget are more likely to have variable costs (e.g. you can spend 10 points to buy a power worth 3 points, a power worth 2 points and a power worth 5 points) whereas this is difficult to do with randomly-rolled powers (compare "roll four mutations" a la Gamma World - no way to implement different costs). Different costing can be done in a very basic way by having separate lists of 'minor' and 'major' powers e.g. Palladium. This also reinforces having power scores for games with random-roll powers - as with skills its typically difficult to have variation for both number of power levels and different costs for each power.


 
c) Power working with an ability check (i.e. 7th Edition Gamma World, a variant of 4E D&D)
 
d) A power may have a skill rating to use, in addition to a rating of its own (e.g. Pathfinder has a Fly spell based off caster level, + a Flying skill for using it).

e) Some powers may be binary – you have the power or you don’t.
(Even in this case, it may be possible for the system to vary how good character's are at powers by adding other powers - 'meta powers' if you like - that apply advantages, let characters spend more PPs, add bonuses with them, or whatever.Its just a question of whether this is frequent enough that it becomes more awkward this way than just having ratings).


Including attribute modifier in a power formula has an unbalancing effect by increasing the importance of that attribute for a character. Generally skills are useable untrained, so that attributes can be important on skill checks whether these are learned or not, but a character who gets several unique CON-based Powers will have their CON become more important, though its cost is unchanged.
(Buying abilities separately, but up to a cap determined by attribute, mitigates this, e.g. Linking in DC Heroes).
 
As an example Aberrant has powers which are rated from 1 to 5, but a normal check is [attribute dice+power dice] - similar to how skills operate in its parent Storyteller system. However, for standard power activation checks attributes and “Mega Attributes” were more important that power rating, though some things (such as damage dice) depended solely on power rating. This caused power rating to be very important for some powers (Energy Blast), and not worth increasing with others, even though both had the same per-point cost. Advantages also increased the cost per point of power rating, so these were more affordable at lower power ratings.
 
Separate power ratings also decrease overall impact of high attributes on the game (good for game balance), reduces racial typecasting (i.e. all of race X are good with power Y).

Superhero games are usually more likely to have different power ratings for characters, whereas post-apocalyptic games have more yes/no abilities - partly because that generally works fine for creepy mutations like crab hands or antennae, partly since PA games are fixed at a lower power level and don't want to simulate planet-shattering potential levels of power.
 
 
Power Determination
 
 
Powers might be determined by random roll or be point-based.
Pros/Cons of random rolling:
 
*faster character generation
*does feels appropriate (IMHO) for Gamma World type games.
*doesn’t allow players to build specific concepts
*possibly unfair. A random system might just randomly determine which powers a character gets (which may be OK if the designer has designed an array of fairly useful powers; possibly separating them into “major” and “minor” lists before rolling), but if a random roll also determines how much of each power (i.e. +d4 extra arms), hopeless or overpowered characters may be possible.
Gamma World has traditionally used a random array of mutant powers; earlier editions gave each character d4 physical + d4 mental, while by 4E PCs only rolled for the 'split' of mutations (0-5 physical based on a d6 roll, with the remaining 5 mutations being mental; more might be gained still via a roll on the table of 'roll twice', or extra d3 mental from a 'dual brain', and a bad roll could give some 'defect' mutations). Earlier ancestor Metamorphosis Alpha lists opposing mutations (e.g. a character can't have both 'wings' and 'total carapace'). Gamma World's power list is sometimes quirky since some mutations are more for the monsters - e.g. "symbiotic attachment" is more designed for a "Puppet Master" type monster that attaches to a PC (control via physical control, though it could be slightly useful for a beast riding character).
The more recent Mutant Epoch RPG has another very impressive list of specific (non-effect-based) random mutations; its notable for including with appearance penalties for each disfiguring mutation; RPG deadEarth had a huge list of "radiation manipulations", with the possibility of getting more in play; it also had a number of interesting 'meta' mutations (removing or altering other mutations) but also oddly included a number of personality disorders, religious observances and other things on the tables. ("The danger on deadEarth isn't that the Giant Radiation Ants will eat you. It's that they'll call to your house with pamphlets. Or iron and fold your clothing. -Balbinus). PCs could also roll fatal mutations in character generation (if not their last mutation a character could keep rolling to see if another mutation cancelled the effect). Number of radiations rolled increases with age (as does skills), though stats decrease. Mutations formed a 'list' with some mutations have position-dependent effects e.g. affecting the prior rolled mutation or mutations 'above' them in the list only. See rpg.net thread  http://forum.rpg.net/showthread.php?473443-Necro-deadEarth-why-isn-t-this-game-on-anyone-s-quot-Worst-Games-List-quot.
Another mutant RPG, Mutazoids, has characters roll for various features like head shape, eyes, etc. separately for each.
An interesting twist on random mutations might be to have each mutation randomly roll body location (one 'spikes' mutation that could have different effects in different spots). Defect side effects could happen if it replaces what's normally at that location (the way a mutant gene replaces a normal version of a gene), and/or there could be a roll to see if it just is extra ability, and perhaps a character might be allowed a number of re-rolls or shifts around which might have to be used if someone rolls something lethal, like both lungs being replaced by something except gills.

7th Ed. Gamma World (the D&D-4 compatible GW), gives characters mutations that change continually, based on power cards, due to reality flux (7E GW is partially radioactive but is due to a collision of a huge number of parallel worlds, not just nuclear war). While still random a character's power suite is only stable inasmuch as its based off the player's deck.

(http://i1239.photobucket.com/albums/ff507/BSJ17/GammaWorld_zps10076eeb.jpg)

Point based or selectable lists of powers - are used to let characters be built to a particular concept. In purchase systems Limitations to powers frequently have a cost per point (Hero, DC Heroes), though this makes accounting more complex. As noted previously under advantages/disadvantages) Hero distinguishes between adjustments applied per point and “adders” (which have a base cost). Systems may also have varying costs for powers depending on how powerful they are. MSH lets characters raise a score one "rank" by choosing a limitation, even though it generates powers randomly; this provides an erratic increase in rating, due to the way rank numbers increase (2/4/6/10/20/30/40/50/75/100), though allowed limitations also change between ranks.
 
Random roll power determination will usually give weird sets of powers which may be fine (the idea being that a Gamma World mutant should be as weird as possible). Superhero games using point buy may desire characters to have 'themes'; Aberrant for example has no specific rules, but, expects the GM to enforce character-building to some sort of motif (it being suggested that's psychologically necessary and only a couple of super-beings like Divis Mal have outgrown that). "Mutant City Blues" for detective game Gumshoe apparently has a 'Quade Diagram' where less-related powers cost more points; this is intended to support the detective idea as multiple very-unrelated powers could suggest multiple perpetrators at a crime scene.


Power Design
 
Evolution in design of power lists has tended toward more flexible, generic powers. A game might have separate mutations for “Radiating Eyes” (bolts of radiation from eyes), “Hands of Power” (bolt of energy from hands) and “mental blast” (telepathic attack), or these could be covered by a single “Energy Blast” type power. More broadly, a single damage power might include a variety of attacks.
 
Broader powers work better where power advantages or limitations can be applied to better adjust exactly what a power does, or where there is a loose rule framework that allows reasonable interpretation (Savage Worlds would let you get away with saying your Bolt is “fire” and having reasonable effects; in HERO you may need to define detailed advantages/disadvantages for “continuing to burn” or “doesn’t work underwater” if you want those things).
Another thing to consider with broader, more flexible powers is that rolling several abilities into one can complexify rules text (if it needs to note caveats that previously applied across several powers). Consolidation of powers that have similar mechanics into one can be risky if the abilities should be costed differently e.g. (from one of my games) Extra Legs and Extra Arms might both give an extra reroll or action, working similarly, but the ability to make an extra attack is probably much more valuable than an extra movement roll, so they may be better off as different powers.
 
Unusual uses of Powers
PCs occasionally attempt to use powers in unusual ways or beyond their nominal limits.
 
Hero has a power use skill which can be rolled against for unusual situations - Superman crushing coal into diamonds, or frying an opponent you can't hurt with your Jet Boots (which are actually the Flight power). However, using a given trick more than once requires permanent point expenditure to buy whatever power is being copied.
 
Similarly, TriStat dX lets the GM give characters 'attributes' (powers) for free, giving them a cost (from advancement points) if 'circumstances change  and the attribute becomes useful on a regular basis'. Consequently, a player being creative may get charged character points, which they wouldn't if they didn't work out a use for it.

MSH has Power Stunts which can be learned; each attempt to use a stunt you don't have costs a considerable number of Karma points (which are both 'safety valve' points and an advancement currency), and requires a power roll at Red (most difficult) intensity. 3 successful attempts adds a Stunt to the characters' capabilities permanently, for free use thereafter. This is one of the only instances where using advancement currency to boost die rolls works well, IMHO; in any case I find this slightly more logical than the Hero approach, and it gives away no freebies.
Defined Marvel Super Heroes characters sometimes come with some 'power stunts' they use from the comics, as well as some variations in their individual power description from the default listed.
 
DC Heroes doesn't have unusual situation power use rules, but does allow expenditure of Hero Points to temporarily increase ratings to increase areas/durations/etc ('Pushing'). Potentially a character could buy a low rating in a new power on the spot (with GM permission) and immediately Push it for greater effect, but the point costs involved would be quite high.
 
Aberrant allows temporary duplication of some advantages on powers with a Quantum roll ('maxing' a power). This costs power points and botching a roll results in a character gaining Taint, a somewhat bad thing since this permanent gain gives a character physical and mental aberrations.

Unusual elaborations on powers system
The Mutant Crawl Classics (MCC) variant of Dungeon Crawl Classics has mutations which appear similar to its spell 'klutz' system, with use of a mutation requiring a roll that can give a defect or alter the landscape, etc.  Passive mutations (like # arms) can be re-rolled when a level is gained (rolls get +level so a reroll will eventually be worthwhile; Luck or taking ability damage for eating radioactive stuff also give bonuses). Defects also have their own tables, with a '1' giving a reroll (potentially better than a '2') but usually also a second defect, and a 20+ sometimes being beneficial; re-rolling defects with level advancement may change them excessively i.e. an 'oversized body part' might be a head one level, then hands another level (different penalties).  MCC characters can also gain or lose mutations if they roll a 1 (lose) or 20 (gain) making a Fort save vs. radiation damage; the craziness of MCC is such that a character might roll a 20 and gain a mutation, but then its a defect, then another good roll makes it beneficial.
Appearance is level-based in MCC - a mutant gets a level-based initiative bonus from 'horror' -though specific mutations also have set adjustments e.g. to AI recognition, with defects likely to become less horrific after some level advancement re-rolls.

Note: one interesting comparison between systems is that what may be a "power" in one system may be just a built-in feature of all characters in another system, due to changes in the underlying abstractions of the system or how values are allowed to scale. Examples here include:
3E D&D spell/item healing vs. 4E D&D 'healing surges'
Bonus actions from Haste only, vs. bonus actions from the action system
Armour vs. 'soak'.
Luck as a special super-power vs. built-in rerolls (bennies, Willpower, karma), or even an extra dice on all actions (Savage Worlds' 'wild die')
Reality control or Wish as a power, vs. shared authorial control for players.
'Powers' in this sense could stretch to include things given by magic items too: a 3E D&D character can freely level-up and take a level of a different class, while an AD&D character (who wasn't human) could do that with a "Hat of Difference" (1e Unearthed Arcana/2e Encyclopaedia Magica).

A result of that, for instance, is that converting a written adventure from one system to another may sometimes involve adding extra powers or magical items, to try to maintain a particular outcome or have a character with the same sort of feel. This could also be an approach when trying to convert PCs between systems, but may be seen as less kosher - preserving system 'artefacts' in a different rules set being to give a converted character an unfair advantage over native characters (generated in that system).

Edit notes: note on PA games(*), MCC note (*); 'meta powers' (*); DC Heroes note (*); Invulnerable note (*), most powers-on-attribute-scale systems being random note (*); power activation notes (*), Feral Machine note (*)

Flexibility of powers
Comparing say supers vs. wizards: a super might have only one or a few abilities, while a wizard-type character might have several to dozens of spells. [This difference is forcibly avoided in effects-based games; wizardry might sometimes be explicitly defined as a power to get around problems there, or IIRC Hero has 'power framework' rules and the like].
However, super abilities would tend to be more flexible; they may be equivalent to several 'spells' each in terms of what can be achieved. One thing I found interesting for example (in a game I'm running) is to compare Gamma World 4E telepathy with AD&D psionics; Gamma World has one power called 'telepathy' with a number of functions including scanning and communication; by contrast in 2E AD&D there's a somewhat wizard like 'psionicist' class which has an entire 'discipline' called Telepathy, including contact (to get telepathic powers to work on a target), one-way telepathy that can distract (send thoughts), two-way telepathy (mindlink), defense modes, attack modes, etc. - with definitions of whether language is necessary, exact ranges, etc.
One Gamma World power does a noticeable chunk of what the whole discipline does. Given the choice between which approach to use, the detailed list of specific effects would also let someone pick up a few unrelated powers that could be useful.

Post-apocalyptic mutant games do vary from superhero games in that a superhero is most likely to have a few powers that are similar thematically, while a mutant has a varied assortment of weird powers. Supers games may have 'big' powers with various special abilities, or extra enhancements.

the superpowers section seems a bit "Aberrent heavy" I assume this is becuase it's your go to supers game. However it feels a bit odd becuase its not in most people's top 5 Supers games (I would predict these would be Hero, Champions, M&M, MSH, V&V...), unlike using D&D as a standard for Fantasy games.

Also there is a fundamental design decision in Supers games, does the system work as a physic's engine or is it there to emulate the genre. Generally with Supers more than any other game genre it's the second choice that carries the day.

Lastly do you consider feats in 4e to be super powers? In many ways they play like super powers and in a 4e modern game you could basically include all the same feats and they would feel like super powers. On that basis should you include levels and feat trees as an alternate super power advancement paradigm?

Hi Jibba Jibba, thanks.
  My main supers game these days is MSH (though that's just a few one-offs). I have played more Aberrant than anything else (two campaigns of it) but not since soon after it came out. What I will do is add more references to some of the other discussion, and move the discussion of Aberrant mega-attributes to the Attributes section since it’s a bit off-topic. I should admit I've used Aberrant as the example of why powers getting bonuses off ability scores are bad partly since I've probably flamed 4E enough already :)
 
  Genre emulation vs. realism I guess is important; I hadn't thought of that but this probably should get discussion in some sort of "considerations for designing different genres" type post, rather than here, which was intended to be about super powers/mutant powers, not supers games generally? Thanks, anyway.
 

  On the feats: Feats in D20 System derivative games can be used to buy some abilities that look like powers, and some abilities that aren't.
 
  I guess powers in 4E (or 7E Gamma World) also are also bit super-ish (Fighter 2 utility "Regeneration" comes to mind); but from what I know I think 4E feats are generally more limited than 3.x feats and usually just give minor damage and save boosts and the like. There may be some by now that let you do stuff like you used to be able to do in 3.x – aasimar shooting Searing Light from their eyes, Fire Resistance, Draconic Wings, etc.
 
  A 'tree' structure (feat chain) isn't often used for super powers since supers tend to start out with most of their powers; its easier to just make more powerful abilities cost more. There are  3.x power-type feats that work like this, but I think this is largely due to powers being shoehorned into the existing structure perhaps originally meant to prevent fighters getting stuff like Manyshot or Whirlwind Attack at 1st level.

  Though come to think of it Vampire Disciplines are sort of super-power ish as well, and also something like feat trees in practice (buying each new dot adds an all-new ability). This has the added advantage over a feat tree that you have a number (the Discipline rating) which can be rolled for checks if needed.  

  With regard to whether feat trees are themselves a good idea, there’s a Frank Trollman piece here that’s of interest (the “Failure of Feats” bit about a third of the way day): this basically points out that in D&D switching feat chains means your high-level character is now getting a 1st-level appropriate feat; his solution to that to remove trap options was the multi-functional scaling Tome feats.
  http://www.tgdmb.com/viewtopic.php?t=33294&postdays=0&postorder=asc&start=2

The following is a quickie basic super powers list, with some general notes.
The same powers list might basically apply to spells, psionics or other power design, as well as mutant powers. These are fairly generic powers; subvariations are listed after the semicolon. Other specific powers may be combinations or flavourings of these. I doubt this is exhaustive, though I’ve looked through a few systems to compile it.
 
 
Aid: assist ally (roll or statistic). May also be represented as another power with a "useable on others" type advantage.
 
Absorption/Armour/Damage resistance- absorb damage or effect. Psychic shield or other 'armour' powers (social armour? resistance to knockback? etc?) may use same system as regular armour. This might also be a subtype of Power Resistance, to the "Damage" power.
 
Afflict e.g. Disorient, Stun, Curse, Devolution, etc. This might apply a defined "condition" like weakened/dazed, or it might give a target a Disadvantage, with these largely replacing conditions.
 
Animal/Plant Control; speak to animals/plants
 
Astral Projection; more likely a magic or psi power.
 
Bestow Power to others (e.g. “grant mutation, psionic "Psychic Surgery"). Needs tight controls on use.
 
Clone - create duplicates of character.
 
Computer Interface
 
Damage: Claws, Disintegrate, Bolt, Mental Blast, Poison, Weapon, Immolation (damage aura), Breath Weapon.
This may break down into a number of more specific powers. Choices like different energy types are likely to require different sorts of resistances. Damage might be allowed to have multiple types (as in Gamma World 7E for energy types) giving increased ability to bypass resistances.
May include damage to non-HP e.g. attributes or mental HPs, or this may be a separate power.
 
Darkness Generation; Fog, "darkness" to alternate sensory types.
 
Density Control; may (or not) be taken as "always on" for very heavy characters.
 
Digging: DC Heroes has this, with very specific rules on volume (RAPS for power use = volume excavated, possibly reduced by material hardness. The effect of 'hardness' could suggest this power could get an 'armour piercing' type power, even though its not exactly 'damage'.

Dimensional Travel
 
Divination: e.g. Psychometry (generally a psi power), Scrying
 
Duality/Schizm: additional mental actions
 
Duo-Dimensionality
 
Elasticity
 
Energy Control: one energy type
 
Enhanced Memory/Total Recall
 
Enhanced Senses: Darkvision, Infravision, UV Vision, Radar, Sonar, Hgt. Smell/Taste, hgt. hearing, Telescopic/Microscopic vision, Directional hearing, hypersensitive touch, x-ray vision. May give vulnerabilities to sensory attacks.
 
Environmental Adaptation; water breathing, vacuum, temperature adaptation
 
Extended Lifespan
 
Extra Body Parts; e.g. Extra Limbs, redundant internal organs; this power may also be represented by taking other powers (e.g. multiple actions or extra HPs) and flavouring it appropriately
Detection: various e.g. Life, particular power category, particular Power, weakness detection
 
Flash: deactivates target senses
 
Flight: Floating Disk; Levitation, gliding (winged may be a disadvantage; body part as power focus).
 
Force Field
 
Healing: Resurrection, Damage Transfer. Regeneration may be form of healing applicable to self, but is more likely to be an ongoing power. Healing usually has firm limits regardless of whether most powers are unlimited use.
 
Independent Body Parts - separate body parts to act independently; Swarm
 
Internal Dimension
 
Illusion Generation
 
Immobilize; Stun Ray, Web, Entangle, etc.
 
Intangibility; Gaseous Form; Permeation (e.g. "Meld into stone")
 
Invisibility
 
Kinetic control: Telekinesis, Gravity Control; Magnetic Control may be TK with limitation "metal only".
 
Light Generation
 
Luck: (adjust dice rolls). May be an attribute in some systems rather than a power.
 
Matter Creation
 
Metempsychosis (Personality Transfer)
 
Mind Control: Hypnosis, Domination, Pheromones, Emotion Control
 
Movement (other): Climbing, Jumping, Water Walking, digging
 
Multiple Lives; may be variant of Healing (Resurrection) with target: self.
 
Negate Super Powers
 
Omni-power: duplicate various powers, usually at additional cost. Selection of multiple powers may be limited i.e. a "power framework". Shapeshift may be a specific example of this.
 
Premonition
 
Power Resistance: e.g. specific power (Poison Immunity, Illusion Immunity (true seeing).
 
Power Reflection: (specific power, powers generally)
 
Power Vampirism/Transferral
This usually is temporary, since permanent power transfer is difficult to balance. The fairly-unbalanced World of Synnibarr has permanent power absorbtion (letting a character take anothers classes, mutations, etc.) but this can be a limited number of times, and if the target is higher level they have to save vs. 'burning up'. There are also intrinsic limits on # mutations, and Guilds for the various classes also mean that unusual powers might be noted and punished as murder.  
Rogue of the X-men in FASERIP can permanently absorb powers as is established in the comics, but loses a Psyche rank if she does so (becoming an unplayable mess of multiple personalities if this falls to zero); stealing powers could also be punished under the games' Karma rules.
The Big Bang Comics RPG sometimes always new powers to be gained, but with a character having to take a Qualification after levelling-up, in order to help balance the power gain.
Vampire lets characters steal 'generation' and dots of things off other characters with 'diablerie', but the character gets only minor increases and it leaves black spots in the aura that can be noticed with the Auspex power, leading to retribution for Camarilla characters, though there is a Merit that conceals this. Mage has a 'Shattered Avatar' merit that lets characters share their avatar/soul with other mages, who might be killed to increase it (or seek to kill them).
 
Regeneration
 
Shapeshift
 
Shield
 
Size Control: (grow, shrink) - may be super-attribute if game has Size score.
 
Skill Boost; super linguistics, Mechanical/Economic/etc. genius
 
Sound Imitation
 
Summon
 
Suspended Animation
 
Sustenance: eat anything, solar sustenance (as plant), reduced needs.
 
Super-Attribute
 
Super-Speed: in games with a SPD attribute, may just be a super-attribute
 
Telepathy/Empathy
 
 
Time Travel/Time Control: will probably destroy your campaign. Oh well.
 
Transform (creatures)
 
Transmutation; change state or condition of matter
 
Travel: Teleport, Warp, Teleport Object, Dream Travel
 
Voodoo (zombies)
 
Weather Manipulation
 
 
 
 
Note: Random roll mutation systems may include "defects" which are included on the mutation tables to be accidentally rolled instead of a beneficial mutation (e.g. Gamma World through to 6E).

Edit Note: Interesting thread here on the worst powers ever: http://forum.rpg.net/showthread.php?501260-Absolute-Worst-Powers-Abilities-Ever (http://forum.rpg.net/showthread.php?501260-Absolute-Worst-Powers-Abilities-Ever)

Here I'm discussing the idea of limitations or advantages that modify specific powers.
These can be subsets of a general advantage/disadvantage system used by characters, or this may be a specific subsystem just for powers. (Some of this is applicable to general advantage/disadvantage systems).

Alternatives to Advantage Systems:
Sometimes instead of a separate 'advantage' system, a character might add extra abilities to a power just by selecting a different power (meta-power as it were). (This doesn't let the system duplicate disadvantages, though).
A power might also gain extra special abilities from having a higher rating if characters can purchase variable ratings, or characters may be able to purchase special skills which apply extra effects. Sometimes a power may allow customization options which carry inherent customization drawbacks (e.g. 'electrical, -1 damage per die but ignores AC of metal armour'... or something like that).

Variables in costing limitations
Variables in properly costing a limitation are:
*severity of limitation
*frequency of limitation
*strength of power affected (number of points in it)

Severity is somewhat circumstance-dependent; indeed there may be situations where a disadvantage becomes beneficial. "Energy blast affects only mutants" is helpful when you're trying to hit a mutant who is grappling your girlfriend to carry her off, even though it means that later on, the robots in the wastes won't be affected. "Requires oxygen" in a blast type power might logically be used to suffocate opponents in close confines.

Frequency of a limitation occurring is somewhat campaign-dependent, but designers frequently assume a likelihood and use this to preset different discounts for different disadvantages, based more or less on the first two factors; potentially a GM can adjust costs if they really need to (i.e. "only useable underwater" in an aquatic game).

The third factor (strength of powers) may be inapplicable depending on the system - e.g. if powers have no individual ratings i.e. are just level-based or use ability checks. Its more often not bothered with. Note that if a disadvantage has a proportional benefit, characters with high power ratings are compensated for taking it more fairly. On the other hand, if a disadvantage has a fixed benefit, characters should probably not cripple their strongest power; bad design in such power systems occasionally give away weak powers for free (Golden D20).

Most existing systems consider only some of these, sometimes none of them - a trade-off between complexity and game balance.
From simplest to most complex, more or less:

*all disadvantages worth same number of points. If powers themselves are fixed in cost (i.e. selecting 1 Hindrance gives you 1 Edge/power) then having a negative hindrance that affects two powers is equivalent to buying those two powers at half cost. The disadvantages can themselves be designed to be somewhat equivalent [in severity and frequency].

*To pay for a disadvantage, Marvel Super Heroes (FASERIP), as noted previously bumps up scores to the next highest Rank, an erratic increase which is a good deal if your attribute is 10 (a 100% increase), and probably a bad idea if your score is 30 or 40 (an increase of only 33% or 25%). This is probably the simplest system that gives any sort of proportional benefit from taking a disadvantage; the erratic increases are somewhat excusable in that some limitations can only be taken if your power rating is low. There is no extra benefit for taking a disadvantage that's particularly bad, though (e.g. "power useable only once ever").
MSH has 'power stunts' (extra uses for powers) that basically are advantages.

*advantage/disadvantage cost varies by which is selected, but with no proportional changes in power rating (you get +5 points for having your Laser Blast not work underwater, or +10 if it only works on blue objects). (Ars Magica has a lot of flaws that work this way, though with magic rather than super powers).

*A I was working on uses a relatively quick n' dirty modifier of 1/2 cost for a disadvantage, +1/2 cost for an advantage; cost is unchanged if one of each is selected.

*Aberrant has power 'Extras' that increase their costs (a level 1 power with an Extra becomes a level 2 power for cost purposes), but no limitations. It doesn't have general Merits/Flaws for characters (in the core book, anyway).

*Amber gives powers a point cost, with characters able to buy a 'block' power with various aspects or a 'partial power' that does just some stuff (going on thread info; I believe each power has an individual partial power cost scheme, perhaps similar to how DC Heroes runs skills/subskills).

*GURPS may apply modifiers as percentages e.g. -30% to cost (IIRC).

*Fuzion IIRC has base disadvantage/advantage costs, which are also modified for [Frequency x Severity]. (actually its general disadvantage system).

*DC Heroes applies modifiers to both 'base cost' to buy 0 points of a power (0 points is a defined quantity; not having a power has a null value), and a 'factor cost' (from 1 to 10) to purchase a number of points in it; this requires using a table. Advantages/Disadvantages modify Factor Cost but rarely base value, so Disadvantages don't readily allow characters to buy up large numbers of different powers cheaply. More rarely a character can modify a Power by taking a second Power -   "Self-Link" for instance has a whole power write up, though has a fixed cost of 50 points, or a character with Power Reserve and Energy Absorption can also take an advantage "Energy absorption adds to Power Reserve".

*Hero adds limitations of various values (-1/4, -1/2, -1, etc) to a base value of 1, with a negative number becoming a divisor to the base cost. This lets alot of modifiers be stacked onto a power - potentially abusable but allowing for very detailed customization. Hero modifiers are sufficiently detailed that they require campaign-dependent adjudication (will the PCs be going into Vacuum alot, so that "powers doesn't work in Vacuum" is viable as a limitation? This is considered less scientifically than Fuzion, but the overall process is probably more complex). Hero also has 'adders' with fixed cost, rather than variable cost.

*Invulnerable has especially lengthy lists of 'enhancements' for each power - many powers having 10+ possible enhancements. Enhancements are binary things (you have it or you don't), with characters getting 1-10 'free' enhancements based on their power level (unless traded in for attribute points); this is slightly awkward in that Enhancements can cost more or less - they cost the same as the first level of the power - so characters should pick expensive enhancements for free e.g. for hyper-attributes. Slightly worse than this, the same Enhancement is sometimes available for different Powers at different costs (e.g. Adhesion is the same from Extra Body Parts or Elemental Control, but elemental control is Expensive whereas extra body parts is cheap). Its interesting as a game that gives out lots of enhancements as part of power design (the example Human Torch type character has half a dozen enhancements for their elemental fire power). It has Power Modifiers as well; these can be applied just to enhancements (e.g. fire control has 'flight' as an enhancement, so a super-fast modifier can be applied to that) or the whole power.

Now a question I don't have an answer to: Disadvantage systems may encounter a sort of philosophical problem in design; how much is something a Disadvantage that the players should buy, and how much should be hard-coded into the rules itself? Should constructs be immune to death ray because they have a power that gives them resistance to it (costing them points), or should I logically have to buy a Disadvantage so it doesn't work on them (giving me points)?  Should water have Resistance (fire) or should my fire blast have the disadvantage "doesn't work underwater?"


Also, below is a partial list of Advantages/Disadvantages (one list since many are reversible).

Armour Piercing/Low Penetration   -requires system to be able to adjust armour penetration, or gets messy
Counter [specific attack advantage] i.e. Impervious (ignores armour piercing)    -may be costed as cheaper than equivalent attack advantage; difficult for defenders to optimize all defenses.
Ignore defender resistance i.e. no saving throw, Aggravated damage - generally unbalanced
Secondary Effect e.g. condition applied as well as damage
Quicken/Slow        -if extra attack becomes a "free action" to use.
Additional Roll Required to function (Disadvantage) e.g. skill check (this is a poor balancing mechanism with variable cost disadvantages, since this will have little effect if other score is high; it may work somewhat for fixed-cost disadvantages as can be balanced for a worst-case scenario i.e. maxed out skill). HERO 'requires a skill roll' limitation is also problematic in that it [4E] suggests a character making the skill roll by X can increase the effectiveness/active points by 10%, making the limitation in some ways a bonus.
High Damage/ Low Damage - poorly designed advantage usually; often the main benefit of rating increase is extra damage making this a min/max dodge.
Burning (Continuing Damage)
Area        Clearly an advantage, though if can't be turned off it has its downsides.
Reduced Power Point Cost   / Increased Power Point Cost   - these can be problematic combined with powers that can generate PPs (giving a loop generating infinite power points).
No Range/Extra Range
Limited to specific body part: e.g. defensive power limited to one hit location.
Useable Less Often (e.g. daily or even once-only). (variant of reduced power point cost)
Always On/Uncontrolled Power    -mixed benefits/penalties; may be either an advantage or disadvantage.
Extra fumble effect (usually poorly balanced as a variable cost disadvantage, although "friendly fire" damage becomes worse as damage values increases)
Increased/decreased maximum value  -   decreased value generally a poor balancer - you wouldn't have raised it above the threshold anyway. Increase may be OK, but deliberately leads to "all eggs in one basket" characters.
Focus (Item) - an advantage for generic supers powers. Potentially leads to complications like having some dude stealing your powersuit, so this disadvantage might theoretically lead to other people getting free powers, if not carefully considered. See Tech discussions earlier. A similar disadvantage might be use to require focus "body part" for a power e.g. winged flight might give a character a Focus, since their Flight power could be damaged by called shots.
Mega-Scale-a HERO 6E advantage for massively upsizing an area affected; can be used for speed or range as well.
Usage Limitation (i.e. doesn't work against yellow objects, works only in a specific case) - good for creating more specific powers out of general powers e.g. a generic super-attribute power could be customized to represent anything from dwarf stability (+4 Strength applicable against being moved only) and poison resistance (+4 Con for checks against poison) to . This sort of disadvantage requires fine judgment of how often specific situations arise in costing.
Powered by X: has particularly variable (by campaign conditions) circumstantial effectiveness.
Code of Conduct: perhaps a good one for replicating Silver age type supers, and keeping PCs on the straight-and-narrow.
Linked: value of power must equal controlling attribute. Makes raising powers more difficult, adds attribute-dependence without adding extra value to attribute score for characters who don't have the power. DC Heroes uses this for powers and skills. It also builds on this with a "Mystic Link" power which converts a physical or mental power to a 'mystical' power for 10 points, changing the link attribute from the normal default to 'Aura' (the magic stat).
Random: power is generated randomly.

Defining Characteristics
Psionics (mental powers) tends to be less spectacular than magic, fitting into a sort of mythology of the paranormal IRL. Characters tend to have only one or a few psionic powers, as compared to magic where characters may know dozens of spells. It is typically imagined as being rare, and may be unreliable to use.
While often seen as more of an SF thing, AD&D had it (one of lots of extra details to sell it over OD&D), and various fantasy fiction has included psi powers even if not named as such - the idea of "Gifts" in some romantic fantasy series. Some stories or RPGs may also have magic thats' "actually psionics" if trying to give it more scientific plausibility; in RPGs Tunnels and Trolls used this explanation, in fiction there's Stasheff's Warlock series, and perhaps Julian May's Saga of the Exiles books; that last and T&T however have very spectacular "psionics". In fiction, psionics often invokes a lot of superstition and witch-burning, with telepathy in particular having little social acceptability.
 
Power Acquisition
Characters may have a number of racially-predetermined psi powers, a class providing them with powers (possibly increasing with level). Bonus psionic "wild talents" are also sometimes randomly rolled (an old AD&D tradition being to give everyone, or at least those with high mental stats, a base 1% chance of psionics), or may be purchased as an Advantage and/or a skill. Systems may also treat Psionic Ability as an attribute (Space Opera). The "wild talent" rules may affect the design of a psionic class - it may require a high psionics roll or give bonuses to rolls e.g. the original Palladium Mind Mage - or they may not quite fit and have quite different mechanics [the 2E AD&D psionicist]
Examples:
 
*HarnMaster gives characters a number of powers rolled based on their Aura attribute (which governed both magic and psionics); each power known is then treated as a skill with its own %. A power usually starts at a low % (making it dormant); Incidents triggering it accidentally might result in improvement checks, until it reaches a certain threshold, at which point a character becomes aware of it and so can train it up normally via practice. Powers scale up based on the character's Skill Index (1/10th of skill).
 
*Masque of the Red Death for 2nd Edition, IIRC, let characters buy "mentalism" proficiencies with non-weapon proficiency slots. This to an extent gives high INT characters more psionic powers, as they have more skill slots.
 
*Rifts gives characters a roll for minor or major psionics, as well as having "racial character classes" with more powers known; a number of classes had a few minor powers or a greater chance than normal of psionics. Especially strong powers are grouped into the [Super] psionics category.
 
*Savage Worlds lets characters learn about 3 powers by taking a Arcane Background edge. Using their powers requires a separate Skill. Adding extra powers requires an 'extra power' Edge (giving a single extra power - very conservative, and the system ends up being fairly granular i.e. very limited 'cantrips' or non-combat magic).
 
*GURPS/HERO has character buy powers with character points.
 
*Space Opera as noted treats Psionics as an attribute; classes receive some discretionary points to spent on specific attributes, possibly letting some classes build their psi powers; it could also receive racial bonuses.
(there was a "Psiworld" RPG from the same company, FGU, which I'd imagine probably worked similarly, but haven't seen).
 
*AD&D rolled for psionics randomly; however it limited certain "wild talent" powers by main class for balance reasons i.e. no skin armour for wizards.
 
*2E D&D as well as having a random roll for "wild talents" has a Psionicist class with access to psi powers. Powers are divided into "sciences" (major powers) and "devotions" (minor powers); with more powerful sciences tending to have more complex prerequisite powers. This has the nice effect that a character who is high-level can continue picking up weaker powers, as well as more stronger powers.
Comparatively 3E just gives a "total number of powers known" so once a new power level was achieved, your picks would (optimally) all be of the highest-level powers. 3E D&D also revised powers to be balanced much like spells i.e. there were 1st-level psionic powers through to 9th-level psionic powers, largely slight reskinnings of magic spells and making psions not very different to sorcerers.
 
*Monsters in 3E are interesting in that they treated innate monster ability psi-powers differently to class-based psionics; monsters had "psi-like abilities" (useable x/day or at-will) instead of power points. These are sometimes available to PCs e.g. as racial abilities of psionic races; most of the psionic races get bonus Power Points, but can't do anything with these power points unless they choose a psionic class as well.
 
 
Usage Limitations
Nearly all psionics systems use some sort of system of "power points" to use their powers - even D&D, despite Gary's dislike of "spell points" (as noted in his book Role Playing Mastery). Exceptions/complications:
 
*HarnMaster instead of points has characters roll a check to avoid gaining physical fatigue (measured in "fatigue levels"). Each level gives -5% to all skills.
 
*Talislanta 4E gives characters a skill check to use magic or psionics ("Mysticism"), with a cumulative penalty equal to number of spells cast. This makes power use increasingly likely to result in critical fumbles.
 
*2E AD&D has a character make power checks to see if a power works, with a failed power roll meaning that 1/2 the points are expended. A particular problem power where they didn't think this through is "Dream Travel" letting a party travel via dreams; if a power check is failed, the journey works but is 10% short per point the roll missed by, so failing the roll by exactly 1 by RAW gets a party 90% of the way for half cost. (i.e. this power needs a special proviso that its always full-cost).

*In Dragon Warriors, Mystics make a check to avoid "Psychic Fatigue" - this is a d20 roll under [13 +mystic level - power level]. In comparison, DW Sorcerors have simple level-based "spell points" ; the fatigue roll gives a mystic on average a similar # of highest-level spells to sorcerors, but casting a lower-level spell is still very likely to burn out a mystic, whereas the sorceror can safely output lots of low-level spells.
[In a homebrew version of this I was working on, I was planning on bumping Mystics up to 3 failed fatigue checks/day at target 11+mystic level- power level, using a 2d10 roll instead of d20, and giving sorcerors a linear spell point progression of 7 points/level; about 3 spell levels doubled chance of fatigue, that led to a power level equivalence as follows:
 

Level Mystic Sorcerer
1        0.75   0.5
2          1      1
3                1.5
4                 2
5          2     2.5
6                 3
7               3.5
8          4      4
9         ---   4.5
10        ---    5

 
Note as with hit points, power points may be arbitrary, or may have some other use in the system.
i.e.
 
*IIRC, LegendQuest has separate "mental fatigue" and "physical damage" totals, with Magic (including Mysticism) dealing mental fatigue damage. A proportion of either lost can result in an action penalty.
 
* a system with a Willpower stat could possibly have psi use have a Willpower cost. [World of Synnibarr gives psis power points, but also lets characters burn Constitution points to amplify powers, regardless of whether they're magical, mutation-based, chi-based or psionic; I'd be tempted to modify this to have psionic classes burn Wisdom to fuel their powers in place of Con, to give more differentiation between the power types, if I ever played it].
 
Power point recovery may require full bed rest/meditation, or there may be fixed regeneration of points/hour e.g. 2nd ed. has a table of recovery rate by exertion level. This limited impact of point depletion on need to rest, but could add to accounting. (Tunnels and Trolls magic system is similar; point expenditure here actually reduced character Strength and so combat ability, but conversely GM encounter guidelines encourage wandering monster rolls while PCs attempt to rest. Warrior types could potentially lose STR in combat as well, albeit not as quickly, from using overly heavy weapons or berserking).
 
 
Controlling Attributes for Psionics
Some games have a "psionics" attribute: Aura in HarnMaster, Psionics in Space Opera; Psychic Talent in Dragon Warriors. Wisdom/willpower or an equivalent is the usual prime requisite in other systems, e.g. in Palladium, Mental Endurance is a main factor in determining "Inner Strength Points". Occasionally Intelligence may be used, instead.
Some games also have more complex setups e.g. AD&D modified 'psionic strength' based off all of Int/Wis/Cha.
3E assigned one "discipline" of psionic powers to each attribute, giving some psions Str/Dex/Con based powers - Str for psychokinesis, Dex for psychoportation or Con for psychometabolism, Int for shaping, Wis for clairsentience, Cha for telepathy. 3.5 removed the stat/discipline correlation which psionics based off just one of Int, Wis or Cha, depending on class; it also uses wisdom as a prerequisite for some feats e.g. Rapid Meditation. SW psionics is independent of any attribute, despite there being a "Spirit" stat.
 
2E powers used an ability check to see if powers worked (typically of Int, Wis, or Con) - a new mechanic compared to 1st edition inherited from the skill (Non Weapon Proficiency) rules. For why this is a bad idea, see mutant powers, above; additionally, unlike most classes, Psionicists do not improve at any of their powers as they level up. They gain more powers known and power points but a 3rd level psionicist with Con 18 and disintegrate would have a higher success chance for using it than a 20th level psionicist with a 13 Con and the same power. Psionic Monsters in 2E have to have default listed power scores for psi powers rather than using an ability check, as they have no defined ability scores.
 
Mental Combat
Games may also include “mental combat” rules. 2nd edition D&D had various attack and defense modes, which had different modifiers against each other somewhat similar to the earlier 1e weapons-vs.-armour-type tables. Some games may also have “mental hit points” that may be damaged by psychic attacks. (note that this has tactical effects: psionic and physical attacks vs. a single opponent no longer have any synergy, though parties still function when facing lots of small opponents). Fairly often a mental attack will just do HP damage for simplicity's sake - e.g. 2E "psychic crush" deals damage no different to a sword's, while 4E and 5E do damage normally off HPs although with a "psychic" keyword that comes into play for defining resistances etc. Games where physical damage is subtracted directly from an attribute e.g. CON can in a fairly balanced way subtract mental damage from a mental attribute like INT or WIS - a particularly elaborate system for this is DC Heroes. A "partial synergy" can be established if the 'HP' pools are separated but with damage to either mitigateable by spending a central pool of metagame points - again DC Heroes is an example, where Hero Points can be spent to reduce damage against whichever attribute.

Chi rules (or Ki, the Japanese version) are included in only a few games with an Eastern or martial arts flavour. (At least few that I know of).

*World of Synnibarr:  the author's desire to make everything super-awesome, and interest in martial arts, leads to inclusion of a Ninja class and a "chi" power type. Chi can however do basically anything here: e.g. Ninjas can teleport (Tesseract) with it, or produce light sabres, while the infamous flying grizzly has a laser eye beam that is a chi-based energy attack. Chi's basic advantage in the system is that as it uses internal energy, it is difficult to suppress, unlike magic-based or mutation-based powers which are both envisaged as using an external energy source, "caprenium radiation".
Chi can still be suppressed in unusual circumstances e.g. certain coloured suns can suppress it (different star colours affect other power types).

*Ninjas & Superspies gives characters a Chi score (base value = Physical Endurance; some forms may double this, initially or after some levels) which powers various martial arts abilities; compare to Psionics which is powered by Mental Endurance or Magic which uses a separately rolled PPE (Potential Psychic Energy) score.
Positive Chi is required for normal healing; there are "negative Chi" abilities which require a character replace their normal chi with dark chi temporarily. The dreaded "Dim mak" ability prevents characters from recovering chi normally, leading to eventual death. The softer or more spiritual martial arts forms have more Chi powers; a number of chi attacks are delivered with 1-finger strikes.

*D&D 3.x has a monk class which has ki powers; most of these operate using the standard spell-like ability rules.

*The Way of the Tiger gamebooks had "Inner Force" points which could be spent to double damage from martial arts attacks.

*Weapons of the Gods: I've only glanced at this and mostly forgotten any details but WotG's main contribution to Chi, that I recall, is that gay characters are forced to take a particular discipline to prevent themselves getting Chi depletion.
(WotG is also notable for having the fairly bad idea of levels (ranks) that go backward from 5th (most crap) to 1st (awesome); leading to a BBEG who is off the scale with a level of "below 1st rank". (Gygax's Lejendary Adventures did the same thing, with 13th rank being the worst.).
Weapons of the Gods, the first edition only apparently, has about five different pools for 'Chi', all of which regenerate at the same rate but promoting switching-up strategies to not bleed any particular pool too dry.

Next time: onward to Magic, I think
..

“Sadira kept her hand open. One after the other, the cacti drooped, then browned and withered. . . Even then, she did not stop, until the soil itself turned black and lifeless.
...Though the sorceress believed she had been justified in saving herself then, the present issue was less clear. . . If she resorted to defiler magic to save herself from eventual death, would she use it out of simple convenience the next time?”  
-       The Amber Enchantress (Troy Denning).
   
Magic is perhaps the game subsystem with the widest latitude for the prospective game designer. Most other game systems must correspond in some fashion to reality; a magic system is however entirely fanciful and its basic principles of operation can be anything the designer wishes. Fiction contains any number of basic ideas for how it works, its limitations and so on, which can translate to any number of game mechanics.

Magic might be the direct rewriting of reality by belief which requires a spell only because the wizard believes it does (as in Mage: the Ascension), or it might be a call to spirits or other-planar creatures that are compelled to obey the instructions, or a speaking of true names of the things being affected (a la Earthsea), or even a form of psionics but where the wizard needs to speak certain words to "focus" themselves, or something.

Magic itself may be easy or difficult to learn, work perfectly or only sporadically (a 'klutz roll'/skill roll), and be based on various attributes. Most systems (and much source fiction) places limits on how much magic a wizard can use: this can include spell memorization (e.g. Jack Vance or Terry Pratchett), mental or physical exhaustion (perhaps suggesting some form of spell points, or even a tie in to fatigue points or a condition track), or even require some sort of energy from the environment; Dark Sun where magic sucks dry plant life had an interesting concept which was however poorly represented within D&D mechanics, while in fiction the idea of mana being a finite resource being steadily depleted by wizards is explored in some depth in a number of Larry Niven’s works (e.g. ‘What good is a glass dagger?’; or ‘The Magic Goes Away’). The Gaming Den has tossed around the idea of a "winds of fate" matrix for power use, with a character able to use only a subset of powers from their matrix each round. Use of magic can also have moral or at least roleplaying consequences.


Magic use in source material is sometimes linked to characters personality/feelings, though that's sometimes an issue in that game systems leave that largely to GM fiat. (for instance, Star Wars D6 has a 'Concentration' Force power with difficulty to use based on if the character is currently angry or fearful, something fuzzy the game mechanics are otherwise silent on and so possibly requiring GM adjudication of what a PC is currently feeling).
Apart from resource usage, the behind the scenes limitations and principles of how magic works are often fairly badly defined.  (D&D 3E is a particular offender in this regard with magic that can basically do anything; my pet hate being that even though the combat system doesn’t handle specific injuries – meaning you can’t cut off someone’s hand or head with a frickin’ sword, at least unless its a magic sword – there are spells which can do it, like Grim Revenge or Decapitating Scarf).

In RPGs, Ars Magica sets very clear limits to what magic can accomplish – such as not being able to interfere with souls (and, thus, resurrect the dead), interfere with the divine, or affect ‘spheres above the Lunar’ ; each variety of magic (all PCs use just the one, ‘hermetic’ magic) can break one law. In fiction, another interesting set of principles rather than limitations may be the one from Lyndon Hardy’s ‘Master of the Five Magics’ where each style of magic has underlying rules, if not limits(originally derived from computer RPG 'A Bards Tale').

Another essay on guiding principles in magic which may be of interest is this one by John Kim (discussing how to make magic more evocative of myth and folklore): http://www.darkshire.net/jhkim/rpg/magic/antiscience.html (http://www.darkshire.net/jhkim/rpg/magic/antiscience.html)

Just as super powers systems tend to use references to super powers as a shortcut in designing, fantasy games tend to use references to magic. Rolemaster had classes partly defined through new 'spell lists'; D&D (most versions) use the spell system as a library of standard conditions, good and bad, which can lead to warriors' speed being described as being like use of a Haste spell or rangers getting 'spells' to represent special abilities that may have been intended to be special but not precisely magical. (forum post by one of the designers of FantasyCraft here (http://www.crafty-games.com/forum/index.php?topic=4647.15) on this). (Occasionally something gets twisted fairly oddly by this e.g. Sharn in 3.0 D&D get 'haste' as an ability -an extra 'partial action'- to represent their three heads' ability to let them cast 2 spells/round).

Magical spells are often broken down into 'levels' restricting access to stronger effects.

(http://i1239.photobucket.com/albums/ff507/BSJ17/3a01c44f4d1eaaf1g_zpscc217846.jpg)

"If you belong to the class of the Warrior then set aside this text, for the touch of iron is harsh in your blood, and you will never cast a spell." – the Book of Magic, Crusaders of Khazan
 
 
 
Whether a character can use magic may be an innate 'gift' of some kind and/or require a particular class or skills. Some variants include:
 
 
*magic-use limited by class. If multiclassing is allowed, most any character can theoretically use magic with additional training. In the case of D&D through to 3E, different classes require different key attributes; a character's maximum ability score determines what spells they can cast, and so whether characters have any magical potential. Generally though, limiting spells to a particular class is enough to keep it rare. (A couple of weirder class systems deliberately scorn niche protection and let anyone use magic anyway - e.g. Rolemaster would let your fighter learn spell lists, but at greater skill point costs. I'm not sure this doesn't miss the entire point of a class system, though).
 
*a 'Power' attribute. For most systems which have these they largely determine how much magic a character can use, but it can potentially also determine if a character can. Odds of magic use in the general population can then be related to likely power ratings (although PCs may well roll Power in an unusual way). Power as an attribute might do very little for non-mages (in point-buy systems, this gives the mundane an opportunity to get a leg up with regard to other attributes like Str or Con), or it might influence e.g. whether a character can use certain magic items (e.g. in Dragon Warriors, a character with 8 or less Psychic Talent, cannot use magic rings) or a character’s resistance to magic/saving throws.
 
*Talislanta characters have Magic ratings determining raw magical ability - magic itself is a d20 skill roll (certain classes get this as part of their classes, while others may be able to learn it separately). Certain racial types are also totally unable to use magic; the warrior race of thralls are racially incapable of understanding it, while dual-enchephalic Sindarins lose one of their brains (and several Int points) if they use magic.
 
*Tunnels and Trolls magical ability is a surprisingly complex affair; spells require you to be the right Type (Class) to use magic, and have a minimum IQ and DEX depending on the spells' level. While the game has character levels, these don’t affect what level of spell a character can use – only what level of spell NPCs are willing to teach the character. Later editions also have a Power (“Kremm”) attribute which works as spell points; Warriors do still have a Power attribute though it only determines their magic resistance.
 
*Other games have a "Magic rating" only for wizards. Mage: the Ascension gives mages an "Arete" rating representing their understanding of "universal Truth" (in Mage, the idea that reality is a consensual hallucination the mage can control); this IIRC limits their maximum Sphere ratings (in different magic types). 1 point of Arete makes a character a Mage, rather than a normal human ("sleeper"). This sort of mechanic also showcases how a number of Storyteller games have an expensive “Uber Stat” which correlates highly with character power, sort of like level but not quite – Generation, Rank and Quantum being some others of these for different types of character.
 
*Magic use might be a Merit of some sort: this is particularly likely in games which are purely skill-based rather than class-based, where otherwise every character might pick up a few ranks in sorcery.
 
*Magic use might even be a racial feature; not a common approach, but Kevin J. Anderson's fantasy novel "Gamearth" has an RPG world where only characters descended from the 'Sorceror' race can use spells, with the proportion of sorcerer blood determining amount of magical ability.

*In some games a characters magical ability might change over time; for example a couple of science fantasy games make cyberware or bionics off-limits to wizards. Shadowrun gives characters an "Essence" rating, starting at 6; if this falls due to Cyberware characters also lose Magic points (rounding down). This limits the maximum Force of spell a mage can cast without risking physical damage, rather than just mental fatigue (at least in 1E SR).
Rifts likewise has magic depletion for cyberware , but without a defined Essence mechanic; cybernetics reduces magical ability (range/effect) by 25%, while extensive bionics forces a change to the Cyborg ('Borg') OCC, removing all spellcasting and reducing Potential Psychic Energy (PPE) to d4.
Synnibarr lets characters have up to 75% 'biomass replaced' before affecting magic use or other powers, totally removing it. Extra limbs and wings etc. could give characters extra biomass (>100% to start), letting them fit in additional bionics and still cast spells. % biomass lost also cost that proportion of base hit points.
(An opposite approach that could work might be for magic to interfere with cyberware, instead of cyberware with magic. For instance in fiction, Jim Butcher's Harry Dresden books' title character has magic that interferes with electrical equipment nearby - this was then also cause problems with any sort of implant, not that its an issue in his mileau.)
While on the topic of cyberware, Cyberpunk has point depletion for cyberware as well (it costs Humanity points, calculated off [Empathy attribute x 10] –though it has no magic this at least slows down the entire party becoming robots. With the peculiar feature that combat characters start off with high Empathy scores i.e. are Gandhi until they finish cybering up.
Battlelords of the 23rd Century has cyberware costing Constitution points (probably easier than the % multiplication of base hit points for Synnibarr). (I don't recall if there are bonus 'HPs' for cyberware to offset the loss of 'meat' points - possibly).
Heroes Unlimited has just expensive bionics (borgs get a several million dollar budget). A couple of games have 'bioware' systems - I think modern Shadowrun includes a few (lower essence costs), while the Amazing Engine game Kromosome was built around it. Rifts Atlantis has 'bio-wizardry' which is basically identical to Rifts bionics, but the only class with built-in 'bio-borg' abilities is optional (Conservator).

Note that the more character generation resources (class, race, levels, skill points, stat points, merits, etc.) are burned up to become a spellcaster, the more reliant a character is forced to be on magic. If magic is a total investment, it must also be frequently used for overcoming obstacles.  

 

Excellent, I was a bit afraid you dropped this thread :). Will you post more on the subject of magic? (if such, tell me, I'll remove this post for cohesion).

Just busy post-holidays, and I was running a game (trying out Savage Worlds) over the weekend and stuff. Definitely more coming on magic - you can delete the post if you like, though then I'll have to edit this post into something useful so it doesn't seem like I'm talking to myself :)

Magic may sometimes involve a skill roll, or have a set chance of failure (e.g. gamebooks like Demonspawn series giving magic a "fundamental failure rate". 2E D&D had % spell failure for clerics based purely on their Wisdom  score, irrespective of level; perhaps representing an idea that the  (foolish) PC will have succumbed to some temptation requiring their  deity to punish them by holding out on granting a miracle.
Difficult circumstances may also add extra chances of failure e.g. D&D 3.5's "Combat Casting" rolls and % spell failure due to armour. Mage has consequences for casting spells near "sleepers" who don't believe in it - this causes accumulation of Paradox points and potential paradox backlash.

*A spell may also allow a separate saving roll, and/or require an attack vs. a target creatures' defense number (Armour class or what-have-you). For more on saving rolls see Adventuring Situations and Combat Actions - Defensive actions. Usually each time a spell is cast a save is allowed (the point being that they get at least a fighting chance) although Arduin was noteworthy in allowing saves once only - if a save vs. fireball fails, the target will always be susceptible (until their level improves), or if it succeeds will always succeed (unless the wizards' save improves) - this also went against the idea of the save representing 'dodging' instead saying that 'the mage's fireball is not quite the right brand of magic to 'cook' our orc with'. On the plus side this does incentivize changing up tactics and using different spells, rather than repeating a save-or-die until they fail.

*Systems can also require a roll to see how well a spell worked; D&D wild mages for instance roll for caster level variation in their spells, which in 2E required checking a table. 3E replaced this with "lower caster level by 3 and add d6 with each spell", a more elegant mechanic which was however immediately abused by munchkins who didn't particularly care for wild magic as a concept, but figured out that Practiced Spellcaster would cancel the -3 and just give them a caster level bonus.

*Spellcasting can also have a roll to determine not success, but amount of 'fatigue' or lost magic points for casting a spell; miscasting (spell fizzle) might occur only on a critical fumble, rather than a normal failure i.e. comparing this with a normal "Unreliable" magic system:
[U]Result:[/U]              [U]Unreliable Magic[/U]        [U]Variable Fatigue [/U]
Critical Failure      Caster becomes walrus       Spell Fails
Failure                  Spell Fails              Spell Works, extra cost
Success                Spell Works               Spell Works, normal cost
Crit. Success         Spell works really well     Spell works, low cost
Spells may also include some form of fumble table, to handle critical failures on your spellcasting roll (if these are not purely up to the GM to imagine). Depending on system these might be light-hearted or deadly, precisely defined or merely suggestive.

*2E D&D wild magic included a d100 table of 100 random effects, with 01-50 being "affects caster" results and 51-00 being "affects target" results. The table was constructed so that adding a character's level to the roll was usually a bonus (00 or better indicating spell works at triple effect). Protection from wild surge spells also sometimes allowed a character to roll twice and take the best result.

*Talislanta magic uses its generic action table where 1s (on d20) are  mishaps. When I played this, these happened very often, including some  nasty friendly fire casualties - but I'll grant this may just have been  dick GMing. Mishaps left up to GM interpretation left them free to plug in their own mishap table.

*2E's psionics system used a d20 roll under ability (Blackjack method i.e. higher under your score is better) and for each power defined 20 (fumble), Power Score (exceptional success) and often 1 (marginal success) results. Similarly, Masque of the Red Death required a Spellcraft NWP check for spellcasting by 'adepts' (Wizards). Both of these are problematic due to making a class feature level-independent, and strongly encouraging maximizing a score (it tries to fix this by spreading checks around 3 scores - Wis/Int/Con; still, psionicists vary in power enormously depending on whether a game uses a weaker or stronger stat generation method). The check to see if the power worked, was often also the roll the target has to roll against, although only if they were making an ability check (d20 under stat) - saves use a different mechanic and so couldn't get a modifier worked out except rarely (e.g. a power score result with disintegration penalizes the result by -5). Powers failed frequently ('double jeopardy') since a successful roll might still require an attack roll as well. Another quirk is that a failed power roll cost 1/2 PSPs but powers also failed if the opponent's resistance roll passes, but at full cost.

*Different Worlds #2 describes the cult of Cacodemon for Runequest; initiates can summon their master with a roll under POW on d100; if successful it costs the amount of POW rolled, so it "eats the POW of the initiate entirely if the exact amount of POW is rolled" (i.e. it eats their soul or something).

*original Advanced Fighting Fantasy has an "Oops!" only on snake eyes on 2d6, with a roll on the table including the nasty "caster disappears leaving only a pair of smoking boots" result.

*Arduin spell failures may give reverse results for spells - with catastrophic results. The example of a "Magick Phumble" in the book for a lowly Create Water has it destroying an equivalent volume of water instead - giving an almost certain TPK as everyone in the area starting with the caster suffers a Horrid Wilting type death via dehydration.
Arduin tends to design spells to frequently be unreliable with various specific, individual spell-by-spell conditions or caveats, as well as countermeasures.

*Rolemaster, as always, has tables for this, not just for Oops but for varying degrees of success.

*reportedly, Mark Swanson invented a 'klutz' system for 0D&D where each spell had a chance of failure, increasingly cumulatively each time it was used (other spells tracked % separately). If klutzed the roll was checked again to see if the spell 'double-klutzed' i.e. rebound on caster.

*in Fantasy Wargaming, Spellcasting has a 'staged resolution' system where a wizard must establish a 'link' to a target before casting a spell. A magic-using target can resist by sending a 'desist' or 'counterspell' back through the link before the attacker's spell is cast. See here for notes - http://www.skotos.net/articles/BSTG_54.shtml (http://www.skotos.net/articles/BSTG_54.shtml)

*the Demonspawn books have a roll for individual spells to work, plus also have a roll at the start of a section where the hero (a barbarian with a distaste for magic) determines if they can stomach using it...as a character-specific flaw, a similar roll could be duplicated in other games with disadvantage rules, e.g. a DC Heroes character could have a 'minor irrational attraction' to not using magic.

*Ravenloft for 2E AD&D requires a d% 'powers check' to see if the Dark Powers notice a spell being cast and interfere.

[EDIT NOTE] * Potentially a spell could have a guaranteed basic effect without a check, but with skill checks be required to add extra add-ons or increase the effect - an interesting compromise in reliability.

Most systems limit how often magic can be used. Some methods...

# Spells Per Day: Palladium FRPG (the original one) and Heroes Unlimited versions of Palladium used this; characters can cast a fixed number of spells, chosen as they go, regardless of which spell this is. Simple book keeping is fairly simple but spells must be designed more carefully to prevent one spell being too good/overused; they might be balanced by varying chances of success, casting time, or exceptional resource costs like a GP cost. Very powerful spells might have a cost of (2) or (3) normal spells, making this into a crude spell point system. Generally however, this system avoids the problem where a character might just spend their entire day's spell points to nuke everything in an imbalanced way, and then be useless/need to rest immediately.

Vancian memorization: this gives a character high-level spells alongside low-level spells, meaning that characters have a high rate of advancement. The spell point characters point reserve might give them a 2nd level spell instead of their existing 1st level spells; the memorization system usually gives a character a 2nd level spell as well as their 1st level spells.
The main drawback of spell memorization for the caster is that spells must be pre-prepared to suit the situation; this lets spells have somewhat greater effects than they otherwise would have, without being unbalanced. A character with their 1st level spell may have to choose between Shield (protection vs. enemy magic users with magic missile), Sleep (zaps enemy fighters), or Tenser's Floating Disc (letting you carry out a hoard of copper pieces). This rewards intelligent play, but adds excessive book keeping (a particular nuisance with NPCs) as more spells pile up.
4E D&D is essentially this for most classes, though some resources instead function per encounter or at-will.
The pre-preparation involved in Vancian memorization also sometimes has meant spells are designed to be individually more versatile i.e. yes you took Otiluke's Freezing Sphere but it can be cast in a couple of different ways to do somewhat different things. OTOH, systems without preparation are more likely to divide the sub-effects into different spells for more clarify in the spell description- compare 3E dispel magic with 5E's separate dispel magic and counterspell, now that the opportunity cost of taking both is relatively reduced.
Have various 'spell slots' of different levels lets mechanics hang off level exchanges in a way that spell points can't. For instance, one obscure 3E sourcebook has a 'Netherese Arcanist' feat that lets a character break down a higher level spell into multiple lower-level slots (3 1st in place of one 3rd-level spell, for instance).
As with spells-per-day, this prevents characters burning all their spell points in one go, though with more complexity than that.

Recharge Magic: an obscure 3.5 optional rule (Unearthed Arcana) - something similar is more common in MMOs (cooldown timers). This makes a spell "offline" for a while after use, how long depending on its level.

Progressive Check Penalties: Talislanta 4E uses a check to cast spells, with a cumulative -1 per prior spell cast. This forces characters to move to lower-level spells as their day progresses or suffer an increasing chance of a mishap occurring.

The Blood Sword method: this series of gamebooks had an adaptation of spell memorization where a wizard had to ready a spell into memory before it could be used (taking an action), and had to make a spellcasting roll to get off a spell; a character could adventure with some spells pre-readied to avoid this extra time, but each spell readied gave them a -1 to Psychic Ability, i.e. a penalty on their rolls to cast spells. Prepared spells could be changed freely in between encounters. Player choices were further complicated by spells having different casting penalties, and the possibility of the spellcasting stat being used for other game functions (i.e. rolled against to resist enemy psychic attacks).

Spell Points: while only slightly harder to keep track of than spells per day, these allow for spells that use more or less power.
Spell points are likely to be burned through quickly. Unless the character knows they need to conserve power (and is unable to rest) then the most powerful spells tend to be used first. Making this more tactically interesting can be done by either decreasing return on cost for more powerful spells (a 2nd level spell costs many more points than a 1st level spell, but isn't much better) or adding penalties for using up magic - for example, in Tunnels and Trolls through to 5th edition, casting spells cost Strength points which would immediately lower a characters combat ability including what weapons they could use.
As all a wizard's spells are available at any time, there may be some chance of decision paralysis depending on the player and how many spells are involved. Spamming the same damaging spell over and over is also possible, unless targets can take precautions against them or the spells themselves vary in effectiveness based on terrain and enemy type.

Systems may have fixed spell point costs for a given spell level (i.e. all 3rd level spells cost 5 points); in others each spell has its own unique cost (slightly more book keeping; more likely if characters have a lot of spell points since otherwise there isn't room for much variation). Costs may be fixed, modified by spellcasting roll (see prior post), have slight random variation, or have a fixed subtraction for higher-level characters, giving high-level wizards who can cast cantrip-type spells more or less at will. This principle can also be used if a high level character should be able to use more spells, but where spells drain a resource that doesn't increase with level, like an ability score (as with T&T characters).
Some other spell point related odds and ends:

*Dragon Warriors lets Sorcerers cancel durational spells to regain 1/2 the used magic points. Spells in DW have a variable duration (roll an expiry check as either 12 on 2d6 each round or 25% per minute), so the character has an incentive to cancel used spells as soon as possible. One rulebook adventure for DW has a trapped corridor which drained Magic Points from victims; clever players could avoid this by layering on as many durational spells as possible, walking through, then cancelling them.

*Rifts has a pretty evocative magic system. Spell points ('Potential Psychic Energy') are possessed by nonwizards, but can be donated willingly or forcibly taken (they are doubled at the moment of death) by sacrifice. Ley lines (particularly at conjunctions) can also provide PPE.

*Assigning costs for spells is a fairly ad hoc process, but SenZar has a fixed "1 power point = 1 hit point" rule for damaging spells, with spell level increasing the damage cap. (This would also work well for determining spell points a character gains if they have a special power to defensively 'absorb' magic.)
A system with GURPS-esque merits and flaws could also relate the cost of spells that give a target an advantage or disadvantage to the advantage cost (i.e. if Blindness is a 5-pt flaw, blinding an enemy will cost 5 magic points).
Another interesting 'effect-based' costing was Tunnels & Trolls Omniflex, letting characters rearrange their permanent attribute scores (keeping the same total). 5E gives this a flat cost of 186 temporary Strength (impossible to meet without significant magical stat gains, special cost reductions, or a cooperative ritual); Deluxe instead gives it a Wizardry cost equal to the # points moved from one stat to another.

'Powering up' spells is sometimes allowed for extra spell points. Arduin Adventure lets characters do this for example - paying the full cost of the spell for +50% effect - spells are cheaper enough that this tends to be fairly broken (potential for any wizard who could cast fireball to do it at x4 power for triple the Hit Points of any PC). While the cost was higher, the spell's 'level' didn't change. Tunnels and Trolls, or 5th Edition D&D, let characters 'level up' spells which costs more points / a bigger slot - in these cases with max. effect automatically limited by what spell levels a character can use.

*Monsters or magic items may also siphon off spell points e.g. cerebral parasites for psionicists in D&D.

*The Fantasy Trip and psionics in 2E AD&D charge extra spell points for durational spells while these are running ('maintenance costs).

*5E D&D uses both spell level "slots" for sorcerers and points ('sorcery points') which can be used to pump up spells, converted back into extra spell slots or vice versa (at a poorer conversion rate). Since conversion runs both ways, a sorcerer could use it to change lower-level slots to higher-level slots but inefficiently (e.g. 3 1st = 3 sorcery points = 1 2nd). This also lets sorcerers have more spells than wizards, despite primary casters sharing the same spells/day table to make multiclassing easier.
5E also has an interesting 'encounter power' mechanic in that characters can sometimes get class abilities recharged when rolling initiative if at 0 points (Relentless & manuever dice, Perfect Body & Ki), guaranteeing some use in any combat.

Exceptional Resource Drain: In all of the various systems, exceptional resources may act as an added balancing factor for specific spells. These can include material components with a non-negligible cost, experience points in some systems, or drains to a character (i.e. loss of Constitution points or hit points which might be permanently lost, temporarily lost, borrowed or shared with creatures or constructs); sometimes these costs may be borne by a beneficiary rather than the caster.

Resource usage mechanics are tricky in that they can encourage or enforce a particular encounter workday that character's shouldn't go beyond. Avoiding one set of adventure design problems by having characters always be at maximum fighting strength after an encounter (and hence not wanting to rest) unfortunately generates another set of problems, in that weaker encounters wearing down resources are no longer relevant, so that encounters need to be at the characters' power level exactly (4E D&D).

As with other skills, magical skills can be defined very narrowly or quite broadly. E.g.
 
* A single magic skill. A class based system is more or less this – usually all varieties of magic cast by the character will use the same level, though odd classes may have multiple separate spell lists/caster levels.
 
*skill levels applying to a single branch of magic (a “school” or “mode” etc) i.e. all conjuration type spells might belong to one school, blasts to another and enchantments to a third. Systems letting characters construct spells on the fly might define spell “seeds”, customizable on the fly into specific spells; which may have individual ratings.
 
* In Ars Magicas “nounverber” system, a spell requires two aspects (Form & Technique) with separate bonuses; a spell adds the two most applicable scores i.e. a blast of fire would use Creo (create) + Ignem (fire).
 
*skill levels can be in individual spells. LegendQuest lets characters buy “control levels” in specific spells, which are divided as the character wishes between effect, % success, and range. (It does also have a general magic skill, but this helps only with powering spells). (IMHO, while LQs splitting of control levels is an interesting mechanic, this setup limits wizards to a few spells over and over and so may be s bit dull; the same idea can be applied to a system with just one magic skill – it would also work very well with a dice pool system like that of Heroic Golden Turbulence).
 
*systems with skill specialization rules can have characters who have general magic ratings, but higher values in specific schools/spells, even where “Magic” is a single skill.
Aside from skill specialization, a game system might also have multiple wizard specialties off a single Magic skill by giving spells benefits from different character attributes i.e. a system might have a raw Power attribute that modifies spell damage and an Intelligence modifier for illusions and subtler enchantments (perhaps effects involving saving throws), leading wizards with the same spell magic skill and spell lists to still prefer different spells. Merits/flaws can also modify a wizard’s preferences.
 
If each spell is a skill, it follows that skill points must be expended to learn a new spell (unless a spell can be used untrained). Other systems usually learn spells individually separate to the magic skill; some (Talislanta up to 3rd Ed) do charge XP for characters to learn spells, while other games (D&D) would involve just a probable Gold Piece cost. D&D usually requires a roll to learn spells (significant in AD&D, largely a formality in 3E); Palladium has a spell-learning table which sometimes gives 'half-learned' spells (50% effect).
Rolemaster is interesting in having “spell lists” which once learned level up with the character, unlocking new spells. Some systems do not have individual spells at all and characters need to adapt a basic effect on the spot (Talislanta 4E, and Amazing Engine IIRC), while Ars Magica has rules for both that (“spontaneous magic”) and predefined spells.

Freeform magic systems are somewhat interesting in that they allow more latitude for 'creative' players. In games which also have 'real physics' to some extent, freeform magic may allow players to abuse physics knowledge by applying it e.g. a Mage: the Ascension hermetic wizard player is better able to apply 'Forces' effects if they understand some of what could be done by manipulating heat, magnetism or electricity ('I deflect the bullets by siphoning electricity to generate a magnetic field' or 'I explode the shotgun by manipulating the gunpowder reaction').
Freeform magic systems tend to give less refined results than codified spells, maybe downpowering some classes of effects because inherent limitations can't be considered and countered during the design phase. For instance, consider a spell that 'creates sword of holy fire' vs. 'create ball energy' (both Prime effects in oWoD Mage). The rules note that the sword effect is 'single target' regardless of how many people you hit with it (a bonus) but what isn't considered is that it doesn't mention is that the 'holy sword' variation is actually at a disadvantage because a fireball goes off immediately, while the mage making a weapon has to spend a round casting it (and not hitting anyone). (likewise, 'speed' effects are disadvantaged by requiring an action, reflexive defensive effects require specific action rules for that, and writing a generic option for 'quickened spells' may well lead to this just being abused for fireballs).

Part of our system is that we use spell points, but we use 8 different power sources, and different spells need different types and combinations of sources.  So part of the cost is based on different types of spell points/spell skills.

More powerful magics often use more types of spell skills as well as higher point costs.

we also have a recovery skill and a success skill in each type.  We have some casters who have a few levels in fire, but as many levels in recovery and can get back their whole amount of fire points in a few hours.

The StarCluster variants with magic - Blood Games II/OHMAS/Outremer and Book of Jalan - generally use up the linked attribute for the skill. If the magic is based on STR, it will cost a point of STR to use it. I know it isn't the only example of this, too.

-clash

Quote from: LordVreeg;506532Part of our system is that we use spell points, but we use 8 different power sources, and different spells need different types and combinations of sources.  So part of the cost is based on different types of spell points/spell skills.

More powerful magics often use more types of spell skills as well as higher point costs.

we also have a recovery skill and a success skill in each type.  We have some casters who have a few levels in fire, but as many levels in recovery and can get back their whole amount of fire points in a few hours.

Thanks LordVreeg. I hadn't considered systems which have multiple sets of spell points at all. Come to think of that, I think Ars Magica may have a very distantly related idea (pawns of vis, or stored magical energy, often only work for a particular type of spell), and there are systems where you can multiclass and have different sets of resources powering different spell lists, but I hadn't seen that idea exactly before.
The variable recovery skill is a new one on me too.
Thanks!

Quote from: flyingmice;506587The StarCluster variants with magic - Blood Games II/OHMAS/Outremer and Book of Jalan - generally use up the linked attribute for the skill. If the magic is based on STR, it will cost a point of STR to use it. I know it isn't the only example of this, too.

-clash

Tunnels and Trolls which I noted in spell points is quite similar, actually . I bundled ability damage based spellcasting into Spell Points since its the same basic principle (x points, y cost) although perhaps I should break it out more..?
I love systems that do that, actually, since it adds considerations to spellcasting that can deter players just burning through all their points, and since characters don't get unbalanced extra value out of the spellcasting ability score- when you've burned your high STR up  for spells you lose all the usual bonuses for beating up people. Slight additional overhead in recalculating bonuses occasionally of course.

EDIT: have found there are a couple of OSR games (e.g. Microlite D20) which burn 'hit points' as spell points. Interesting way to make wizards squishier in games where everyone has the same HP. This approach does need safeguards to prevent magical healing loops (the original version of Advanced Fighting Fantasy has a problem where a Stamina spell costs stamina to cast - a wizard can heal back to almost full after every fight, the only problem being the chance of fumble).

Quote from: Bloody Stupid Johnson;506679Tunnels and Trolls which I noted in spell points is quite similar, actually . I bundled ability damage based spellcasting into Spell Points since its the same basic principle (x points, y cost) although perhaps I should break it out more..?
I love systems that do that, actually, since it adds considerations to spellcasting that can deter players just burning through all their points, and since characters don't get unbalanced extra value out of the spellcasting ability score- when you've burned your high STR up  for spells you lose all the usual bonuses for beating up people. Slight additional overhead in recalculating bonuses occasionally of course.

I missed the reference to T&T, but T&T IRC only uses STR, while the SC games use all the attributes. It forces spellcasters to cast different spells, using different attributes, to spread the loss around, and since the SC analog of HP is a multiple of the character's physical attributes, it damages the spellcaster directly as well.

-clash

Quote from: Bloody Stupid Johnson;506679Thanks LordVreeg. I hadn't considered systems which have multiple
sets of spell points at all. Come to think of that, I think Ars Magica may have a very distantly related idea (pawns of vis, or stored magical energy, often only work for a particular type of spell), and there are systems where you can multiclass and have different sets of resources powering different spell lists, but I hadn't seen that idea exactly before.
The variable recovery skill is a new one on me too.
Thanks!

welcome.
I try to run a truly mutant system...  :)
Not just a rehashed mix of other peeps rules.

Quote from: flyingmice;506687I missed the reference to T&T, but T&T IRC only uses STR, while the SC games use all the attributes. It forces spellcasters to cast different spells, using different attributes, to spread the loss around, and since the SC analog of HP is a multiple of the character's physical attributes, it damages the spellcaster directly as well.

-clash

Ah I see...so Outremor effectively has multiple spell point pools as well! Cool, thanks. Spreading the damage around should make min/maxing harder as well...

Quote from: LordVreeg;506689welcome.
I try to run a truly mutant system...  :)
Not just a rehashed mix of other peeps rules.

Mutant is good...

This is only an incomplete listing which I’ll go back to later and add to (maybe), but please feel free to suggest anything I’ve missed and I’ll add it here.
 
D&D: arcane (wizard, sorcerer), divine (cleric, druid, bard (depending on edition, may share spell lists with druids/wizards).
2E has psionics, wild magic, rune magic; 3E has binders (entities inhabit caster to give them special powers depending on entity), truename magic, shadowcasting, elemental magic (shukenja), an oriental wizard variant (wu jen), warlocks. Assassins, demologists, blighters, and a few others other specialized characters have unique spell lists; however most types of magic are fairly similar. FR Magic of Faerun IIRC includes gem magic, gnome artificers. Eberron includes an ‘Artificer’ class.
 
Palladium Fantasy: Wizardry, Psionics (Mind Mage), Diabolism (rune magic), warlockry (elemental), witchcraft, Alchemy, healing; priests gain limited wizard spells+ unique special abilities. In supplements- Necromancy, Shamanism.
+Rifts includes Techno-wizardry, Tattoo Magic, the bio-magic of the Splugorth, gem magic, temporal magic, biomancy (hippie nature magic), mystic smithing, nature magic, fire sorcery, whale spellsingers & ‘Koral’ shaping.
+Mystic China: Chi magic, mudras
 
LegendQuest: druidic, healing, illusion, necromancy, sorcery, spellsinging, alchemy, enchantment, mentalism.
 
Talislanta: Biomancy, Cryptomancy, Erythrian Battle Magic, Invocation, Mysticism, Natural Magic, Necromancy, Pyromancy, Ritual Invocation, Sorcery, Thaumaturgy, Witchcraft, Wizardry
 
Dragon Warriors: sorcery, mysticism (psionics), elementalist (includes evil “Darkness” elementalists), warlock (battle-mage/fighter)
 
Shadowrun: hermetic, shamanic, technomancy
 
Mage: the Ascension has several ‘flavours’ of magic, but with all sharing the same basic magic rules. Types include the Technocracy, virtual adepts, order of Hermes, Euthanatos, etc.
 
Ars Magica: Hermetic, Hedge and Witchcraft
 
 
Fiction:
Interesting fictional examples of worlds with multiple magic systems I can think of:
 
 Master of the Five Magics: Alchemy, Sorcery (mind control), Wizardry (demons), (item creation), Thaumaturgy, Magic (item creation)
 
The Misenchanted Sword series: sorcery (technology?), wizardry, witchcraft (psionic?), demonology, warlockry (telekinetic), theurgy (divine magic).
 
Jack Vance’s short story “Green Magic” has colour coded magicks (White, Black, Purple, Green).

This is probably the last post on magic, though its entirely possible I've missed major subtopics. Apologies that this one is a bit random.
 
 
Power limits: maximum spell level/spell point cost of spell useable is typically limited by a character number gauging their spellcasting power; this might be the characters level, an attribute score (s), or a specific skill score. Spell levels may be equal to character level, or interspersed; for D&D wizards there are only 9 spell levels (across 20+ character levels) - with the memorization system giving a character a new spell level each level would also mean a new spell slot, and so an inordinate number of spells.
3E D&D has 'metamagic feats' which let a character adjust the level of a spell to add some extra effect, while 5E D&D lets characters expend higher-level spell slots for e.g. more damage.
 
Spells with levels sometimes have a 'magic point' cost connected to the spell level, while in other systems (Savage Worlds, Tunnels and Trolls) spell 'difficulty' and 'energy cost' are not connected to each other; games like this usually have 'spell points' growing much more slowly with level, since increases aren't automatically necessary to use higher-level spells; levelling up may instead unlock spells which use power more efficiently (lower point costs).
 Damage is usually connected to spell level in some way. SenZar has a set conversion rate between power pool points/damage, with level only increasing the damage cap, while in Talislanta 4E (IIRC) spells have level-based damage with the caster determining level as the spell is cast (this also modifies the success chance of casting, with the unfortunate side effect a higher level spell is less likely to 'critical' and so could do less damage than a low-level spell despite the higher cost).
Most other systems determine damage/effect on a spell-by-spell basis (Spell A does X base damage, Spell B does Y base damage). Ability modifiers may apply to damage (for example, for 4E D&D wizards who get +Int to damage for most spells). 'Effect-based (in the HERO sense) magic systems can have spells that deal damage based off a power rating assigned, which is not particularly compatible with the idea of 'spell levels'. Spells may also automatically scale up based off caster level/magic skill; the simplest case being D&D here (up to say 3E like fireball doing d6/level; 5E's approach where a fireball is fixed 8s6 unless you spend a spell slot being a change to more resource-based). As noted previously, LegendQuest has an interesting system where a magic-user distributes 'control levels' (equal to their skill with a given spell) across various aspects like damage, range, etc.

Games often let characters spend extra resources to pump the power of spells. D&D 3E has 'metamagic feats', D&D 2E has additional spells that sometimes augment other spells (e.g. the 'Vocalize' spell in Complete Wizard lets a wizard cast another spell silently, while 'Squaring the circle' in Tome of Magic increases a spell's range). SenZar lets characters spend extra power to boost area of effect, while Savage Worlds lets a character spend extra power points on bolt/blast to increase the damage. Synnibarr lets multiple characters pool their power to cast stronger spells and has a 'Winds of Enforcement' spell that lets wizards of high enough level multiply the effect and drain of a spell, with chance of backlash if too much power is used.

Implements/aids to magic: 4E D&D gave wizards staves which, like enchanted weapons for fighters, add ‘plusses’ to the wizards’ powers (staff +3 = +3 to attack rolls and damage with a wizard spell, assuming this spell has the ‘implement’ keyword). (Not in itself a bad change, IMHO, though a radical departure from prior editions where staves contained a number of charges of bonus spells)
Tunnels and Trolls allows wizards to have magic staves which subtract the wizards’ level from the Strength cost to cast a spell; the normal ‘ordinaire’ staff is slightly expensive (100 GP), although a wizard can use a L1 spell to construct a ‘makeshift staff’, which would possibly explode when first used (1st level save on Luck to not explode) and eventually burn out (after a given amount of use). It also had ‘deluxe staves’ – demons bound into staff form - which were semi-sentient and indestructible, learning any spells cast through them. A spellcasting aid could also take the form of a ring, enchanted jewel, etc.
Dragon Warriors lets sorcerors create a staff, but at a cost of their own permanent spell points; 2 spell points lost forever become 3 in the staff, which can be used only for the staffs particular sublist of spells (depending on its theme). Staves were effectively indestructible, but losing them was a major hazard to the owner (reminiscent of Sauron and his magic ring).
 
Power components: extra ingredients might add extra effects/power to a spell, or absorb some of the cost.



Magic Resistance aka Spell resistance: games frequently have magic resistance as a monster quality. Tactically, in terms of how much the wizard is boned, this parallels weapon immunity or damage reduction to the fighter types, or perhaps heavy armour. While armour more commonly (across game systems in general) reduces damage, magic resistance tends to negate or bounce a spell completely rather than reduce its effect, presumably since in most systems it is difficult to adjudicate what happens with a reduced effect spell (much like when a rings of spell turning makes a target take 60% of a charm person...). D&D golems are interesting in that the original D&D golem is probably immune to magic as a lazy shortcut to listing lots of specific immunities due to its material and lack of mind or metabolism; by 3E the golem had 'magic immunity' as a canonical feature even though all the specific immunities granted by the construct type, mindless condition, etc. and explicitly defined.
If an “armour bypass roll" system is in use for armour, then magic may function analogously; or if the game is e.g. a dice-pool system and the effects of 1 success, 2 successes, 3 successes etc. on a spellcasting roll are determinable, magic resistance might be partial; as an example I will mention Arkham Horror here although its a boardgame rather than an RPG – here characters get bonus dice on Fight rolls (successes equal damage) for either weapons or spells, with resistances halving the bonus dice and Immunity negating it – for example a monster with Magical Immunity ignores a spell, while a monster with Physical Resistance takes only ½ the bonus dice from weapons – the character’s base combat dice still apply.
In other approaches I vaguely recall seeing a magic system where MR instead functioned by reducing spell duration, so a spell was thrown off more quickly, and there are specific cases (e.g. some anti-psionic feats in 3E) where using an ability costs more points vs. a resistant target. Valley of the Pharaohs contained a monster from Egyptian mythology, which was difficult to affect with magic because spells attacking it required speaking its true name, which was inordinately long and thus increased the casting time of spells).
As well as a monster/racial ability, magic resistance may also be gained from class (the Nega-Psychic in Beyond the Supernatural?) or advantages (e.g. Savage Worlds' Arcane Resistance Edge, giving +2 on opposed rolls and +2 Toughness vs. magical damage).

Also, some misc things (quoting from Ron Edwards' Fantasy Heartbreakers essay)

Quote from: HeartbreakersHahlmabrea: A character learns several spells in a given category, but may cast them in any combination for synergistic effects. Improvising novel combinations and outcomes is highly encouraged and supported by many examples in the text. The best thing about this system is that combining spells actually reduces the chance for Spell Error, rather than increasing it - creating incentive to combine and be creative.
Legendary Lives: A character knows a category or two of magic, with no further compartmentalization - no individual spells. Instead, the player may customize applications of the category on the fly during play. So if you know "Fire" spells, anything and everything about or using fire is yours to do. It's limited only by "cost" (0-5) as set completely freely by the GM, which is the one sour note in the mix, as it sounds to me like a recipe for bitter argument. (LL's system is similar to than Ars Magica's, but more sketchy and flexible.)...
...Forge: Out of Chaos: The player picks a character's spells, but each one is heavily randomized for many aspects, including points to cast it, degree of side effects, distance, duration, and other things. One begins with an allotment of re-rolls for these aspects of the spells, and increasing the character's level includes more re-rolls, permitting the player either to add new spells or refine the old ones as desired.
Dawnfire: First of all, every character is a magic character in this setting, with Flow Points and access to a variety of magically-oriented abilities; "magic users" are simply those who have optimized the same abilities that everyone has. Second, the game includes the universally-accessible mechanic called bullshitting, which is just about the neatest magical mechanic I've seen in print. To "bullshit" is to cast any spell in the book or that the player can make up, regardless of what is or isn't written on the character's sheet. Anyone can try it, any time; having a certain skill makes it a little safer, but that skill is not necessary.

Dawnfire also deserves some special mention for its encouragement to customize the magically-oriented characters as desired, such that one character might be a singing bard-type or whatever ... this is pretty standard, until I got to the suggestion regarding "na?ve" magic-guys - who must bullshit all their spells and never realize that they are casting magic. The player must describe all the outcomes of their spells accordingly, manipulating elements of the environment to suit.

Good and Bad Power Writeups
A few spells (or similar things) are badly written, largely due to interaction with other rules, that they more or less don't work RAW. A particular problem is when a spell's casting time offsets its actual use.
*e.g. initiative issues - 2E D&D 'energy containment' is a defensive power which basically negates incoming energy attacks. However, it doesn't have a duration and can't be maintained, so probably requires successfully guessing what the monsters are doing, and declaration of action use, before initiative - I'm not 100% sure. (by comparison Star Wars D6 [2E] absorb/dissipate energy clearly does require an action, but lasts for a round afterwards).
*in 3E D&D, Xephs (a psionic race) have a supernatural power which increases their movement speed, but there's no indication this has an unusual casting time, so by RAW it takes a standard action to use and thus limits the xeph to a single move. The power lasts about 3 rounds so it could be useful, but is limited to edge case use by dodgy design, probably unintentionally.

*conversely in possibly good, or at least interesting, design, 4E D&D has healing powers like Healing Word operate as single target close bursts ("one ally in burst") rather than being ranged attacks; consequently these powers don't trigger opportunity attacks as ranged attacks do (discussion here (http://forum.rpg.net/showthread.php?402940-4e-Single-target-powers-Ranged-or-Burst)). Slightly similar maybe 3E Faerie Fire is a burst which affects a 5-ft radius as its intended to affect invisible creatures and would be stopped by the rules prohibiting targeting vs. full concealment if it was a ranged attack.

Keywords
Keywords are an idea that I believe was particularly popular with CCGs, that sort of made the jump to RPGs; they start appearing e.g. in 3E D&D spell descriptions (tags like [Fire], or [Mind affecting]) and can be useful. In 4E these were used more often, sometimes initially not doing much but with the idea that later feats/powers would combo off them.

Some games use an informal keyword approach where a word that's part of the name of the power, or for some card games any text on the card, becomes a keyword. For example, from Feng Shui, Integration of the Clouds (fu power) lets PCs 'combine use of two fu powers in one action; affected powers must share a word in their titles (such as 'Fox' or 'Fire'. Fu powers with contradictory conditions may not be combined. Pay chi cost for both, but only the highest shot [i.e. action point/initiative delay] cost. While a fairly cool trick, this obviously adds a need for oversight on power titles (which would otherwise be just fluff text), which rapidly becomes problematic as # powers increase. Its also largely an arbitrary restriction unless the writer has taken pains when naming their powers, might generates a conflict between clarity in power naming and banning combinations (Pro-X and anti-X powers both include X), and - in this case - brings up a question of whether the same power can be activated twice. May generate interesting linguistic problems in translation, or homophone issues e.g. if 'wind' (air) and 'wind' (watch) are the same word.

Naming Conventions
Spells are often named fancifully or after its alleged creator (one D&D spell, Nystul's Magic Aura, is instead named after the player). While fun extensive grimoire's have the potential to be annoying where indexed alphabetically since e.g. "Sharthyd's Spell of Evil Detection" is under S, rather than D for Detect Evil. Or may be a mix of that and things like "Speed up Spell, Jon's" depending on exact name structure (Compleat Arduin).

Next - monsters and NPCs.

“The Gibbelins eat, as is well known, nothing less good than man. Their evil tower is joined to Terra Cognita, to the lands we know, by a bridge. Their hoard is beyond reason; avarice has no use for it; they have a separate cellar for emeralds and a separate cellar for sapphires; they have filled a hole with gold and dig it up when they need it. And the only use that is known for their ridiculous wealth is to attract to their larder a continual supply of food.”
-The Hoard of the Gibbelins; Dunsany.
 
OK, monsters.
Other game systems interrelating to the monster rules include: hit location, hit points, Size, special abilities/powers, attacks per round, attribute scores, races, movement/miniatures, NPCs.
Weapon rules also often interact regarding natural weapons. A monster might have a single damage range representing multiple weapons (opening up more options for the DM describing attacks) or bite/claw/tail slap might have distinct damage ranges and attack bonuses. The latter can sometimes turn into the monster spamming the heaviest damage attack over and over [SenZar], or lots of rolls as each item is checked separately e.g. a 3E dragon has five physical attacks normally -2 claws, a bite and 2 wing slaps - as well as distinct rules for other options such as tail slaps or crushes. D&D4 monsters alternate attack bits by switching between powers with various cooldown times. (Another way to represent multiple natural attacks might be to add a hit bonus for extra bits, then roll between limbs if they have different damages).

 
Some interesting systems/ideas with regard to monsters:
 
*Tunnels and Trolls has single-stat monsters – very quick to create; a creature’s “Monster Rating” determines both its combat roll (dice+adds) in combat and its hit points. This works largely because T&Ts combat system is quite simple, with all attacks simultaneous and damage equal to difference between both sides attacks. There are guidelines for converting MR back into attributes where necessary e.g. using the score as CON and distributing adds among the stats that give a combat bonus in T&T: Str, Dex and Luck. This is something of a 'kludge', but ends up seeing use when e.g. a monster has to use a ranged weapon (DEX check) or other save. Particular problems occur when a MR-rated creature is used as a PC (e.g. one solo turns a character into a tiger with MR 186).
The MR system also makes stats for conjured creatures very simple (often MR is based off a couple of the wizards's stats added together). Another interesting use of MR is in one solo adventure ('Soul Survivor') where a PC adds together their WIZ and CHR to get an MR to be used in a psychic battle, using normal MR rules (an interesting idea which could be the basis for any sort of weird 'skill challenge' situation perhaps - from CHA+IQ diploma battles to STR+CON pie-eating contests).
T&T sometimes has two-stat monsters with a 'Fighting MR' and a 'Constitutional MR'. (I'd toyed with idea that some other checks could use Con-MR as well e.g. a centaur might have a large Con-MR due to body mass, and use that for STR checks with its horse half too).
Partly T&T derived free rpg Twisting Tunnels (see link in 'multidie additive' post) has a similar MR system, but possibly more useful because its core ability check system is compatible with the "MR" dice, instead of MR being largely on a different scale to other stats that requires conversion- working in a freeform fashion similar to how e.g. 'Over The Edge' traits work:

QuoteA monster’s Hit Dice can be used for anything that makes sense: A dull-witted troll might use its Hit Dice for smashing or devouring hapless delvers, but not for a chess tournament. A cunning sorceress might use her HD for dueling wizards or beguiling warriors, but not for a pie-eating Clash.

(as an aside, I once was fiddling around with an MR-based system for treasure generation, where the GM could use 'effect' from an MR roll to generate not just damage but also how much treasure its carrying and/or what magic items it has - # successes being converted into a + or level of magic item (rolling separately for gold and magic). The main issue I had with this was that inflation in MR didn't give a steep enough gain in magic item power - the dragons didn't have stuff that was much cooler than the orcs did. Potentially fixable, though).


In other more modern games, I suspect the One Roll Engine probably isn’t far behind T&T Monster Rating in complexity since one roll determines hit, damage, hit location and initiative, although at the least a creatures’s hit points are going to be separate in ORE.
Less extremely, Atlantis (Omega system) gives monsters an 'adversary level' which replaces separate Combat Rating [attribute] and skill rating- a monster applies its full level to either attack or defense, then only 1/2 to the other option.
 
*Feng Shui included “mooks” or “minions”, bad guys who died after a single blow, an idea later also in 4E D&D; this did make these guys follow different rules to PCs as regards hit points (e.g. in 4E everyone except them added their Con to HP), and sometimes raises questions like “how did this dude get to 30th level with 1 HP?” or weirdness with the larger monsters (1 HP ogres). In 4E, this is usually related to the idea of monsters having multiple stat blocks; an orc encountered at level 10 might be the 'same' orc as at level 1, with its HP and defense scores however switched out to make it harder to hit (level appropriate) but easier to kill (minion). In a sense this is part of the 4E concept that stats exist only 'on camera' for dealing with PCs, as opposed to the system functioning as a 'physics engine' where the GM can extrapolate rules interactions for worldbuilding.

Minions do however ease tracking on the GM, for large combats. AD&D implemented this effect more or less by having creatures varying from 1 HD to lots of HD, depending on size or level; however, an equivalent effect can also be set up where HPs start out relatively even (i.e. =CON for everybody) by having level differences (e.g. amount an attack roll exceeds defense, or special attacks) significantly adding to damage.
Savage Worlds’ version of this was interesting; most creatures have only 1 Wound, but a damage roll must beat a target’s Toughness to damage it; each +4 rolled over toughness generates 1 “wound”, with just beating it resulting in a target instead being “shaken” ( a second shaken result gives a wound). The system works well for mass combat, but perhaps not as well for combats against single, larger monsters; combat against one may include a few rounds of nothing happening as characters try to get lucky, unless the players are clever enough to work together with tricks/stunts (or get lucky and explode it on round 1).
(Note on getting around HP tracking: its been suggested that lots of HPs can also be tracked by having a "pile" of HPs, equal to [monster HP x number of monsters] and just having monsters die each time points equal to the monster HP are lost. This assumes PCs will focus fire - which they probably would try to do anyway.)
 
*AD&D had monsters without ability scores, which generally worked (they did have Int, and occasionally would require other scores - these could be rolled up or GM assigned if necessary, with Strength probably being the most-needed stat for various combat maneuvers). This generally worked since with or without rolling a statistic, as the monster's capabilities would be largely the same - the AD&D bonus charts gave very few modifiers in the 9-15 range. PCs with very high stats could get unfair advantages over creatures, who had no Con bonuses to their Hit Dice or (usually) Str modifiers for damage. Giant-type monsters in 1E had fairly arbitrary damage but Large weapons were standardized (double normal dice i.e. longsword 2d8) and Str modifiers added in 2E.
Basic occasionally gave larger monsters a + to damage (e.g. orc chieftain - +2 to damage), representing Str.
3E’s universal system applied modifiers to most tasks, and mandated inclusion of attributes - which were often quite high and generated huge modifiers; this made monster creation more complex and made monsters of the same HD/CR vary in challenge considerably (albeit realistically).
4E kept monster statistics, but by fiat disjoined them from the system by declared that monster attributes did not modify their attacks, defences or hit points, in order to keep these precisely level-appropriate. (edit 27/4/2014: to be fair, looking closely at this now it seems that the numbers aren't far off - possibly the designers set monster ability scores after setting values with the role/level table, giving them appropriate numbers in one of each defense pair to get nearly-correct final defense values).
Palladium perhaps also bears mentioning: this has rolls for monster attributes, with this often being useless or unnecessary since there are no attribute checks and combat modifiers start only at very high values.

*3.x D&D also had a complex and somewhat confusing system of monster “types” (undead, fey, animal, magical beast, etc) though these were poorly defined and sometimes overlapping; types could be based conceptually off size (giant), monstrous features (aberration, monstrous humanoid), shape (humanoid, ooze), composition (elemental), or origin (outsider). The types made adjudication of effects such as whether a given spell would work easier but also functioned as classes for monsters, overcomplicating new monster design by setting HD, BAB, and skills. Low-Int but very big monsters would get excessive skill points.
 
*Runequest has one of the best (IMHO) systems for representing monster statistics; it includes both detailed hit location tables specific to each monsters, other monster attributes, and gives monsters Size scores (this automatically feeds into determining hit points, instead of being fairly ad hoc like most games). The system lets monsters have varying armour by location (something D&D tried and struggled with in older editions before giving up), and hit locations let PCs do things like cut the legs off the giant spider etc. Runequest is also noteworthy for having “incomplete creatures” (things without some ability scores, e.g. incorporeal monsters with no Str scores, or soulless monsters with no Power stat), an idea Tweet later adapted into 3E D&D (“nonabilities”). In many cases 'nonabilities' are indistinguishable from scores of 0, although they bypass 'death at zero attribute' rules and prevent attacks against the weak ability (making ghosts ungrappleable for instance).
RuneQuest monsters have stats and skills in the same fashion as do PCs, and can be used as characters directly (although some might make especially powerful PCs).
 
*The Atomik Alienz supplement for Fuzion had an interesting set of choices for SF monster design including circulation (open, closed, osmotic, raw energy, none); type of blood (warm, cold, hydrocarbons, gaseous); composition (silicate, carbon-based, robotic, pure energy), respiratory system (absorption, gills, no respiration), nervous system (electrochemical, semi/superconductor), locomotion method (aquajets, slither, monopod), etc etc. From a biology perspective it was fascinationg though the detail generated was largely a curiosity – the mechanics for Fuzion did not particularly make these details important. I’d have loved to see this written for a game with bleeding rules, detailed hit location (got your spleen!!) and so on.
Things like redundant internal organs or lack of vital organs can also be represented fairly well in games with multiple sorts of HPs (Palladiums Hit Points/SDC, or the Alternity set of three separate types, Mortal/Wound/Stun).
 
*GURPS Lensmen as noted earlier has some really weirdly shaped aliens, something that’s interesting with its minis rules. (GURPS, or any point-based powers system, is probably going to be good for putting together new monsters, though the process may or may not be easy).
 
*Systems may have precise ways of working out how tough a monster encounter will be (“encounter level”), or even prescribing how difficult an encounter should be. The most notable example of the latter may be 3:16 (the High-Ronny-Award Winning Starship Troopers-ish game); this gives the GM a limited number of “Threat Tokens” to use per planet. Successful Fighting rolls let PCs remove Threat Tokens, with each “Threat Token” representing a variable number of aliens, probably lots.
 
4E has a set of statblocks for monster roles (Ambusher, Lurker, Artillery, etc.) at various levels, which are the basis for designing new monsters - one oddity here being that monsters seem to sometimes change types i.e. the younger version of Green Dragon is an ambusher while the older version becomes a controller. Fantasy Craft reportedly uses a numerical system where monsters are rated from 1 in 10 (in roman numerals) for various traits; that value is used with the monster's level to determine its final bonuses in a category, so that it can be threoretically scaled up with level differently in each aspect.

AD&D has only vague CR guidelines. It is interesting in that some monsters require magic weapons to hurt, which has the effect of limiting those to powerful characters indirectly (and probably prevents henchmen or hirelings from helping out unless they can think of something clever to do).

Monsters may sometimes be fit poorly by a 'humanocentric' attribute scale and rules. In particular a single score for e.g. Strength may not represent well creatures which may be very strong in some muscle groups/circumstances and weak in others, like centaurs (upper body strength much less than lower half, and expect chin-ups or climbing to be impossible) or cave fishers (the D&D cave fisher has an 18/00 Strength for the filament it uses to 'fish', but no damage modifier to its pincers; the pit fiend is exactly the opposite, with an 18/00 Strength for melee damage while its tail constrict can be escaped with an unmodified Strength check by the victim. Interestingly if AD&D had used attributes, it would probably end up shoehorned into using the same Str for both). # legs sometimes figures into Balance checks (e.g. 3.5 vs. Trip attacks).
 
In systems that aren't too complex or 'simulational', monsters are often reskinned as other types (many AD&D monsters have notes like 'treat female carnivorous apes as gorillas for HD and attacks, but allow them the same keen senses as the male' (Dragon #133), or 'treat young storm giants like ogres'. This sort of thing can also be handled to an extent by monster advancement (reduction) rules, or even rules for varying a monsters' "ability scores".

Below: from Different Worlds magazine #35, the Star-Devourer is a particularly sexy Lovecraftian worm monster in Superworld (APP -Appearance- of 50). Note the complexity of the stat blocks - in T&T the GM could just assign "Monster Rating: 1000" and be done with it.
(http://i1239.photobucket.com/albums/ff507/BSJ17/StarDev3_zps25f99cd9.png)

Monsters as pets: [section to be expanded]
Link discussing problems with 5E ranger here (http://librarians-and-leviathans.blogspot.com.au/2015/07/a-beastly-problem-animal-companions-in.html) ; tl;dr - ranger companions are selectable based on CR which is partially based on HD, but actually get their own minimum HPs, throwing off many but not all CR estimates. Generally can't benefit from ranger buffs (hunter's mark), but may be able to use own special abilities. Specific problem with Multiattack.

Miscellaneous: HarnMaster shares illustrations between similar monsters, such that the GM may show the PCs the monster illustration from the book without definitively tipping off the players whether they're fighting e.g. a sentient undead (Ahmorvus)(sp?) or just a zombie.

Link on monsters as challenge vs. monsters as simulation on rpg.net (http://forum.rpg.net/showthread.php?769440-3-5-Miniatures-Handbook-was-the-unsung-Monster-Vault-of-3-5). Winning quote here:

Quoteit seems to me that most of the time they started with a goal, and then worked backwards to justify it, so it didn't feel it was really simulating anything in particular either. Natural armor was especially bad because it felt to me like it usually based on the creature's cr rather than how tough its skin looked.

Although, IMHO, it is useful to differentiate some aspects - dodging from armour - to be able to say whether armour can be looted or immobilization will stop a monster, it is possible to go too far.

Attacks per round: how many attacks a monster gets depends a lot on how common multiple actions is in the system, as well as whether a monster is normally designed as a single boss that fights several PCs or as one among a horde. Usually monsters get as many attacks as PCs (or more, for a boss-type monster). D&D is an interesting case in that 4E 'solo' or 5E 'legendary' creatures explicitly get extra actions. In AD&D only fighters got extra attacks with level, so few monsters do; 3E generally kept monster attacks the same as that, despite all PCs now getting extra attacks (based on base attack bonus); the exception being weapon-using monsters which got extra attacks with level; a fire giant (for example) went from 1 attack to 3 due to their Hit Dice, making it more dangerous since its size gave it both huge damage and multiple attacks due to its HD.
Other monsters had multiple attacks due to multiple natural weapons - dragons, krakens, whatever. Or conversely to the fire giant there are epic-level (i.e. over 20th level) monsters that get only 1 or 2 attacks. A hunefer (god mummy) for example gets 2 slams despite a +25 base attack (50 HD), which would entitle it to 4 iterative attacks with a weapon (like a PC); the monster description tries to give them 'unbelievable celerity' by adding Haste as a spell-like ability.

Conceptual note - note that the separate approach for monsters and PCs in 4E, has a slightly peculiar effect that many almost-PC creatures like bandits had monster stat blocks. In 2E or 3E by contrast, something being a monster implied that it was a specific monster race; that could make it raidable by players, using monster-as-PC race creation rules. But its interesting that say something like a 'hag' in 2E (your traditional witch) is weird in being a monster type, while the similar statblock in 4E could have a monster writeup and yet still be just an old lady.

Monster Treasure: monsters in AD&D got a numerical code which tended to generate specific things (gold, gems, potions, weapons, etc)(sometimes weirdly specifically). A bit more abstractly, Dragon Warriors just gave each a rating from 'scant' to 'bountiful' that scaled up fairly non-specifically.
(http://i1239.photobucket.com/albums/ff507/BSJ17/treasuretype_zpsmmovpeys.jpg)
Random generator online:
https://www.cobwebbedforest.co.uk/workshop/Treasure (https://www.cobwebbedforest.co.uk/workshop/Treasure)
(the above is a bit awkward in that it has separate rolls for is there, then how much; for some of these it could be made one roll if there were e.g. d12-2 items or so on). The treasure generation system here is also an example of an 'effect' system, a bit like working out damage after a 'hit' determines there's treasure. In other games this may be more GM-determined.

3E gave monsters a challenge-rating appropriate amount of treasure, which the GM could assign although the amount was reverse engineered from the random treasure generator by level; some monsters had no treasure which others to compensate got double.
(the system didn't balance characters who were levelling by killing more lower-level monsters, which could generate more treasure).
4E was even stricter in how many 'treasure parcels' were found per level.

NPCs are in most systems similar to PCs. By this posts nature, it concerns itself primarily with systems where NPCs are treated differently to PCs, although my personal preference is generally for them to be treated as similarly to PCs as possible.
Systems may do it to ease tracking that would otherwise be too complicated, because of actual assumed differences between PCs and NPCs (e.g. PCs being assumed to be adventurers/heroes and hence exceptional). Systems may treat NPCs as “narrative constructs” rather than fictitious people in a fictitious world - this could include setting PC hit points at a level that makes them readily fall over dramatically (minions), or setting DCs to influence an NPCs at a level-appropriate rating for the PCs.
An extreme case of this would be Apocalypse World, where NPCs have no statistics; they have a health (less than a PC) and may inflict damage (based on weapon), but all rolling is done by PCs, with NPC ability not giving any adjustment. Dungeon World is similar: notably, PCs can get "instant kill" results on NPCs due to rolling for Hack & Slash against lower-level opponents, while NPCs don't roll and just do damage occasionally.
 
More common examples of this include:
*social skills; systems may have NPCs susceptible to intimidate/diplomacy, whereas PCs might not be – since this infringes on a player’s control of the character and their main input into the game (“deprotagonization”).
 
*attributes: HarnMaster has an intelligence score for NPCs; for PCs this is however just called Memory; while it adjusts skill bases identically for both, there is no pressure on the player to roleplay a character as dumb after rolling a low score.
Slave NPCs in Tunnels & Trolls have no 'Luck' or 'Charisma' ratings (a CHA can be bought if you want an especially pretty slave).
 
*damage: Cadillacs & Dinosaurs tracks hit points for NPCs or monsters as a single total, even though PCs instead have HPs for different body locations (e.g. arms, legs, torso, head). This is done for ease of tracking; it tends to reduce NPCs ability to take multiple shots (for PCs, these stack up more slowly unless they happen to be in the same spot). It may also make them less likely to be taken out through shots to low HP locations (the head), though the system also gives a kill roll vs. NPCs shot in the head (recommended to only cause unconsciousness to PCs).
Savage Worlds PCs also have more wounds than normal NPCs, to make PCs last longer rather than for simplification.
 
*dice rolling/core mechanic: Savage Worlds gives most PCs a 'wild die' whereas most NPCs don't get one - peculiarly making PCs more likely to botch (a double-1), although some skills also specifically fail just on a 1 on the 'skill die' i.e. Repair, Persuasion.  Apocalypse World as noted doesn't roll dice for NPCs (or have attributes); Unisystem in some cases doesn't roll dice for NPCs, giving them an average roll for 'muscle', smarts' and 'combat' (cf. 'Cutting Down Excess Rolling' post).

*character details in general. A few games suggest that characters not be constructed using the PC guidelines- the GM just gives them attributes and skills as they see fit (Savage Worlds for instance). In something like GURPS this is also pretty reasonable since NPCs could theoretically be built with whatever # points anyway, and because the GM isn’t going to be able to exactly build every every NPC).
Some adventures go the extra step of avoiding details of characters deliberately, or modifying them on the go. The classic Harlequin adventure for Shadowrun for example, never gives any statistics for the main BBEG because “give something stats and the players are going to kill it”. The GM is expected to modify statistics and fudge dice rolls as required to make sure the PCs fail when opposing him, until they reach the finale.
Some games may just not include NPC rules. e.g. World of Synnibarr has chargen rules primarily aimed at creating adventurers, and its largely unclear what stats a non-adventuring NPC is supposed to have. Many of its shopkeepers etc. that do have stats seem to be just statted as adventurers, and often 50th level to avoid PCs screwing with them, but judging from its fiction probably some NPCs were meant to be non-super and need saving.
 
*reduced randomization (i.e. of stats): where a PC requires a lot of dice-rolling to generate, GM 'modelling' of a character (short cutting the dice rolls) is likely to construct something with more precision and control than what a player gets. The extremest case here is Mutant Epoch, where race (sometimes), attributes and skills are randomized; if the players want to go see a fixit guy to help repair the ancient vehicle they found, the NPC in question can't be randomly built in the same way as the PCs because they'd end up meeting some crazed gladiator or slave courtesan instead.
Even in a random-roll AD&D game, GMs are likely to often assign individual stats to NPCs (e.g. 'the bandit chieftain has Str 16') instead of rolling up everything. (cf. Character Modelling in attribute generation, pg1).
Conversely though, point-buy systems can give an NPC that's only 'partly generated' an advantage - if there's suddenly a question of whether an NPC can prevail due to minor details (if only they had minor skill X, a particular advantage, etc. - like Combat Reflexes to break out of a grapple, or Quick Draw to make a full attack after being surprised, or an extra +2 to a particular save) then having the GM simply choose this may appear unfair. It may be useful for a GM to random-roll a trait then, even when its ordinarily bought.

*Critical hits; NPC antagonists appear for only a combat then die, so from a fun perspective its great for the PCs to gorily decapitate them. The same is perhaps not as fun for players when on the receiving end, however, and is very annoying particularly where character creation is lengthy or long term play is desired. The simplest handwave for this is that only PCs (or special PCs) get to do crits, as seen in the old optional Critical Deck for 3.5 but this is not completely satisfying from a realism perspective. Known other workarounds for this include:
-Warhammer 1E/2E: here all characters have a number of ‘wounds’; only when these are depleted do characters begin to roll on the critical tables. Characters can be permanently maimed, but there is at least a buffer to prevent mighty heroes being shivved by lucky goblins Rolemaster-style. PCs can also spend a ‘Fate Point’ to cancel a death.
-4E D&D has a surprisingly subtle solution to this. A normal critical hit only does max damage (i.e. 8+bonuses for your longsword, instead of d8+bonuses), unless a character has a magical weapon – which ordinarily gives +d6 damage per plus. While PCs are expected to own a magic implement/weapon virtually without fail, this is very uncommon for monsters, even the human-shaped ones (these get a + to hit that replaces the item bonus as a special monster power); consequently their criticals are lame.
- related to that idea, some sort of confirmation roll can be added based off an attribute/skill which NPCs will not necessarily max out, though PCs probably will.
-FantasyCraft requires characters to spend ‘action dice’ to confirm criticals, making crits (I assume) less accessible to mooks. In a similar vein, TORG gives drama deck cards providing special extra results only to PCs.
-Savage Worlds gives PCs the ability to spend a luck point (‘benny’) to ‘soak’, reducing incoming damage (something PCs don’t usually get to roll to avoid).

*Luck point economies.
-Marvel Super Heroes gives villains 'Karma' like PCs, but they regenerate this in different ways or lose it for different reasons to PCs. This is not entirely non-PC like, existing mostly because of the assumption PCs are a particular thing in the world (heroes) that other characters aren't. The karma system is designed to provide roleplaying rewards even though the character is an NPC - the GM gets Karma for a villain when they gloat over a hero for instance[/FONT]
Other games can deny NPCs luck points entirely or give them less, or have a single 'bank' of points for the GM.

*advancement: NPCs may be assumed to be earning XP the way PCs do (e.g. killing monsters), or may have alternative ways to let them earn XP (many Dragon classes in the AD&D period had weird classes which earnt XP for odd non-combat tasks e.g. gravedigging), or this may just be glossed over. Omege here (http://www.therpgsite.com/showthread.php?p=781277#post781277) mentions the idea of
setting NPC's levels off their rolled stats (attributed to Dragon #68 but that actually just gives NPCs a level limit based off stats).

*equipment: 3.x D&D PCs had an "assumed wealth by level" which was calculated using monster wealth and expected encounters to level up; comparatively NPCs just have cash as single monsters (x3 on the assumption some is in consumables) so orders of magnitude less. This contributed to significant disparities in effectiveness between PCs and NPCs at high levels, especially "epic level"(21+).

*magic: magic may be a largely NPC thing in some games (e.g. Call of Cthulhu).

*monster abilities. If PCs can play monsters, they may not get the whole range of potentially game-breaking monster abilities. 3.x generally gave the whole suite of monster abilities. 2E AD&D attempted to start monsters as 1st-level characters, so Large monsters traded in all their monster Hit Dice for +1 hit point per hit die (e.g. a firbolg gets +13 hit points at 1st level) although they also take Large-size weapon damage. 'Adventuring' PC monsters would however get a class, which NPC monsters didn't.

Miscellaneous: NPC personality randomization
*games sometimes have systems to randomize NPC descriptors which essentially come down to RP or player choice in the case of the player characters - i.e. personality traits or other minor traits. D&D sometimes uses random rolls to determine alignment (or in 2E, d100 rolls for NPC 'quirks' like 'spits occasionally' or 'mutters a lot', while Cadillacs & Dinosaurs ( Twilight 2000 ?) interprets playing card results as NPC motivations: Clubs = aggression, Diamonds = greed, hearts = friendly, spades = ambitious, with number determining degree and face cards giving somewhat special results (i.e. Queen of Clubs being 'stubborn' rather than aggressive, Queen of Diamonds being lustful rather than avaricious, etc.) and Aces reversing the result (i.e. Ace of diamonds being generous). In most cases these could be used for PCs, but are unnecessary if the player has their own ideas.
For sets of NPCs, an interesting NPC motivation generator for FATE is the 'Mood of the Room (http://www.deadlyfredly.com/2012/08/the-mood-of-the-room/)' roll using 4DF:
this reads the plus/minus/neutrals on the dice as different factions to give results like +++-; 'on the surface very receptive, but an agenda or traitor behind the scenes'; or ++0- 'your point of view is most strongly represented but loud minorities exist, some preaching opposition and some isolationism'.

Other Unusual NPC Generation Systems of Note: Post-apocalyptic Adventure "Bring me the head of Frank Sinatra" has an (unofficial) Gamma World expansion of Gygax's Random Harlot Subtable, which allows for features including detailed sentient plant bits, multi-gendered harlots and various robot types.

NPC organizations
See note on the 'push pyramid' for managing organizations here (http://www.therpgsite.com/showthread.php?p=500021#post500021)

Quote from: Bloody Stupid Johnson;496055D100 systems.
A d100 system is finely detailed, meaning there are no break points/dead spots for attributes – every point is important, limiting min/maxing. It is slightly slower for multiple rolls (as dice must be paired up as 10s/1s).
D100s handle fine detail very well (exact percentage odds) and is the most "transparent" mechanic to players.
Potentially, a d100 additive system can be sped up slightly by rolling d10+modifiers, with a fail-by-1 triggering a reroll against the ones place.
 
d100 systems occasionally generate additional information using the '1s place' of the d100.
-HarnMaster treats rolls ending in 5 or 0 as critical successes or critical failures, to assess these quickly (if non-intuitively)
-Amazing Engine treats the 1s place as the quality of the result
-Warhammer 1E/2E inverts the attack roll (i.e. 39 would become a 93) and uses this as the hit location roll.

Thought I'd add a few comments.
Top Secret/SI(Designed by Douglas Niles and published by TSR way back in 87, it used all kinds of cool/innovative bits in its design--ads/disads, stun/wound dmg marked as /X, luck points, etc)  pulled two result from attacks for close combat/melee. You'd roll under your Attribute (plus small skill bonus), if you succeed, your damage was based on the tens die (a Price is right/blackjack mechanic) and the ones die determined hit location.

Other percentage systems use doubles on the percentile roll as Special result. Seen some that use exactly = to your Success chance as critical success. A price is right/blackjack variation.

Quote from: Bloody Stupid Johnson;496054Some systems independently vary both target number and # dice (oWoD – particularly Werewolf- and Shadowrun 1e/2e). This unpredictably/erratically increases the number of dice needed to get a given # successes and is an approach that should probably be used rarely. Shadowrun uses d6s and allows target numbers (TNs) over 6 (6s add and roll over).
 
Dice roll systems integrate particularly well, with even damage etc. following the same universal system. Attack roll successes may add to Damage successes giving DEX a percentage flow-through into damage (usually less than Strength since successes are normally converted into extra dice, and have to be rolled again), without the math being excessively clunky.
 
.

There is quite a bit of elaboration or compound systems in this category. For instance, in Silhouette You add your Attribute rating/mod (0 based) to your dice result for your dice pool (based on skill level( (which is made as count highest with bonus for each extra six, plus variants) compared against a variable target number. Last Unicorn games Icon system did the opposite, your Attribute gave you the number of dice in your dice pool (d6), where you count highest, while your skill gave a flat add (it also had a drama die taht could add 6, or give fumble chance). This falls into the old modeling skill/training versus talent/Genius.

Quote from: Bloody Stupid Johnson;496058Here I include systems such as West End Games Star Wars and (for combat) Tunnels and Trolls. A pool of dice are rolled and totalled. A problem with this system is that a character's result varies enormously depending on # of dice in a characters pool – making some tasks very easy or impossible for some characters. To match this, Star Wars uses a safety value in that characters can spend Character Points/Force Points to add extra dice when needed. Star Wars also adds a "wild die"; on this dice, 6s are added and re-rolled.
Later editions of T&T include a success counting mechanism as part of combat as well (where 6s count as automatic 'spite damage').

There quite a few variations on additive dice pools as well. Roll x, keep/count only so many dice are common. EABA uses a count highest three, with some special mods for larger than life heroes.   L5R has its roll x keep y rules, with exploding dice.

A variation of this kind of additive system is adding bonus or penalty dice to your add dice. So if you have 3 regular dice +1 bonus die, you keep the 3 highest, while if you have a penalty die, you'd roll and keep the 3 lowest, etc.

Thanks RobMaudib - I haven't read Top Secret so...what's the Stun/Wound marked /x ? And by using 10s place that would be worked out directly i.e. roll 21 = 2 damage, roll 41 = 4 damage?...so that higher skill directly adds to damage?
 
On the doubles on d% - I'd forgotten that one but I think Rolemaster does that for combat rolls (I think Arms Law uses it for weapon breakage).

Quote from: Bloody Stupid Johnson;496054Die pool systems give characters a varying number of dice to be rolled against
a target number, with "successes" or "hits" counted. The first of these that I know of was Shadowrun.
Die pool systems are particularly good for determining how well a character succeeds, but less good at determining if a character succeeds – probabilities are less transparent and in practice designers tend to allocate # successes required for tasks in a fairly ad hoc fashion. 'botch' chances using 1s tend to do odd things.
Some systems independently vary both target number and # dice (oWoD – particularly Werewolf- and Shadowrun 1e/2e). This unpredictably/erratically increases the number of dice needed to get a given # successes and is an approach that should probably be used rarely. Shadowrun uses d6s and allows target numbers (TNs) over 6 (6s add and roll over).
 
Dice roll systems integrate particularly well, with even damage etc. following the same universal system. Attack roll successes may add to Damage successes giving DEX a percentage flow-through into damage (usually less than Strength since successes are normally converted into extra dice, and have to be rolled again), without the math being excessively clunky.
 
A sub-variant of this is the "match counting" system as used in the One Roll Engine (REIGN, Godlike, etc). To succeed in ORE a character needs 2 or more dice to face up the same number. This provides two readouts a "width" and a "height"; The system is particularly good for doing Hit Location (i.e. a character a rolls 3,3,4,4,4,7 might opt to target a character in their "4" location for 3 successes of damage, or in their "3" location for 2 successes of damage. The system handles differing task difficulty only with some trouble, cannot have "fumbles" (since 1s are "left foot" shots); and at least in Godlike, the additional data available is in practice rarely used for most non-combat rolls. In combat it has the slight problem that base damage and initiative are both based off roll "width" (i.e. shots that will kill someone automatically go first).

One of the very earliest and simplest 'dice pool' systems is Prince Valiant, by Greg STafford/Chaosium. http://www.rpg.net/reviews/archive/9/9189.phtml
You added your attribute to your skill to get your 'dice pool' Which is the number of coins you would flip, heads are successes (Gareth Micheal Skarka used this in his Underworld game as well) My hate of D02 kno no limit!

(and yeah I am system archeology geek:) )

Quote from: Bloody Stupid Johnson;512218Thanks RobMaudib - I haven't read Top Secret so...what's the Stun/Wound marked /x ? And by using 10s place that would be worked out directly i.e. roll 21 = 2 damage, roll 41 = 4 damage?...so that higher skill directly adds to damage?
 
On the doubles on d% - I'd forgotten that one but I think Rolemaster does that for combat rolls (I think Arms Law uses it for weapon breakage).

NP. It used a damage silhouette wit hit boxes, where non-lethal damage was marked as slashes in your dmg boxes (total based on Con), and lethal damage was marked as X's With non-lethal quickly recovered, lethal much more slowly, non-lethal could knock you out, lethal kill, they added etc. much like ORE/Godlike, EABA, and others, but way back in '89.

And yep, higher skill, higher damage potential for unarmed/melee weaps. (firearms were random dice )

Yeah, I've seen the doubles for special success in a couple spots.

Thanks again! Mind if I go back and edit in some of your notes (with attribution to you), to keep info as organized as possible for any prospective designers) ?
(if not that's also fine; I'm feeling pretty lazy...).
 
Checking quickly, Shadowrun and Prince Valiant both seem to be '89, though I haven't found more exact publication dates than that with a quick search.

Quote from: Bloody Stupid Johnson;496205Aside from dice, cards are seen in some games e.g.
.

Castle Falkenstein, from R. Talsorian games, directly used cards for action resolution.   http://www.rpg.net/news+reviews/reviews/rev_1610.html

Card values were from 2-10, the different suits mapped to action types, needed to have right suit to get full bonus. Jokers counted as 15. Brief overview in 4th from last paragraph of that review.

Quote from: Bloody Stupid Johnson;512259Thanks again! Mind if I go back and edit in some of your notes (with attribution to you), to keep info as organized as possible for any prospective designers) ?
(if not that's also fine; I'm feeling pretty lazy...).
 
Checking quickly, Shadowrun and Prince Valiant both seem to be '89, though I haven't found more exact publication dates than that with a quick search.

Sure, glad to make it more comprehensive overview. (Why I responded to indvidual sections)

Great work btw. The general rule on mechanics is, its probably been done before, if only on some web published game:)

Oh yeah, more discussion of open-ending mechanics is probably warranted. Main way to get around flat die-distributions, give remote chance of success, etc. Lots of variations common. (ars magica's stress die, roll d10,on a 1, roll again and double result, keep doubling, a 0 on it is a botch) All die open-end/explode, single die can open-end explode (star wars), etc.  DC heroes used an open-ending 2d10 roll compared to your chart, roll again and add on doubles. Why it had a high handling time in addition to the action+result chart (and loss most of the simplicity of the standard d% action chart ala MSH) though it was rock-solid and industrial strength at least:)

(Column shift idea was common for handling bonuses/penalties in such systems, along with color coded results. GW3rd had the most complicated/detailed overloaded success chart, nearly every effect had a sub table of results with lots and lots and lots of conditions ala D20 (sick, nauseus, shaken, unbalanced, whatevs)

Oh, you should probably describe what attributes are used for/represent (inherent ability in an area, usual possessed by all creatures/entities in a game systems. (not always, early D&D mobs, or don't have all of them.), balanced against skills (typically defined as learned abilities, specialized knowledge.)  And their relationship and weighting. from no significant effect, 1/2 ability (stat + skill), to bulk of ability (Warhammer/old TSR systems) (lots of variation in here including no set attributes in OTE, Fudge, variants of Cortex, etc., as well as no particular skills in like Strands of Fate.)

Cheers! and thanks.
 
Will add section on open-ended rolls (although I think this means I have to go re-read MetaScape and lose San) and further commentary on attributes/ weighting. Yeah seem likes there's no idea so weird that someone won't put it into an RPG, just to be original. (apparently 5E D&D is going to let characters with minimum ability scores pass some checks automatically, like Dragon Warriors was doing in, IIRC, '86).

Quote from: Bloody Stupid Johnson;512413Cheers! and thanks.
 
Will add section on open-ended rolls (although I think this means I have to go re-read MetaScape and lose San) and further commentary on attributes/ weighting. Yeah seem likes there's no idea so weird that someone won't put it into an RPG, just to be original. (apparently 5E D&D is going to let characters with minimum ability scores pass some checks automatically, like Dragon Warriors was doing in, IIRC, '86).

Oh was thinking in the about cutting down on rolling Whispering Vault deserves a mention as it had all character/player only rolls. Pretty cool game.

Also, some discussion of problems related to opposed rolls, because of effectively doubling variance. Was reading about people complaining about FATE,think it was Dresden files, where because of the granular trait range versus the effective 8dF variance, you get some huge variation of results in combat.

Quote from: RobMuadib;512436Oh was thinking in the about cutting down on rolling Whispering Vault deserves a mention as it had all character/player only rolls. Pretty cool game.
 
Also, some discussion of problems related to opposed rolls, because of effectively doubling variance. Was reading about people complaining about FATE,think it was Dresden files, where because of the granular trait range versus the effective 8dF variance, you get some huge variation of results in combat.

Have gone back through and added some notes, though not done as yet. Thanks again! BTW, found that Space 1889 ('88 release) used some target number type stuff too (just in combat) -stumbled across it looking up a Shadowrun 1e review in Dragon to see if they'd mentioned a release date.
 
Not overly familiar with Whispering Vault, though I've seen the player rolls idea - I think Icons has all player rolls as well [d6-d6]; a thread roundabout here somewhere on ICONS suggested rolling 1d for both PC and NPC for opposed rolls as a fix.
I'm surprised that there's a problem though, actually. I'd have thought an (effectively) 8d3 roll would be a very tight bell-curve of results, though I've never sat down and crunched the relative probabilities.

Quote from: Bloody Stupid Johnson;512680Have gone back through and added some notes, though not done as yet. Thanks again! BTW, found that Space 1889 ('88 release) used some target number type stuff too (just in combat) -stumbled across it looking up a Shadowrun 1e review in Dragon to see if they'd mentioned a release date.
 
Not overly familiar with Whispering Vault, though I've seen the player rolls idea - I think Icons has all player rolls as well [d6-d6]; a thread roundabout here somewhere on ICONS suggested rolling 1d for both PC and NPC for opposed rolls as a fix.
I'm surprised that there's a problem though, actually. I'd have thought an (effectively) 8d3 roll would be a very tight bell-curve of results, though I've never sat down and crunched the relative probabilities.

It's not just the potential variance, its the variance plus FUDGE/FATES tight/granular trait/results scale... Because +/- 4 is extreme result for general rolls, doubling the variance makes it more common, so you have the potential for 'blow outs' relative to the scale. it's easy to go 'off the chart' because of the doubled range of results from opposed rolls. Most often comes up as gotcha's in combat. Just something to pay attention too in designing.

Quote from: Bloody Stupid Johnson;507383This is only an incomplete listing which I’ll go back to later and add to (maybe), but please feel free to suggest anything I’ve missed and I’ll add it here.
 
Ars Magica: ?

Ars magica has one of the most flavorful and innovative magic systems. Its primary 'schools' are Hermetic, Hedge magic (wizardry outside of hermetic tradition), and witchcraft (via Infernal powers).

an extensive overview of system can be found at  http://en.wikipedia.org/wiki/Ars_Magica (lot of innovative bits in that game.)

QuoteThe focus of the game is the magic system. There are 15 Arts divided into 5 Techniques and 10 Forms. The Techniques are what one does and the Forms are the objects one does it to or with. This is sometimes called a "Verb/Noun" magic-system. The Arts are named in Latin.

The Techniques are named after the corresponding first-person singular present tense indicative mood Latin verb.

    Creo is the technique that lets the Magus create from nothingness, or make something a more "perfect" examplar of its kind; this includes healing as healed bodies are "more perfect" than wounded bodies.
    Intellego lets the Magus perceive or understand.
    Muto lets the Magus change the basic characteristics of something, giving something capabilities not naturally associated with its kind.
    Perdo lets the Magus destroy, deteriorate, make something age and other similar effects - essentially, making something a worse example of its kind.
    Rego lets the Magus control or manipulate something without affecting its basic characteristics.

The Forms are named after the corresponding singular accusative Latin noun.

    Animal is used for animals. Since bacteria were unknown in medieval times, illnesses are evil spirits, which come under Vim.
    Auram is used for anything that has to do with the air, including lightning. Weather phenomena such as rain and hail may be covered by Auram or Aquam.
    Aquam is used for water, or any other liquid. This includes ice in the 5th edition; In 4th edition, Ice was Terram, since it is a solid.
    Corpus (the incorrect declension Corporem was used in older editions) is used for the human body.
    Herbam is used for plants and fungi, and their products - cotton, wood, flour, etc.
    Ignem is used for fire, and fire's basic effects of light and heat.
    Imaginem deals with images, sounds, and other senses, though humans' ability to perceive them is part of Mentem.
    Mentem deals with intelligence and the mind, such as human or ghosts. The minds of animals are not affected by Mentem but by Animal.
    Terram stands for earth and minerals, or any other non-living solid.
    Vim has to do with pure magic; many spells to ban or control demons and other supernatural beings also belong to this Art, as such beings often have a form that expresses magically.

Quote from: Bloody Stupid Johnson;496045Attribute scores may be used directly in game mechanics or may have secondary “modifiers” which are used by the game mechanics – compare e.g. GURPS (roll under stat on 3d6) or White Wolf (roll dice equal to the stat) and D&D 3E (Strength score of 13 = +1 modifier on Strength rolls on d20). In some games modifiers are used only during character generation (i.e. Dragon Warriors) and so do not take up character sheet real estate, though break points may still exist. Dragon Warriors is also interesting in having basically two varieties of modifiers; though not named explicitly stats can give a larger 'primary' modifier, or a smaller 'secondary' modifier, depending on how strongly they influence a derived attribute. Most derived attributes are affected by one primary and one secondary modifier.
 

Oh yeah, was gonna talk about Minor/secondary modifiers a bit. Like in Runequest some versions of BRP. You have category modifiers for certain skills, which give a bonus based on your basic attributes. Like combat skills might have a primary modifer based on STR (+1/per point overunder 10) and Dex and secondary for SIZ (+1/2pts over 10/under etc). Because it's percentile, these are relatively small influence.

Another thing to consider is how fewer important attributes can lead to serious min/maxing especially in GURPS. while systems like Silhouette, or Paragon HDL and Interlock, with 10 or more attributes and stat+skill pairings reduce this problem. It also circumvents 'dump statting' somewhat. Especially if you have like reflexes/agility/dexterity  So one might affect your initiative speed, the next your dodging ability, and the last to hit with ranged weapons. So you can't focus on stat for max effectiveness and dump the others as much. All of this contributes to feel of system, and kinds of characters it produces. (i.e. gurps talented amateurs, while RQ's its all about skill specialization and experience/training is more important)

(getting more into elaboration and effects of system types, but useful to consider ramifications of your mechanic choices.)

Quote from: RobMuadib;512751It's not just the potential variance, its the variance plus FUDGE/FATES tight/granular trait/results scale... Because +/- 4 is extreme result for general rolls, doubling the variance makes it more common, so you have the potential for 'blow outs' relative to the scale. it's easy to go 'off the chart' because of the doubled range of results from opposed rolls. Most often comes up as gotcha's in combat. Just something to pay attention too in designing.

Checked into this some more and indeed you are correct.
Used an online dice calculator at www.anydice.com (http://www.anydice.com/) (there are no doubt others around - Troll, etc. - just found this one lying around).
 
4dF distribution (using 4d3-8, since each dF equates to d3-2)
(http://i1239.photobucket.com/albums/ff507/BSJ17/4dF.jpg)
 
 
8dF distribution (8d3-16)
 
(http://i1239.photobucket.com/albums/ff507/BSJ17/8dF.jpg)
 
 
In the first post on attributes I've added further discussion on balance and # attributes - although I'd contend that the problem with GURPS is GURPS-specific (i.e. some of the stats suck, at least for some settings) rather than fundamental to low numbers of stats. IMHO, a high numbers of stats come with their own possible problems (getting a high attribute requires less trade-offs since you can spread the cost around. I'm open to being convinced though (and would link to any interesting discussion, irrespective of my own opinion).

Quote from: RobMuadib;512752Ars magica has one of the most flavorful and innovative magic systems. Its primary 'schools' are Hermetic, Hedge magic (wizardry outside of hermetic tradition), and witchcraft (via Infernal powers).
 
an extensive overview of system can be found at http://en.wikipedia.org/wiki/Ars_Magica (lot of innovative bits in that game.)

Thanks for that - comprehensive. I'm familiar with the system - at least in outline - though I only touched on it briefly in post #84 in a single line or so.
With the post you quoted I was looking largely at types of magic; so Hermetic, Hedge and Witchcraft here (adding). I vaguely recall that there were a set of inviolate rules of magic in Ars Magica which each of the non-hermetic schools can break just one law of (e.g. affecting spheres above the lunar, or immortal souls) which I thought was a great idea, but can't recall any specific details of. It may have been in a supplement I browsed rather than the core rules.

Thought of a more detailed/realistic system. Millennium's end sticks out in my mind, as it used a fairly complicated non-ablative invidual body location wound based system.

It used 'Trauma Levels' and had a detailed damage table (though not on the order Phoenix Command's ultra hardcore system. Which has great big scary damage tables by ultra-fine body location and shot direction etc.) Paraphrasing...

QuoteMilleniums end uses a non-ablative damage system that rates individual wounds on a one to twenty five scale of severity. The scale operates in units called trauma levels with a TL of 1 least damaging, 25 most. Wound of TL over 25 is instantly fatal.  TL's are not added together unless 2 or more wounds occur in same body zone. So a character may survive several near-fatal wounds at once.  TL indicates severity of wound, but nothing about its effects. Wound effects include impairment, unconsciousness, blood loss, broken bones and shock.  

The delivered damage (DD) of an attack is determined prior to use of Damage Table(DT). DD is then plugged into Damage Table. DD = base damage of weapon (Fixed for firearms based on bullet type), Minus armor at location, then multiplied by a location modifier (1.6 for head, 0.8 for arms/legs, 0.6 for hands feat.) (and possibly a mass modifier, usually 1.0). This gives your final Trauma Level.

All wounds cause Impairment based on TL and damage type (concussive, impact, puncture, cut burn, and Hydrostatic Shock (ballistic injuries), with effects of impairment logically based on Wound area.(which are percentile modifiers, so vary quite widely, and are finely detailed.)

There is chance of stunning based TL/Body zone, and modified by damage type. This gives a stun chance modifier, which is subtracted from percentile Con roll, with very large penalties for big hits/sensitive locations.

Blood loss, most wound bleed. Check for serious Blood Loss after each wound, compare trauma level by body zone, modified for Damage type. This gives blood loss rate, amount of time will pass in minutes, before character loses one unit of blood. With 4 units lost meaning death. (for humans, one unit = 2pints (useful info for vampire's grabbing roadkill I guess). Blood loss = auto shock, and gives a decline rate modifier for eventually fatal wounds.

There is also the chance for Broken bones or severed limb (Consult limb loss sub-table!). Shock leaves you stunned (also caused by TL 20 or higher, left untreated, shock leads to death).

Eventual fatal injury is shown as an E result on Damage table, as determined from TL and damage location. This gives decline rate, which gets progressively shorter, until TL passes 26. at which point they die.

So as you see, damage determination in this system is slightly less excruciating than actually getting shot. Generally, major concerns of Damage are Impairment, Incapacitation and Eventually Fatal/Deadly damage. Hit point systems just attach this to absolute numbers (0 hp's, -10 hp's), while detailed systems can require a painful amount of effect determination.

FEEL OF COMBAT
Oh yeah another thing that bear's mentioning with the more abstract systems with increasing hit points is how normal threats (i.e. falling) become trivial (the old saw about high level fighters being able to jump off a cliff and get up and fight with no ill effects.) So you have to add kludges like the massive damage rules etc.

Another thing is the overall speed and feel of combat. Does it resolve quickly, or does it end up like D&D combat with everyone hacking on each other for several rounds, etc. You should design it for the effect you want out of combat. Do you end up with lots of corpses in a gritty system, do people cut and run after getting wounded. Does everyone just get knocked out and roughed up like in Super Heroic systems. Each type of system works better for some things than others.

The more heroic the game system, the less lasting effects of damage there should be, and the more of a beating character's can take. While gritty systems can end up with lots of dead character's, often to the extent that combat is effectively MORE deadly than real life, lots of people die every time there is combat, instead of people getting wounded, fleeing combat and dying without medical attention. Indeed, because most game systems don't include any morale systems, lots of fight are to the death, while in real life, people cut and run if possible.

Another thing is on Impairment, in real life, people can be wounded and not really notice any significant effects of the wound due to adrenaline, unless a bone is broken, the body part is mangled outright. In some famous cases of suspects on PCP, they can take over a dozen gunshots to the torso and not even be slowed down. (In reality people only drop immediately if they take major damage to the CNS (Brain, spine, neck), or the heart is directly damaged) People can be shot without realizing it. While at the same time they can drop for purely psychological reasons, or die of shock from a shot to the foot.

Most often impairment is used in RPG's so people can be beat down and rendered ineffective, the death spiral, instead of just eventually dying. Incapacitation is used to make for an effective end to combat, without necessarily people dying, especially in Heroic/Super Heroic realities.  Needless to say there is HUGE amount of variation in combat systems.

Quote from: RobMuadib;512932FEEL OF COMBAT
Oh yeah another thing that bear's mentioning with the more abstract systems with increasing hit points is how normal threats (i.e. falling) become trivial (the old saw about high level fighters being able to jump off a cliff and get up and fight with no ill effects.) So you have to add kludges like the massive damage rules etc.
 
Another thing is the overall speed and feel of combat. Does it resolve quickly, or does it end up like D&D combat with everyone hacking on each other for several rounds, etc. You should design it for the effect you want out of combat. Do you end up with lots of corpses in a gritty system, do people cut and run after getting wounded. Does everyone just get knocked out and roughed up like in Super Heroic systems. Each type of system works better for some things than others.
 
The more heroic the game system, the less lasting effects of damage there should be, and the more of a beating character's can take. While gritty systems can end up with lots of dead character's, often to the extent that combat is effectively MORE deadly than real life, lots of people die every time there is combat, instead of people getting wounded, fleeing combat and dying without medical attention. Indeed, because most game systems don't include any morale systems, lots of fight are to the death, while in real life, people cut and run if possible.
 
Another thing is on Impairment, in real life, people can be wounded and not really notice any significant effects of the wound due to adrenaline, unless a bone is broken, the body part is mangled outright. In some famous cases of suspects on PCP, they can take over a dozen gunshots to the torso and not even be slowed down. (In reality people only drop immediately if they take major damage to the CNS (Brain, spine, neck), or the heart is directly damaged) People can be shot without realizing it. While at the same time they can drop for purely psychological reasons, or die of shock from a shot to the foot.
 
Most often impairment is used in RPG's so people can be beat down and rendered ineffective, the death spiral, instead of just eventually dying. Incapacitation is used to make for an effective end to combat, without necessarily people dying, especially in Heroic/Super Heroic realities. Needless to say there is HUGE amount of variation in combat systems.

Nice - I've quoted this up into the combat section here.

Quote from: Bloody Stupid Johnson;497762.

Quote from: RobMuadib;512287Oh yeah, more discussion of open-ending mechanics is probably warranted. Main way to get around flat die-distributions, give remote chance of success, etc. Lots of variations common. (ars magica's stress die, roll d10,on a 1, roll again and double result, keep doubling, a 0 on it is a botch) All die open-end/explode, single die can open-end explode (star wars), etc. DC heroes used an open-ending 2d10 roll compared to your chart, roll again and add on doubles.

OK attempting this topic... :)
 
The most merciful thing in the world, I think, is the inability of the inferior roleplayer to correlate all MetaScapeII's contents. We live on a placid island of roleplaying ignorance in the midst of black seas of infinite levels, and it was not meant that we should voyage far. The booklets, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of roleplaying, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.
-from thread "Metascape: Pretentious Much?" on TBP
 
 
Many games allow 'open-endedness' in results. This can be seen, perhaps, as a case of the more general question of how to deal with PCs attempting very difficult or virtually impossible actions, which should have a very low chance of success (if any). Rolling up can also have an impact on 'margin of success' and so effect. In a take-highest dice pool system, open-ending is also useful to fix the issue that the highest result on a single die is the most common result e.g. reducing chance of ties.
Sometimes rolling up is desired as a way of letting characters 'push their luck', so that a rollup is something a player may take but with risks - as in DC Heroes where a double-1 rolling up causes the action to fail.
Systems where higher is better on rolls often have ways of directly converting a roll into effect, so that rolling up /an increase in the raw dice roll can be used. In roll-under systems there's sometimes an extra roll, but it doesn't add directly (the same applies in miscellaneous other systems - cf. notes on 3E, bughunters, below).

Some options include:
 
*Auto-Win!: a roll of maximum on the dice automatically passes: e.g. 20 on d20 automatically hits.
(special cases: T&T 7E and later uses this in a way in combat with 'spite damage' - 6s on d6 in the combat pool are automatic damage that go through armour, though much less than what a character actually rolling higher in combat is likely to do).

*Special bonus: Capes, Cowls and VillainsFoul  is a d12 take highest system (usually maxing out at about 3 dice), but sometimes extra Trait bonus. A natural '12' on d12 lets characters double the extra Trait Bonus (e.g. +3 to +6).
Another thing that's maybe similar to this is the "Repeating 20" in 1st Ed. AD&D's combat tables. There is a row of six 20s with a natural 20 counting as the highest 20, sort of (IIRC) treating a roll of natural 20 as getting five column shifts/being equivalent to a '25', rather than have it be an automatic success.

*Additional roll: a very good/maximum roll will succeed, providing the character passes a second, separate, die roll.
3E D&Ds critical hit confirms are a good example of this (with fairly sound math backing it up). One of the weirder instances of this would be the Bughunters! game (Amazing Engine) Donor Background Table. Rolls are d100+PC Position score (the social status attribute); rolls of 100+ make the character reroll vs. target number 100. 1 successful extra roll makes them a Corporate Executive (or equivalent), 2 makes them a Millionare or Government Leader and 3 successful extra rolls makes them a Billionaire - this system being intended to keep Billionaires rare in spite of the basic Position attribute being somewhat variable, such that it was not possible to build a d100 table reducing it to a set 2% or so. (starting Position is not just rolled randomly but with varying pool of dice depending on PC prioritization, and with new PCs even able to get experience bonuses to stats due to the "Player Core" rules rules, where multiple characters by the same player can share XP).
Similar to this is Aria's  Shifting entire 'result':

Quote from: woodelf;91104result shifts: some mechanics, rather than  simply adding more to the number the die generates on a particularly good result (or subtracting on a particularly poor result), instead shift the entire result. Aria, frex: if you roll a 10 or 1 (on a d10), you then roll again, and if the new roll is a failure or success (respectively), the result is one step worse or better than it would've been just by applying the 10 or the 1 to your skill. And it can repeat, if you continue to roll 10s or 1s. What's distinct about this is that (1) it does this even if that first roll isn't a failure/success, so you can turn a failure into a success, and vice versa, in this way; and (2) it shifts by steps of result, rather than simply adding more numbers to the [numerical] result.

*It's going to Cost You: Shadowrun 4E has a "Long Shot" rule letting a character perform a normally (slightly) impossible stunt by spending a point of Edge. This lets characters attempt very difficult tasks, but rarely and at cost.
(See also earlier post on 'safety valves').
 
*variable difficulty: Alternity expresses difficulty factors as dice (i.e. "impossible" -3d20 to character skill). Almost any roll can theoretically be made given a low roll for penalty.
 
*special result (if using a table of results). This relates more often to 'qualitative' results rather than raw numbers but characters can roll a result on a table that gives overwhelming success, or 'roll twice' etc.

The common solution to the problem however is to allow "rolling up" of some kind. Here certain rolls increase further, so that any target number can theoretically be made - it just becomes increasingly less likely the more ridiculous the number required is. Rolling up is sometimes seen for damage systems, even when not used for other mechanics - e.g. HackMaster damage or the 2nd ed. D&D arquebus (d10, 10s roll and add)(Combat & Tactics later made the rolling up a function of the Knockdown die, rather than the base damage die).
 
Examples include:
*Doubles roll up - (Tunnels and Trolls, DC Heroes). DC Heroes has the additional rule that double-1 automatically fails - even on successive rolls - so that PCs may wish to not re-roll in case they mess up. Note the probability curve of doubles-roll-up is odd looking (screwing up one of the main reasons to use multiple dice to begin with, although in T&Ts case its partly to limit the game to using six-sided-dice), but normally any number can be rolled (unlike the "maximums reroll" method). Chance of doubles on two dice is the same as rolling any given number on the dice i.e. 1-in-6 on 2d6.
Unlike where maximums roll up, doubles rolling up alters basic success chances for most characters, not just those attempting to make unlikely rolls.
Doubles rolling up makes extra dice as a bonus or penalty (i.e. take lowest or take highest ala BoL (http://www.therpgsite.com/showthread.php?p=496174&highlight=barbarians+lemuria#post496174) bonus dice/penalty dice, similar to 5E advantage/disadvantage) more awkward - not usually used. Potentially these can be colour-coded and not count toward a double; or bonus dice increasing odds of doubles could be a feature rather than a bug. and/or a 'penalty die' could also block rolling-up.
Freerpg Hi-Lo Heroes uses 2d6 (take higher or lower), but with the rule that doubles are added together instead. This way of counting doubles might barely be called 'rolling up' (it happens only once and there's no extra roll), but does periodically drive up the die roll considerably. 'Silent Death' damage rolls (cf. Damage) work similarly.

*a roll of 1 is rerolled, with new roll doubled (Ars Magica stress die).

*rolling up on some lolrandomly chosen numbers. In 2E Creative Campaigning by Jacquays, a flintlock does d12 damage will 'rolling up' on 8,10, or 12. Presumably the number of rolls triggering this is to keep roll up frequency higher than smaller weapons, like the flintlock pistol that deals d8 with roll up on 8. Having some lower numbers roll up partly reduces discontinuities (e.g. a 10 or 12 can still be rolled, with 8+2 or 8+4,10+2 respectively) although irregularly, much more rarely than other numbers in the range.
 
*Maximum rolls again and adds (various). Usually this means that certain numbers become unrollable (if a d10 rerolls on a "10", you can't roll a 10 since that will become at least an 11), giving a "discontinuity" or "jump" in the progression (this is mostly an aesthetic thing though - it generally has little or no functional consequence). Some system may add a roll of [die-1] etc. The added reroll needn't necessarily be the same sort of die originally rolled. In most cases, rolling up maximums will have little effect on success chance but may cause blowouts in margin-of-success.
Elaborations of this include:
-Shadowrun 1E had a d6 dice pool system where individual dice rolled up, so difficulties could be over 6. This wasn't always satisfying since a high roll only let character reach ridiculous difficulties, not increase the 'effect' of their success. A character might roll a 20 on one of their normal dice (initial 6-reroll of 6-reroll of 6-reroll of 2) but this still only counted as one success ( which might not even be enough to pass the task anyway, if it needed 2+ successes).
-JoeNuttall in his blog (http://explorebeneathandbeyond.blogspot.co.uk/ (http://explorebeneathandbeyond.blogspot.co.uk/))suggests a method whereby a roll is 2d10 and a roll of 10 is replaced with another 2d10 roll (and so on) instead of adding directly.
-Savage Worlds rolls up maximums, but in Savage Worlds' step-die system chance of maximum being rolled ("acing") decreases as the die grows larger. This leads to a mathematically oddity that the chances of reaching TN 6 is slightly (about 2%) more likely using d4 than using d6 i.e. a lower skill is better in this one case. The same happens with d6/d8 vs. TN 8, and d10/d12 vs. TN 12. Unlike most other systems there are usually no gaps in numbers that can be rolled for Savage Worlds, since a character will roll two dice and take the best - as long as they are different sizes (i.e. d6+d4) any result is possible.
A Step die system can also potentially reroll using [die of next size] rather than adding i.e. 4 on d4 lets the character roll a d6, then take whichever roll is higher. This makes rolling up much less dramatic, however. Another fix for Savage Worlds probabilities is to reroll and add [dice-1].
EDIT: It is also interesting to compare the psychology of Savage Worlds' rolling up system with other games. In most cases "raises" have primarily a narrative effect and don't give dramatic increases in power (e.g. 27 to hit = +d6 to damage...), but adding the rolls directly to get a big number makes them feel huge. (Another game with say a dice pool and a rule where '10s give you an extra dice to roll' might have explodes be as important mechanically, but still feel less dramatic).
In Savage Worlds exploding/Acing is fairly necessary for getting the system to work - as otherwise e.g. large Parry ratings would be unhittable. Its interesting to compare vs. Cortex, which has no rolling up but which lets story points be spent to similarly narrow gaps in ability, controllably.
[Note that where step dice are used and maximum rolls up, you can increase the chance of rolling up by 'stepping down' the die and adding a compensatory bonus - for instance replacing d10 with [d6+4] increases chance of getting into the 11+ range from 10% to 16%. This would also need the original roll to be used when 'rolling up' however.]
-MasterBook uses a 2d10 roll where either die rolling a "10" adds and rerolls, conventionally enough. However, it also sometimes limits if roll-ups are possible: a character can be "stymied" meaning one of their roll-ups (whether from rolling 10s on the dice or by spending luck Points, called Life Points in MB) is cancelled. Shatterzone is very similar but on a double-10 only a single 10 rerolls unless the character has a 'specialty'. Untrained characters don't get to roll up in either system.  The rolling up in both is a somewhat curious design decision given that the bell curve effect of rolling 2d10 (deliberately chosen for that reason) is mostly invalidated by having a 19% chance of a roll up event [giving an average result in this case of 10+2d10 = 21 result, before considering any secondary explosions]. It also very slightly biases rolls in favour of the attacker on skill rolls, though only slightly since if one roll was a 10 they probably would've succeeded anyway).
-Bedrock Games in-development 'The Meddlers' RPG uses a d4-take-highest dice pool, with an optional rule that if a character rolls multiple 4s, the d4 rolls up. An interesting idea in that one die can't roll up, roll-ups are relatively rare despite using d4s; this also eliminates the discontinuity (making both 4 and 4+ rollable).
-D6 system (adding together a number of d6s) allows "rolling up" only on a single die, the Wild Die (normally a different colour to the other dice).This gives a fairly limited increase compared to potential dice pool size.
-Last Unicorn Games' 'ICON' system as in Star Trek (not to be confused with the 'Icons' supers RPG) uses a d6 take-highest dice pool -the highest roll adds to skill rating. One of the dice is designed as a 'Drama Die' - if a 6 is rolled, the second highest die is added to the total as well.
-Similar to this, Silhoutte uses multiple d6s, with the highest roll (+bonuses) taken, but any additional '6s' each add a further +1.
-Anima: Beyond Fantasy is a d100 additive system where high rolls explode (like Rolemaster) but with the wrinkle (reportedly) that the first roll explodes on 91+, the second 92+, the third needs 93+, etc. (A sort of interesting idea, but IMHO making a difference so rarely that its probably not worth the bother).
-original Cortex "Meta-talents" (super-skills) have a "Better, Faster, Stronger" stunt effect; if either dice rolls max. a Plot Point can be spent to reroll the dice and add. (Cortex doesn't otherwise open-end the way Savage Worlds does).
-one friends' step-die system (Savage Worlds descended) allows for a 'catastrophe token' to be spend on a roll, a form of safety valve, for a +2 if declared in advance or +1 after. Maximum rolls on the dice normally roll up, and if this takes the roll to the maximum (say a 6 on d8 is raised to 8), then the dice roll up. Note the point spending is less likely to generate 'rolling up' with larger dice.

A dice pool system might 'roll up' maximums by adding to the dice rolls, or by just getting bonus dice. Shadowrun 1E does the former (Target Numbers can exceed 6, so 6s roll up and add again so that some of the dice can technically be considered to be rolls of "8" or "10"). oWoD Storyteller did the other version with Specialties: any 10s rolled granted characters a bonus dice, to try to score extra successes. This limited target numbers to no more than 10, but meant characters' possible # successes were open-ended. (It would also be possible to have a system where the player could choose to either roll up, or treat the number as a bonus die - which might be either before or after rolling).
-Rolemaster uses additive d100, with rerolls at 96-100. This scale is fine enough that slight modifications can be made to the likelihood of reroll (i.e. something might up the reroll chance to a roll of 95-100, or 94-100).
-Earthdawn allows maximums to roll and add normally. In 2E ED, there's an 'Ice mace and chain' power which damages a character, and hinders them unless 'bonus damage' is rolled for the mace which makes it shatter. Since ED is a step-dice system a powerful wizard's mace may be slightly less likely to shatter usually, though the step die progression is erratic enough that the odds fluctuate weirdly.
-Infinite Power is a multidie-additive d8 system where any 8s rolled reroll and add; a normal stat of say 2 would mean 2d8, 8s add and roll over; roll ups therefore occur fairly frequently and slow down the roll (nearly a quarter of the time with just 2d8).

MetaScape possibly warrants special mention here - it has an odd scale system where you can both roll up and roll down - using a custom d16 labelled (C), t, 1,1,1,1,1,1, 2,2,2,2,2,4,4,8,16.
A standard roll in Metascape has a designation such as "6L" or "8H" or "10LV" which breaks down as follows:
*The first number is a normal die type (i.e. d6 for 6L, or d8 for 8H); Metascape only uses d6 thru d10.
*L, M or H indicate a "category" of either Light (x1), Medium (x2) or Heavy (x4).
*Finally the last letter in the code is a scale multiplier or "type"-this letter is omitted for "personal" scale (x1), but also includes B or bantam (x/10), V or Vehicle (x10), S for Ship (x100), W for World (x1000), C for Celestial (x10000), G for Galactic (x100,000) or U for Universal (x a million).
A roll in Metascape is multiplicative and uses the normal die (i.e. d6) x the doubling die result x the multiplier for Light/Medium/heavy. Note that a "16" rerolls and the result multiplies again.
 
For the special results, a "(c)" changes the category toward Light (i.e. a x4 would become a x2), while the "t" changes the category toward personal - dividing the multiplier by 10 unless it was Bantam, which instead goes up to x1. For either a (C) or t the d16 is rerolled unless the multiplier is already x1, in which case it counts as a 1.
Circumstantial adjustments can also be applied to the dice/category/type.
For example a roll of "8LV" would be a d8 x 1 (light) x 10 (vehicle), times the custom d16. If the d8 rolled a 3 and the d16 a 2, result would be [3x2x10] = 60. If the roll was a 3 and a 16, the die would be rolled again - if the reroll was a 2 the final would be [3x16x10x2] or 960.

Thought in closing:
 "Open-ended rolls sounded like a fun way to have exceptional results on occasion, but in practise in every system I've ever used them in (with the notable exception of TORG, which keeps them in check via its results table) the fact that the GM rolls far more dice per session than the PCs means that exploding dice inevitably turn in to exploding PCs." - Grymbok

Generally single-die systems where dice size is d12 or smaller have problems with either explode/autosuccess or fumbles being too common...possibly a reason for why single-d10 systems [Unisystem, Cyberpunk/Interlock] are rarer than single-d20 based systems (along from D&D founder effects)

Note: averages for rolling up on normal polyhedral dice are in post 192 by ggroy.

Rolling up in character generation
'Rolling up' may be seen in character generation (if it uses rolling) as well as active rolls during the game - although this is not so much about reaching impossible difficulties. For example, Tunnels and Trolls 7E and Deluxe roll stats with 3d6, triples add and roll over. Palladium allows a bonus +d6 if a 16-18 is rolled on 3d6 (or 12 if rolled on 2d6 in Palladium Fantasy).
Weirder elaborations here include Team Characters in TMNT (Palladium); all characters in the team must be the same animal type e.g. turtle, and if any of them roll a 16-18 and so roll up they all get the same +d6 to that stat.
Character generation is more complex than a single roll/result value, so may have 'feedback loops' involving multiple quantities (increase in X leads to increase in Y that leads back to increase in X) ala older HERO (buying down derived attributes to buy up the base score again) or World of Synnibarr (where a high stat gives bonus 'skill points' that can be spent to get skills or mutations that then increase the stat again). Another case may be the infamous (and disputed) Pun-Pun (http://www.dandwiki.com/wiki/Pun-Pun_(3.5e_Optimized_Character_Build)) D&D 3.5 build. Character generation is also more likely to include qualitative 'rolling up' on tables and the like i.e. where a character rolls a random skill (mutation, psi power, whatever) and gets a "roll twice" result.

Quote from: Bloody Stupid Johnson;513155OK attempting this topic... :)
 
The most merciful thing in the world, I think, is the inability of the inferior roleplayer to correlate all MetaScapeII's contents. We live on a placid island of roleplaying ignorance in the midst of black seas of infinite levels, and it was not meant that we should voyage far. The booklets, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of roleplaying, and of our frightful position therein, that we shall either go mad from the revelation or flee from the light into the peace and safety of a new dark age.
-from thread "Metascape: Pretentious Much?" on TBP
 
MetaScape possibly warrants special mention here - it has an odd scale system where you can both roll up and roll down - using a custom d16 labelled (C), t, 1,1,1,1,1,1, 2,2,2,2,2,4,4,8,16.
A standard roll in Metascape has a designation such as "6L" or "8H" or "10LV" which breaks down as follows:
*The first number is a normal die type (i.e. d6 for 6L, or d8 for 8H); Metascape only uses d6 thru d10.
*L, M or H indicate a "category" of either Light (x1), Medium (x2) or Heavy (x4).
*Finally the last letter in the code is a scale multiplier or "type"-this letter is omitted for "personal" scale (x1), but also includes B or bantam (x/10), V or Vehicle (x10), S for Ship (x100), W for World (x1000), C for Celestial (x10000), G for Galactic (x100,000) or U for Universal (x a million).
A roll in Metascape is multiplicative and uses the normal die (i.e. d6) x the doubling die result x the multiplier for Light/Medium/heavy. Note that a "16" rerolls and the result multiplies again.
 
For the special results, a "(c)" changes the category toward Light (i.e. a x4 would become a x2), while the "t" changes the category toward personal - dividing the multiplier by 10 unless it was Bantam, which instead goes up to x1. For either a (C) or t the d16 is rerolled unless the multiplier is already x1, in which case it counts as a 1.
Circumstantial adjustments can also be applied to the dice/category/type.
For example a roll of "8LV" would be a d8 x 1 (light) x 10 (vehicle), times the custom d16. If the d8 rolled a 3 and the d16 a 2, result would be [3x2x10] = 60. If the roll was a 3 and a 16, the die would be rolled again - if the reroll was a 2 the final would be [3x16x10x2] or 960.

Wow, I was not aware the awesomeness that is Metascape. That is some impressive open-ending there. I will have to attempt to assimilate it's superior intellect at some point, rather like the Necromonicon, it will make me starkly aware of my insignificance in the great cosmic awfulness that is the universe:) Oh now, There is now a Metascape 3rd edition (  http://youtu.be/zsf9D0IpOLU ) For those who would dare their sanity and test their intellect  http://metascapegame.blogspot.com/

Oh, and this bit in the announcement, you too can someday be raised to a second class citizen by toiling for you ominscient masters

QuoteCongratulations to Trevor Nielsen. For his years of dedicated playtesting and design help. I've moved him up in the credits to Master Playtester!

Thought I'd add one of the quirkier 'open ending/up rolling' systems I've encountered, from Cthulhutech. Rolls are made by rolling a number of D10 equal to your skill expertise (1 to 4) plus optional specialty dice, and take the highest roll. You add your Base = to your attribute score. However, there are two 'up-rolling' options. you can take the highest set of multiples and add them together, or if you have 3 or more dice, you can count the highest 'straight' as in poker. So if you rolled a 9,4,5,6 you could add the 4-5-6 'straight' to get 15 for your roll.