BSJ, did you ever do an overview of critical hit systems, what they do in a game and different ways to do them?  Trying to remember...I know we did Hp and damage and combat....

Hi Lord Vreeg! Not exactly. I touched on both 'effect' systems in general, and on damage/HPs, but I missed doing crits specifically. I'll have a go at it.

OK here we go...Thanks again Lord Vreeg. Comments welcome as always.
 
Thought of interest...

Quote from: Arturick;702112I've read posts by, and spoken with, DM's who thought that critical fumbles were a necessary balance to critical hits. This doesn't make sense, because ENEMY critical hits are the balance to PC critical hits.

Critical Hits: a critical hit might be defined as a situation where a target takes extraordinary damage or an extraordinary effect as a result of an attack. While the earliest versions of D&D didn't have these formally they were popular as houserules and later optional rules. IIRC, the first system with these (and fumbles) may have been Arduin. The traditional D&D example would be the simple 20 to hit = double damage rule (often paired with 1 = fumble). Enthusiasts also frequently added charts of specific injury and death results (Dragon #44 having one attempt at this). In a way these are perhaps a sort of early 'class feature' for the fighter since spells typically don't get criticals - although monsters usually get them as well, so fighters are also frequently on the receiving end.  Critical tables based off to-hit roll often include "extra damage" results, whereas systems which instead roll specific impairments based off damage (Savage Worlds incapacitated) just give descriptive effects.
Commonly a critical hit is triggered by a particularly high (or low) natural result - such as 20 on d20 to hit for D&D, or under say 10% of weapon skill in BRP to get an 'impale' (or knockback with a non-impaling weapon, such as a greatsword). Occasionally a second independent roll is used e.g. AD&D monk gets a separate % chance of instant kill based on level and opponent armour class; in 3E a second 'confirmation roll' is made against the target's AC to see if a high roll is indeed a critical. In 2nd Ed. D&Ds Combat and Tactics module, a critical required generally an 18-20, which was also 5 or more over the targets AC to prevent all hits on high-AC targets being criticals, with a critical dealing extra damage and an additional effect based on a hit location roll unless the target saved vs. death. An optional S&P fighter ability 'Coup de Gras' (Dragon #257) could let fighters get a Str check which if made improved weapon size one step for critical purposes.
The exact likelihood of a critical occurring may depend on weapon skill, specific weapon used (e.g. 3E weapons have a varying 'threat range' of either 20, 19-20 or 18-20, as well as a varying damage multiplier); J Arcane's "Drums of War" RPG includes a system where characters have an exact percentage chance of critical; a 2d10 (added together) roll to hit is also read as a percentage to see if a crit occurs. (The recent 'fallout' game apparently has a Luck rating which modifies chance of sometimes getting a killing blow, which could be an interesting crit mechanic).
Extra damage for criticals may be weapon-independent (if a table is consulted with set effects), or might be some sort of multiplier to base damage. Even with tables, different weapons may get a different table.
 
Systems with universal mechanics may use the same crit procedure for both attack rolls and other subsystems- e.g Talislanta has partial successes and criticals for all actions, while Marvel Super Heroes has tables of Green, Yellow and Red results which in combat translate to e.g. Slams, Stuns or Kills (actual amount of damage inflicted never changes, though Kill results cause Endurance loss in addition to the raw Health damage). Rolemaster has tables of specific results for everything, combat or otherwise, based off total dice roll+bonus. These sort of criticals of specific effects can have problems in situations where a result is inapplicable (I've seen someone punch off someone's head in a Warhammer game; in one of Hargraves' Arduin games he once gave a PC three rolls to get an applicable critical (i.e. one to the torso) when trying to stab the 'Ultimate Demon' with a unicorn horn, its only weakness).
 
Many systems do not have criticals exactly, with high damage rolls instead emerging from the normal hit/damage process. Most commonly, systems may add bonus damage for a good to-hit result; for instance in a dice pool game, extra successes on the attack roll may convert to bonus damage dice. In a pool system it is difficult to have an exceptional result that occurs a fixed percentage of the time (except perhaps by having one of the dice be a 'wild die'). Some systems may also have open-ended or exploding damage dice (e.g. maximums roll up such as in Hackmaster, Savage Worlds).
Something like a 'critical' can result in some games from very high/exploding dice + the systems' wound penalties. NPCs can have significant wound effects from losing most of their HPs, rather than the criticals occurring alongside the HP system e.g. a Savage Worlds' character might take a shot to the 'unmentionables' as a result of taking enough wounds to roll on the incapacitation chart.
 
More complex systems may have something like a critical that flows through a few steps.
*Earthdawn, a roll to hit over a certain margin is an 'armour defeating hit' and deals more damage. This is more likely to result in damage greater than a target's wound threshold, and so giving a specific effect.
*In HarnMaster, comparison of attack (normal or critical success) and defense (normal or critical success) gives a number of damage dice which are adjusted for armour and etc. and matched with hit location. High results have specific effects depending on location e.g. Sever rolls made be made for a limb to see if its cut off, or Kill rolls (Endurance check or die) for vital locations.
 
*aside from bonus damage or specific effects, some systems as noted previously have multiple types of hit points, with a 'critical' bypassing low-grade hit points to hit the PCs in the more vital points. This makes characters relatively fragile despite large HPs - IMHO more or less negating the point of having a lot of HPs. While its not inevitable, some systems (d20, SAGA) have had scaling issues where damage ramps up steadily to keep up with the major HP pool, and criticals converting the same amount of damage directly to wound damage caused criticals to go from minor annoyance at low level to an instant kill at higher levels.
 
Non-damage based critical effects can also exist. In Dragon Age, special effects can be triggered off a high result on one of the character's attack dice (the Dragon Die); the player can choose exact critical ["stunt"] effect - this can include extra movement, rapid reload, knock prone, bonus to defense, disarm, extra damage, pierce armour, a second attack or change to initiative). Some games may have specific rules handling critical results for non-damaging special moves such as tripping or grappling e.g. 2nd Edition AD&Ds Combat and Tactics. Another 2E optional rule was for a 20 to grant an additional attack, rather than a bonus to damage.

A common concern with criticals is the effects of them on NPCs as opposed to NPCs. While criticals may be fun for PCs (when applied to NPCs), having PCs die messily is often seen as a problem, particularly in games with lengthy character generation. Many systems have mechanics (often fairly metagame) that limit the PCs exposure to critical hits, for instance:
*the old 3E 3rd-party "Deck of Critical Hits" supplement comes with instructions that only PCs and exceptional NPCs are allowed to use it.
*FantasyCraft gives characters "action dice" which must be spent to 'activate' a critical, making them unaffordable to mooks.
*Warhammer 1E/2E has specific injuries that appear only after the Wounds score has been depleted, so when the character would be mostly dead in any event. Savage Worlds has injury effects that occur on 'incapacitation' -as a result of the PCs total health, not a single hit. Similarly, Werewolf: the apocalypse PCs can spend Rage to take a 'battle scar' (permanent impairment) instead of being killed/incapacitated.
Perhaps this sort of effect isn't a true critical, but it serves a similar purpose in the fiction of the game world.
*Characters may get some sort of points to either negate death in general (Fate Points) or to reroll some of the checks resulting in being criticalled.
*4E D&D has the slightly divergent goals of keeping criticals (because they're fun) and also neutering them (because they're dangerous to PCs and unbalanced). Criticals exist there as almost a 'legacy mechanic' where damage is maximized rather than doubled, plus any bonus from a 'high-crit' weapon (+d10). The main source of bonus damage is however magical weapons (+d6 per +) which will not usually be owned or used by NPCs or monsters, thus keeping crits PC-only. Instead of random criticals, a similar role is taken up by occasional-use powers dealing additional damage or effects - in effect giving characters a guaranteed set of criticals throughout the day rather than relying on chance, and removing these from the hands of monsters (which have to rely on their own set of powers). Occasionally a daily power involving lots of dice will still critical, dealing largeish damage.
7th Ed. Gamma World, a descendant, gives PCs extra critical powers based on their type - a character gets extra damage/effects on criticals at 2nd and 6th level, the first from one of their types and the second from their other type.
*systems where PCs only roll dice [e.g. Dungeon World] don't give crits to NPCs. Unless an equivalent results from a PC fumble.

Pathfinder has a number of critical-based feats (Critical Focus, Stunning Critical, Critical Mastery, etc) which let experienced characters add special effects to their crits, such as stunning. Making these a specific ability indirectly reduces NPC-on-PC extra effects (they will probably be less commonly found on monsters than in fighter builds), probably a side effect rather than the direct design intent though.

The permanent injury aspect of some critical systems is another tricky question. Many systems e.g. Rolemaster include a number of spells to repair the effects of critical hits, although this is also a question of genre/feel of the game. Permanent impairments generally mix poorly with balanced, point-buy systems since a point-built character has a precisely quantifiable value, and as a mass-manufactured item is quite replaceable -in such systems taking a permanent injury gives an immediate incentive to kill and replace the character, particularly if treasure or levels of a replacement character is guaranteed to be equivalent.
 
Also worth mentioning in more detail is the 3rd Edition critical hit system. Most weapons in 3E can potentially (with confirmation roll) critical on natural 19-20, but with a few only 20s will critical and some critical on 18-20. To balance the variable 'threat range' they also have different damage multipliers, keeping the bonus to DPS relatively constant; thus a longsword is 1d8, 19-20 x2, while a battleaxe is 1d8, but x3 on a 20, the same average damage. To keep relative strength of criticals the same for weapons after adding bonuses, feats or powers that improve threat range normally double or triple the range, calculated by counting numbers that would be a 'threat' i.e. doubling 19-20 (two numbers) becomes 17-20 (four numbers). (This sort of calculation is easier with roll-under).
The relative balance of criticals in 3E is sometimes thrown out by magical weapons, which may have specific effects on criticals - these, then, are optimally only designed as weapons with a wider threat range, regardless of the damage multiplier of a critical. The best example might be 3.0 vorpal, which decapitates a target on a critical instead of dealing damage - this is obviously better with an 18-20 threat range scimitar than with a 20-only battleaxe.
One magical items allow reduction of criticals - Fortification for example gives a fixed % chance (25% for light, 75% for moderate, 100% for heavy) of negating the critical. An item could also modify the 'confirm' AC, theoretically (actually the only thing that works sort of this way is the 'power critical' feat, which adds +4 to the confirmation roll).
There is also a 'maiming' weapon power [3.0 Miniatures Handbook], which replaces the fixed crit multiplier with a rolled number e.g. x2 to x1d4, x3 to x1d6 or x4 to x1d8 [deemed imbalanced and revised to a fixed bonus amount in 3.5 Magic Item Compendium].

A fine distinction between some systems is whether critical effects can be 'pulled' (deliberately not applied) or not. Some games/GMs may assume that high roll = more awesome for PCs, others that a critical represents the chance of something gruesome happening to the guy being attacked. If you're trying to drop but not kill someone, should a critical roll mean your roll was really accurate and drops them with no extra damage, or that you accidentally deal double damage anyway? (Rolemaster somewhere has a practice fighting damage table for situations like these).

Critical hit rules may sometimes be called upon by traps - whether because those are meant to be especially deadly (roll on a table), or because the specific nature of a trap means it will most likely affect a particular hit location or the like (specific injury rules)- reaching into a hole, pulling a lever that's actually a blade, getting cut through the shins, etc.

See here for a link of interest on historical development of critical hits in D&D.
 
Fumbles: a few systems also have critical fumbles - the most notorious probably being Rolemaster. Often these use a table of results which can include things such as falling over, breaking a weapon, stabbing yourself/a companion. DCC has Fumble tables which are modified by luck and armour (armour sets the fumble die used, with armour wearing classes like fighters or dwarves having the ability to spend Luck to negate fumbles, and obviously a more armour-themed fumble chart (i.e. in full plate you can fall onto your back and be unable to get up turtle-style).
Fumbles sometimes allow a second 'save' to negate, as otherwise multiple attacks or two weapon fighting can result in skilled fighters fumbling more often overall.
Fumbles for ranged weapons can include an 'out of ammo' result, so that the fumble rule negates a need for ammo tracking, though the result will not necessarily always make sense. (cf. Dungeon World Volley action)

Fumbles sometimes exist as specific effects in specific cases (for example, Wilders in 3.5 have a specific chance of "psychic enervation" whenever they use a power, which has a specified effect. Other games will specify when a fumble occurs but not the effects, causing a GM judgment call.
Fumble effects fairly often are left up to GM fiat (particularly if players deliberately add them to a normally fumble-less game). A fiat adjudication, compared to use of a table, does have an effect in that the GM will generally feel obligated to not "metagame" either for or against the player and will give a PC an effect that works against them, regardless of any resistances or conditions that would negate it. A table result conversely might let a character ignore a fumble due to prior preparation. In other words if your PC has Boots of Levitation they may be able to ignore a 'slip in blood' result off a table, but a fumble that isn't defined would probably have the GM choose a different calamity instead so as to not have the player feel they're being unfairly aided for or against- the boots won't help. (Some systems might of course just demand that inappropriate results be rerolled anyway - this is something that works best if the severity isn't being considered in the random roll as well i.e. a player who has to reroll the 'slip in blood' result due to their magic boots and gets a 'head cut off' result instead may not be impressed).
Natural weapons / unarmed attacks tend to be harder to improvise fumbles for, compared to actual weapons - i.e. 'break weapon' results are unduly harsh and 'drop' results can't be applied.

Good overview.
Am on iPad so short comments...you don't really go into why people use critical hit systems and what the frequency and effect really add or subtractvfrom the game.  Because crates wrenched to lethality.
Or how their lethality might interact with other subsystems.  Early double damage on a 20 matters when fritters have 10 to 40 hp, not so much with 20 to 80 hp.

Quote from: Bloody Stupid Johnson;567848*aside from bonus damage or specific effects, some systems as noted previously have multiple types of hit points, with a 'critical' bypassing low-grade hit points to hit the PCs in the more vital points. This makes characters relatively fragile despite large HPs - IMHO more or less negating the point of having a lot of HPs. While its not inevitable, some systems (d20, SAGA) have had scaling issues where damage ramps up steadily to keep up with the major HP pool, and criticals converting the same amount of damage directly to wound damage caused criticals to go from minor annoyance at low level to an instant kill at higher levels.

Are you referring to Star Wars Saga here, or some other game? IIRC, it was d20 Star Wars that would have had issues with the VP/WP split. I can't even remember if damage scales in that game it's been so long since I've played it.

But Star Wars Saga pretty much uses a similar crit-like mechanism to my own game. Going over a massive damage threshold pushes the victim along a condition track. I think in Saga's case both massive damage threshold and weapon damage scaled with level.

Quote from: beejazz;568014Are you referring to Star Wars Saga here, or some other game? IIRC, it was d20 Star Wars that would have had issues with the VP/WP split. I can't even remember if damage scales in that game it's been so long since I've played it.
 
But Star Wars Saga pretty much uses a similar crit-like mechanism to my own game. Going over a massive damage threshold pushes the victim along a condition track. I think in Saga's case both massive damage threshold and weapon damage scaled with level.

Ah, you got me there (right in the wound points . You're quite right it was Star Wars d20, not SAGA with which I'm not super familiar. The older d20 game has stuff like sneak attack that scales up with level.
Also hmm...perhaps I've neglected discussion of condition tracks as well, beyond say Shadowrun I'm not too familiar with these.
 

Quote from: LordVreeg;568009Good overview.
Am on iPad so short comments...you don't really go into why people use critical hit systems and what the frequency and effect really add or subtractvfrom the game. Because crates wrenched to lethality.
Or how their lethality might interact with other subsystems. Early double damage on a 20 matters when fritters have 10 to 40 hp, not so much with 20 to 80 hp.

NP, Good points. Quite right on the lethality. As to why - I put fun as the top reason. Perhaps added verisimilitude - if you're going to have one-eyed dwarves and scarred mercenaries in games, rules for crits bring the setting into line with the world, as in your rule...
Another reason sometimes advocated is just to make combat more deadly - Skills & Powers for 2E took that approach i.e. it mentions wanting to make fighters take notice of crossbows pointed at them, although in this case its something of a patch since it may have been better to just give characters less HPs to begin with.

Doh, messed up with AD&D monks as well. The d% roll for insta-kill isn't all the time, its only after they successfully 'stun', which occurs on a hit roll 5 over the minimum needed to hit. Not that different to rolling 'confirmation'. To date then, there are no games I know of where the critical roll is made wholly separately to the attack roll and on every roll.

Quote from: Bloody Stupid Johnson;568158Doh, messed up with AD&D monks as well. The d% roll for insta-kill isn't all the time, its only after they successfully 'stun', which occurs on a hit roll 5 over the minimum needed to hit. Not that different to rolling 'confirmation'. To date then, there are no games I know of where the critical roll is made wholly separately to the attack roll and on every roll.

If no one else is using that crit mechanic we should port it in for the collaborative design thread. A second D10 that crits on a 10 (failure if the person would have failed, success if the person would have succeeded).

Mostly joking. Seems weird.

Quote from: beejazz;568162If no one else is using that crit mechanic we should port it in for the collaborative design thread. A second D10 that crits on a 10 (failure if the person would have failed, success if the person would have succeeded).
 
Mostly joking. Seems weird.

Its a stupid idea, obviously - at least in tabletop rather than a computer RPG. The closest you get to it is probably HarnMaster, which is d100 roll-under with every number ending in 5 or 0 being a critical success (if you made the roll) or a critical failure (if you blew it). Ensures that 20% of either are critical (on average), instead of having high skills cause a blowout in effect, as in additive margin-of-success type games.

EDIT: OK, I now have a game system where you're supposed to roll a chance of critical separately in addition to the attack roll - in the Arduin (original trilogy compendium) vorpal weapons roll a 20% chance of critical on every hit (20s decapitate instead of the normal critical), sharpness weapons roll a 10% chance of critical.

I actually use a double critical system, in a way.
Weapons already do a good amount of damage in Celtricia, but they have a dividing die.  Smaller weapons generally have a lower divider.  
A Gladius does an unadjusted 2d6+14/d8.  A Claymore does  2d8+17/d5.  So rolling a '1' on the divider is sort of a mini crititical as it is, though armor has a protection roll with a divider as well.
This follows with giant creatures, etc, btw...no one likes fighting big creatures in celtricia, since pretty much every giant is using a d4 divider on their already massive damage...reflecting pysics, as it were.

On top of this, there are criticals on 07% or higher for a normal person that reduce the dividing die.  
 http://celtricia.pbworks.com/w/page/22481009/Critical%20Hits
And one of the things that changes a game is whether the skill of the character or creature can increase or decrease the critical hit ability.  For example, in our last online session of the Steel Isle Game (the log is somewhere here), we had some mid-level (uper middle level on one) characters fighting a gnoll ambush.  So for the PCs doing the major fighting, one had a +33% to hit with his pilum, one had a +44% to hit with his Shamsheer.  For every 10% a creature has as a 'to hit' bonus, they also gain 1% on their ability to critical (reflecting their expertise), so these 2 actually had a 10% and 11% chance to critical, respectively.

Quote from: LordVreeg;568201I actually use a double critical system, in a way.
Weapons already do a good amount of damage in Celtricia, but they have a dividing die. Smaller weapons generally have a lower divider.
A Gladius does an unadjusted 2d6+14/d8. A Claymore does 2d8+17/d5. So rolling a '1' on the divider is sort of a mini crititical as it is, though armor has a protection roll with a divider as well.
This follows with giant creatures, etc, btw...no one likes fighting big creatures in celtricia, since pretty much every giant is using a d4 divider on their already massive damage...reflecting pysics, as it were.
 
On top of this, there are criticals on 07% or higher for a normal person that reduce the dividing die.
http://celtricia.pbworks.com/w/page/22481009/Critical%20Hits
And one of the things that changes a game is whether the skill of the character or creature can increase or decrease the critical hit ability. For example, in our last online session of the Steel Isle Game (the log is somewhere here), we had some mid-level (uper middle level on one) characters fighting a gnoll ambush. So for the PCs doing the major fighting, one had a +33% to hit with his pilum, one had a +44% to hit with his Shamsheer. For every 10% a creature has as a 'to hit' bonus, they also gain 1% on their ability to critical (reflecting their expertise), so these 2 actually had a 10% and 11% chance to critical, respectively.

ooh intricate...congratulations. I've never tried building anything this complex, but I mostly see what you're doing here, I'm not sure I have any useful criticism of it since it seems the percentages are all very tightly controlled to get the final effect you want, but...
 
*I assume that dividing die shifting to d4 for an 04 or less makes criticals for some weapons particularly bad (daggers or bows, mentioned?) since the base damage for these was designed to factor in the larger dividing die?.
 
*I note that you have two separate effects that are skill-based - one being the increase in the chance of a critical roll itself (+1% per 10% added to the base 07), and the second being the critical effect itself being mainly skill-driven (roll under to-hit% to get the dividing die bonus). Perhaps a bit of unnecessary redundancy there since both independently factor into the same final effect; you might in theory be able to tweak either one or the other to get the same final result more simply..? Or not, depending on how happy you are with the current exact %s.
 
*The dividing die itself is interesting since it would work to give occasional massive spikes in damage, with each doubling of damage being half as common. The negative dividing die results look like they give horrendous amounts of damage, but you need both a high skill and a lucky roll to do it, and otherwise I guess a critical couldn't do more damage than a lucky dividing die roll (apart from the 01 armour minimization effect).
 
*No extra special effects for an 01 on your second critical roll?...

I think this thread should be stickied. It contains a hell of a lot of useful information, information which would benefit any game designer.

I wouldn't object!

[edit note: Complexity post moved here, from pg.17, to go with hybridization post]

Another general topic, just summarizing some thoughts...
Reading various arguments on the topic I come to the conclusion people mean different things when they mean something is complex e.g. I've seen arguments on whether 2E D&D (with all its exception rules for various issues) is more complex than 4E (with its unified but more term-heavy resolution). Or whether 3E is more complex than Hero.

In a general way, complexity of a ruleset can be viewed in a few ways. Details can be 'front-loaded' into character generation, or 'back-loaded' to occur during play - for instance, by precalculating skill values vs. requiring a roll, or determining situational modifiers beforehand. HERO is another game where adherents often insist its quite simple in play, once the parameters of the characters powers are considered. Games which have rules for lots of specific situations might be considered more complex, although, many of these rules may not come up in play - Rolemaster has lots of tables (but is often considered less complex than 3E, which has fiddlier rules for skill interactions).
Another interesting case, 2nd Edition D&D has many different subsystems for skills, ability checks, saves, climbing, opening doors, etc. but frequently IMHO has fairly non-intrusive rules - compared to say 3E where rules for social interaction & perception will generate dice rolls frequently in the course of play. The games with more baroque mechanics have more individual rules, but there may be less action-at-a-distance requiring sub-rules to precisely shape what occurs for individual skills (Palladium for instance has melee critical rules but no skill critical rules - since skills are d100 rather than d20; 3E has rules which increase the default armour penalty for swim, while Ride has a mix of functions to which armour penalty applies and doesn't apply).

There is also 'tactical' complexity, or decision-making complexity. Needing players to select an informed option requires they understand all the options available, which is particularly a problem if its a permanent character building decision, or there are a lot of options -it sometimes makes sense to sub-divide a list further e.g. into class-specific powers.
If an option has fairly abstract, mechanical effects the player may also need to understand the rules that option affects as well.
I have to pick on FantasyCraft here: the rules are deliberately set up to generate synergies between options, sometimes awkwardly ('iconic specialties'). Options here are also deceptively strong/weak without a full understanding of what they do (e.g. 'Hammer Supremacy' looks like it insta-kills most NPCs who "automatically fail their damage save" until you realize a Tough NPC may require several damage saves to kill). Overall the class, race, proficiency, feat and skill rules seem to me overly byzantine given that a simpler system could have as many options if it wasn't deliberately tiering options (take a Specialty to get a Feat that then gives access to otherwise restricted skills/bonus to a skill) - building deliberate restrictions into specific classes/races/skills and basically running the player through an unnecessary maze of options to optimize their build.

Probably the main factors driving increasing ruleset complexity in general are:
*the desire to make rules more comprehensive* - that is, taking the burden off the game master by defining exact situational modifiers. IMHO this is good to a point, although, after a certain point the system may become bloated with too many rules for normal players to remember, with potentially important rules buried by minutiae.
*adding realism (detail). More abstract rules less perfectly duplicate the 'process' of a realistic system but may need more modifiers to handle specific steps. More detail does make it easier to handle specific circumstances that apply at one step, but don't necessarily generate more realistic results. A particular issue being multiple rolls at multiple stages biasing chance of success downward (3E D&D trip)
*adding gameability to a system. Looking at D&D over time again (2E through 4E), the movement system becomes more intricate to make tactical combat interesting, rather than because of its simulational value. Similarly, FantasyCraft character building is more or less a minigame in itself.
*balance: an extra layer of detail can fix an imbalance between options, or obscure a difference because more circumstances need to be considered (for instance if one weapon does d12 and another 2d6, adding rules for DR, or weapon vs. armour type for the different weapons as well, or other properties). One option being slightly worse may sometimes be an acceptable tradeoff for not taking on extra complexity.

*comprehensiveness is itself driven by a desire to map out gameplay expectations  - different fictional sources, different assumptions about proper lethality and challenge. Different power levels -when 'realism' was seen as a main goal people could sometimes agree on what was 'realistic', but in higher-powered fantasy e.g. anime/wuxia based, what a character should be capable of is unmoored from reality and so harder to agree upon. Naive players/GMs may disagree on rulings and just decide the other person is an idiot, rather than realizing why they did whatever it was; more rules give a roadmap as to what the game will be like, and an opportunity to address problems in advance.

Conversely, benefits of rules-lite: a lighter ruleset lets the GM apply themselves more directly. A GM with a lot of skills can generate a result directly that's no less realistic than what a good ruleset can. Lighter rules also let the GM directly step in to get the rules to work (by contrast, a more complex system involves more exacting design to get it to work) - for instance, the GM may have more wiggle room to set DCs or choose which subsystems apply (cf. controlling bonus and penalty accumulation). The GM can  assign 'effect' as appropriate -  A roll that's outrageously for your character's dice pool might be an average success for twice the dicepool; a GM can reward an extraordinary roll in a rules lite system where no benchmarks are defined, and in doing so also  push back against a lack of 'bonus control'.  Simpler combat systems when run well (as noted way back in Combat Moves), make it possible to describe actions interestingly without this causing an event in the system that makes them suboptimal (e.g. triggering attacks of opportunity)(provided the GM doesn't take a 'its not listed, you can't do that' approach).
While there's less shared and encoded gameplay expectations, this may not be an issue for an established group in any case.

Complexity in character generation particularly can be a side effect of giving extra options; sometimes a question to ask before adding such complexity is 'is this option likely to be used' or 'is this option actually as good as other options'. Complexity could however also be stripped back for most characters by creating extra options in some cases. For instance it might be reasonable to generate a magic-user with a package of spells/abilities (for convenience); someone might want to create a slightly variant wizard e.g. a wizard who casts just one spell, or one spell slightly better, but a system allowing that might involve much more specific detail (buying skills spell-by-spell perhaps). The designer might create an extra one-spell option and/or spell specialist ability, which would come up rarely and works alongside the general template that saves time.

"A complex system that works is invariably found to have evolved from a simple system that worked. A complex system designed from scratch never works and cannot be patched up to make it work. You have to start over with a working simple system." – John Gall

A whole new system can be made in a few different ways. It may be interesting to look at some of the possible methods - although in the wild, systems will often be combinations of rules derived in various ways.
Approaches include:
 
*Built up ex nihilo.
Older games in particular, not having anything else to copy from, were often patterned by directly looking at how something seems to work in reality, and trying to build numbers around it. You can see this in games like Twilight 2000 (where armour values of tanks are modelled based on real depth of armour for instance - designer's notes around this sort of thing in Space Gamer # 75 are interesting...) or explosives damage using a square root of explosive quantity. Or GURPS designer Steve Jackson got weapon weights by bringing medieval weapons to the office and weighing them. Even apart from real-world measures, 80s games show a process going on whereby situations are analyzed and rolls of whatever the designer likes chosen to suit them, without a universal mechanic being involved. At best the figures used in the system are empirical, and at worst wholly arbitrary.
 
Later editions of these same games often tend to replace empirically-derived figures with logically-derived figures; someone sees a pattern in the data and then numbers generated from the pattern (which are similar but not identical) are used to replace the original numbers. Greater abstraction may appear. Values may be rewritten to improve balance, consistency, etc.
　
Another unusual approach starting from nowhere is one of starting with no mechanics and playtesting concept, adding mechanics as you go - idea being to start with a fresh slate and avoid extraneous elements. Erick Wujcik discusses this in regard to Amber in a reply here:
http://forum.rpg.net/showthread.php?126448-The-third-eye-a-game-about-lies
 
*iteration. Modern games are often based on predecessors. The design process isn't much different between a new edition, and a new game inspired by the edition - except inasmuch as that there's less pressure for a new game to remain the same, and indeed there may be a drive to rename or otherwise adjust features enough to avoid legal disputes.
Editions changes vary between reprints with minor changes and sometimes new artwork (Call of Cthulhu though 6E) all the way through to complete redesigns (WHFR 3E). Games where the setting is the main appeal are particularly prone to extensive rebuilding - games where the rules are the main draw (whether due to particularly good design, or due to large amounts of compatible material) are less likely to be rebuilt extensively. D&D has periodical cataclysmic rebuilds (usually with an extra revision mid-edition as well i.e. Greyhawk, Skills & Powers, 3.5 and Essentials) while Gamma World's 7 editions are entirely different games with four versions of its own system (1E presumably derived from Metamorphosis Alpha, 2E incrementally modified, 3E redesigned to due to the universal table fad of the time, 4E largely 2nd ed. D&D compatible, a 5E Alternity version, 6E D20-Modern, and a 7E 4th-ed-D&D variant).
Below complete system replacement, the next most serious rebuild possible is probably a core-roll replacement, where the main dice rolling mechanism is changed; e.g. the 2E/3E D&D transition. (for a discussion of the 2E/3E rebuild specifically see http://www.therpgsite.com/showthread.php?t=25483 ). 0D&D also was largely d6-based (e.g. if using Chainmail for combat resolution), with 'optional' methods using D20 however being more popular/core.
Some other games that have had their core mechanic replaced include Twilight 2000 (from d100 under skill in 1E, to d10 under skill in 2E/GDW House System games, to d20 under [stat+skill] in the 2.2 revision) and Star Frontiers (from d100 to coloured tables in Zebulon's Guide; Alpha Dawn before that had also shifted some checks from stat checks to 1/2 stat + skill level modifier). Other than that, White Wolf LARP had a variant that was d10+stat+skill, rather than the full dice pool; FUDGE actually uses a variety of means to generate modifiers quite easily, and its modifier range of 4dF is often changed to d6-d6 in FATE variants with little effect. 'TriStat dX' evolved to use roll under with 2dX (from d6 to d12 chosen by GM depending on campaign), starting from a 2d6 roll in Sailor Moon and then a 2d10 roll in Silver Age Sentinels. Big Eyes Small Mouth (BESM) 3E then went from roll-under to an additive system, among other changes.
A fairly neat change occurred in Invulnerable as noted in multidie additive (going from d6s equal to stat + 'hyper dice' of [d6x10], to base 3d6+stat as a number + extra d6s for hyper-dice - a change that keeps scaling similar while reducing number of dice and hyper-dice awkwardness).
Significant overhauls (not quite replacement) of core system might include WHFR 1E to 2E (which streamlined all attribute checks to d100 and used the tens place for damage modifiers etc., where these were previously d10) and apparently Icons assembled (which should be interesting as this reportedly went from [d6-d6 player rolls] to both player and GM rolling d6). Another fairly dramatic change was Shadowrun 3E to 4E; this kept dice pools but went from rolling only [skill] in dice to rolling [skill+attribute](more realistic maybe since before stats only modified defaulting, but dice pool size is doubled), as well as having a fixed Target Number for rolls instead of variable by difficulty.
Another example of what not to do may be 'G-Core', a rebuild of Marvel Super Heroes which kept attributes as is (ranging from 2-100+) but tried to drop the tables by making it additive with a roll of [+d10x10].
A core mechanic rebuild will lead to changes in probabilities e.g. high numbers can become more powerful if the new roll is more deterministic or vice-versa, with scale of scores potentially needing to be changed, as well as modifications to account for changes in frequency of criticals/fumbles (base chance, how these scale up or don't), change in availability of information from a roll beyond pass/fail (like 1s place on d100), rescaling of bonuses/penalties, rescaling of outputs, and considering if a mechanic can test only one or multiple values at once.
Games where some sort of modifier is calculated based on attribute already maybe slightly easier to change since the value scale for e.g. stats is already partly isolated from the core mechanic; just replace the modifier table and different numbers will be generated (e.g. you could go from "Str 10 = +0"  to "Str 10 = roll d6").
If an original core mechanic carries with it a lot of design constraints, then probably updating the core system will leave these in (barring a lot of revision) as a sort of evolutionary relic (for instance going from Storyteller to d10+stat+skill, the need to have two scores for everything is less because the die roll makes the difference less noticeable, but you'd keep any skills that exist to make sure there's always two values). Replacing a heavily-constrained core mechanic with another heavily-constrained core mechanic would be likely to mean a lot of compromising and adapting and revising (an example of that might be when a dice roll requiring one value goes to a dice roll requiring two values, as touched on in the section on how mechanics influence character design).

'Derivative' games include many D&D-derived games, while GURPS is sometimes accused of being a HERO knockoff (although it derives from 'The Fantasy Trip', which could also perhaps be considered a wargame in its basic form, before the introduction of the point buy elements etc.). Many cleave close to the original, with addition of one or a few novel ideas and/or replacement of specific problematic subsystems.
In some cases such as Arduin (growing out of OD&D house rules) and Rolemaster (which grew out of the Arms Law supplement adding critical hit tables to D&D) a supplement eventually evolved into its own full system. Flashing Blades similarly is rumoured (I don't know how reliably) to have started as an En Garde supplement, which was declined by GDW and turned into a standalone game. See also other examples discussed here:
http://www.therpgsite.com/showthread.php?t=23091

Naming variables: if something is frequently used or reused by various situations it should probably be named. This creates the possibility of extra mechanical elaborations drawing on something (for instance, consider how AD&D has 'free attacks' for retreating, which were named and fully defined as 'attacks of opportunity and had various feats and combat manuevers keyed into them.

(Edition change note: older games frequently refer to situations fairly ambiguously -subsystems are sometimes expanded by naming a variable and then elaborating on cases using it -e.g. how AD&D free attacks for retreating were expanded into 'attacks of opportunity' in 3E D&D, or addition of 'touch AC' to avoid repeatedly or ambiguously defining AC without armour benefits. When defining how things are named can be important - 5Es 'proficiency in Strength saves' or C&Cs 'primes' by their name assume that the bonuses are inextricably joined to the stat bonus, meaning there's no way to cross-match the way e.g. a 3E character might theoretically roll 'Fortitude modified for Strength bonus' or similar.)

Notes on other rebuilds:
Some interesting notes here on the evolution of Rolemaster from D&D supplement through a number of editions http://forum.rpg.net/showthread.php?709834-Speak-to-me-Of-Rolemaster

The iteration process for established game properties often involves using some degree of fan feedback. One interesting example here is the AD&D 2E design questionaire (see:  http://www.therpgsite.com/showthread.php?t=26216 ), while in recent times both Pathfinder and D&D 5E involved open playtests for design and/or marketing.

Advanced Fighting Fantasy (2nd Ed.) showed an interesting tweaking of the numbers from the 1st edition to increase back-compatibility. AFF-1 used the original rolling system for Skill values from FF, but then added 'special skills' raising effective weapon Skill by another 1-4 points, and making original FF monsters quite weak in comparison; the 2nd edition went back and reduced average Skill values for PCs and also limited special skills slightly (usually 1-2 in value) such that the original FF monsters (such as in Out of the Pit - republished as-is from FF) were again compatible.
Another fairly neat iteration was Mercenaries, Spies and Private Eyes' skill system, based off early Tunnels and Trolls which had languages but no skills. In T&T characters got 1 language per Int point over 12; MSPE characters get 1 'skill point' per Int point, with languages costing 1 skill point each and having an Int minimum of 13. Consequently it more or less grandfathers in the original language rules as part of a more complex system; other skills also often have various Int minimums (or other attribute), can have various costs and then each skill can level-up by earning XP separately.  [Comparatively, later T&T editions (7th ed) went in a different direction for skills, having one significant skill per level and then languages are treated differently]. [MSPE characters/skills are weirdly compatible with GURPS: http://trollbridge.proboards.com/thread/343/mspe-arrived

As an edition change contains numerous changes carried out simultaneously, it sometimes occurs that a change made to fix a problem, is actually unnecessary because other changes have already made this redundant. For example the 3.0 ranger is something often taken as a one-level dip in 3.0, as it gained both Two-Weapon Fighting and Ambidexterity as bonus feats (+Tracking). 3.5 delayed TWF until 2nd level (an issue for 1st level rangers, sometimes causing them to carry around weapons they can't use until Level 2), but also combined TWF and Ambidexterity into a single feat anyway, so that the incentive to dip was already substantially reduced - one level of Fighter can grant TWF in 3.5 (provided there's enough Dex), or it can be purchased with a regular feat easily enough.
Generally a problem caused by a rules interaction between two rules can be fixed by adjusting either problem (such as 3E Cleave and Whirlwind Attack and the 'bag of rats' trick, was fixed by changing Whirlwind in 3.5, when probably Cleave was the problem).

Revised editions are sometimes toted as being more advanced and there can be a drive to add lots of fiddly additional rules to match that - which are often not really justified or are unnecessarily clunky with the original system. An example here is "Advanced Fighting Fantasy" again - it tries to add a dice roll for damage of weapons, but this ends up being complicated by needing a table since it's 'constrained' by the low number of 'hit points' (Stamina) to keeping within about a 1-3 point range. Original FF damage is very simple (2 per weapon hit, 1 or 4 based on test for luck) partly as a result of its scale, which when trying to add weapon variation and randomness actually gets more complicated that say D&D. (Fairly often after rolling on the table you'll end up with just the same 2 damage, anyway).

Something else that can happen is that abilities that seem cool can be used more frequently (rather than being one-off things it becomes a basic building block of the game). I have heard that, for example, magic resistance was unique to the Balrog in 0D&D - whereas this became a part of the standard monster entry in AD&D, and relatively common.

Increase in number of defined abilities - can result in 'feedback', adjustments to the system (revisions via optional rules, edition changes, more content like new classes which get more abilities) where characters are allowed to have more abilities. Some abilities in turn may then be based on # abilities known - these then require minor changes/errata-ing  (the numbers required to get a bonus are reduced, or abilities are broken down into categories where some categories don't give a bonus).

A new version of a game is sometimes an adaptation of a system to a new genre.
This can cause problems, notably values such as STR/damage can rapidly 'blow out' when a fairly gritty system has to suddenly accomodate trolls or dinosaurs (apparently a problem for Unisystem where damage could get quite high).
Finally (on this subtopic) quick-starts are another interesting phenomenon, in that they may use a streamlined set of rules and options. The Trinity (storyteller) QS has only four attributes for instance.

*adaptation: A few RPGs are descended by evolution from non-RPGs, particularly wargames (very occasionally a game seems to appear with computer game roots - e.g. I did know someone trying to design a P&P game based off Morrowind). D&D has (remote) roots in Chainmail; WHFR 1E was strongly related to the Warhammer tabletop miniatures game; Savage Worlds descends from Rail Wars (although that in turn derived from Deadlands, an RPG)(see 'The Making of Savage Worlds -http://www.peginc.com/freebies/SWcore/MakingofSW.pdf . MechWarrior evolved from Battletech (I have no idea how related this is, rules wise).
Another form of adaptation is literary, where a setting from fiction etc. is converted into an RPG. Quite often the license to a game is won by an existing company and so its standard ruleset is employed as the basis, regardless of suitability, with some reworking of character types and/or specific rules to cover situations in the source material. More rarely a custom system is built (sometimes by people with entertainingly little idea, as in cases like Superbabes) .
There are cases where setting-specific rules have later migrated into a core system; Palladium's MDC concept, more or less central to Rifts, originated in Robotech (TM)(R). GURPS Lensmen had a 'compartmentalized mind' advantage (a special ability used by Worsel in the novels, IIRC) which later became a fairly standard GURPS merit. Or the Call of Cthulhu d100 game spell list appeared in CoC d20, and subsequently became D&Dised in the Book of Vile Darkness supplement for 3E. The phrase 'Dark One's Own Luck' in Wheel of Time became the name of a feat in the D20 wheel of time adaptation, then was stolen for a Warlock power in 3.5 (unless its a coincidence), which made it into the player's handbook in 4E along with the warlock, and again in 5E as a 'fiend pact' power.

*Extraction.
Instead of a unpacking a smaller game or fictional inspiration into an RPG (what I've called adaptation), a smaller game might be made by simplifying-down a full RPG. This sometimes creates things that couldn't really be called RPGs, though sometimes it generates things that are, or almost are. For example:
-3E D&D generating the D&D miniatures game
-a number of D&D 4E-based boardgames
-the 'Cardmaster' game derived from AD&D 2E, which works either as a standalone dungeon crawl game (Fastplay rules) or is AD&D compatible; the fastplay rules use a variable die type system unrelated to normal D&D, converting a limited range of levels into various dice types to roll damage or healing or whatever, and including a range of AD&D monsters.

*appropriation/amalgamation.
A game can be built from components taken from two, three, or more different games. This 'magpie' approach may involve some rebuilding of the individual components, since any rule only works in the context of other rules.
A game can be a 'hybrid' of two main games - possibly the most interesting case here would be Fuzion - a hybrid of the Interlock system (most well known as Cyberpunk, descended from Teenagers from Outer Space) and HERO. See design notes on the process archived here --- http://www.therpgsite.com/showthread.php?t=23012 . IMHO this was a fairly peculiar and useless process, given that the resulting system was still far enough from either progenitor that conversion was difficult, with its own functioning as a system limited by the constraints of the merge. Why even do this? AFAIK it was a business decision made by R. Talsorian Games acquiring HERO, on top of already having interlock.
Other than that:
-Palladium looks suspiciously like AD&D, although with RuneQuest (d%) skills added on.
-ICONS is essentially a rebuilding of Marvel Super Heroes using the FATE framework.
-Dungeon World is a rebuilding of Apocalypse World to a D&D setting, with some adoption of underlying D&D concepts like stats and class/race
-freerpg Blood, Guts and Glory is a amalgam of 3.5 D&D and 2nd Edition Rolemaster.
-FantasyCraft evolved from Spycraft, then reincorporated D&D elements like race and magic systems. Spycraft included rules for 'origin' and 'specialty' to distinguish characters who were all human and would otherwise have been dull; FC kept those recognizeable elements + including racial options, ending up with a fairly complex chargen system. Classes occasionally retain odd bits of spycraft heritage e.g. espionage skills are spread out among classes so Assassins don't have sneaking skills (these are a burglar ability).
-BESM d20 is a mix of BESM + d20, or so it is said.
Minor influences: Burning Wheel shows influences from Shadowrun (or so it has been said) e.g. in wound codes. (note)
-Rifts Savage Worlds, in adapting SW to the Rifts setting ended up integrating a bunch of revised Palladium rules; including a class-type system in the form of "Iconic Frameworks", plus terminology (MDC, ISP,PPE) + random table rolls (not exactly like either game; its changing Rifts' unbalanced 'how much' rolls to instead roll which of several things you get, which can be still slightly unbalanced since some options may synergize poorly or be redundant). In places its reimagined Palladium archetypes e.g. the Mystic is a divine caster, while cyberknights get nanotech. Sometimes a bit clunky, and IDK how Rifts will run with a 'tighter' ruleset that reduces GM intervention, or with a highly variable Toughness in place of variable hit points (more intrinsically unbalanced). More 'builds' and SW rules can be slightly fiddlier e.g. with ranged to-hit adjustments.
-T&T had an early article on 'Arduin character types' that as an add-on to 5E T&T included classes including alchemist, 'techno', bard, assassin, barbarian, and merchant. Usually these added-on to existing very general types (Warrior, Wizard, Rogue) and gave extra abilities, so were much like 2E 'kits'. Some had hindrances but not all, and with loose multiclassing possible taking these as a type could be equivalent to something like taking a 'feat' or 'skill' in another game, without there being a system for that.

On specific examples apart from perhaps some 'd20 glut era' things, but generating a new game can require mass production of content, leading to insertion of a number of feats or skills from another game. Since to be useful a character ability has to let a character do something they can't already do, cloning content this way also duplicates fairly arbitrarily any rules those feats are an exception to. Duplicated content may not always be particularly relevant to the overall tenor of the game.

More thoughts on hybridizing games
Stealing a holistic effect - e.g. good overall design - from one game to another, means reshaping game (B) to look like (A), and may be possible even where the games are quite different but means a lot of work (e.g. Icons).

Stealing a dice-rolling gimmick (e.g. Heroic Golden Turbulence coloured dice pools, or One Roll Engine match-counting hit location) depends on the 'host' core mechanic being suited, partial rebuild of core mechanic may be needed in some cases, or it can be easy with a suitably matched system. There can be positive synergy if the gimmick drives a sub-system that's actually useful and does something the other game originally doesn't.

Transplant of a secondary sub-system may work OK provided the new subsystem doesn't conflict w/ original in purpose, require bits that don't exist to work, require probabilities set up like the original game (such as soak systems or multiple-attacks-from-high-initiative systems that would become too swingy if converted to d20/d100), add extra mechanical steps if converted to a different core system, or that work with different numbers of inputs. Numbers convert over more easily if there's some common pattern allowing re-scaling.
A secondary system being added may be useful if fills a missing area of rules in the original game, adds depth to a system that was too simple before, or fixes a rules problem. If it replaces a significant existing subsystem, the rebuild is likely to cause other changes and will have both pros and cons. As The Traveller noted, some rules are foundational and have more rules "downstream" of them e.g. changes to attributes will have more knock-on effects that revising a skill or combat manuever.

Transplant of a basic game idea from one game, to work as a minor sub-system - like adding FATE "aspects" as a minor thing in another system- may work but isn't likely to use the original idea to its fullest potential, without also stealing a bunch of dependent rules to replace existing subsystems. Consequently it may end up producing undue complexity. Going the other way - expanding a minor rule to create a new sub-system- could be very useful but needs you to spot what would be useful and where.
Stealing a subsystem from one game for another could also be useful if in the original game there are underlying conflicts with other rules, that wouldn't happen with the new host game (for instance - D20 Modern classes like Strong Hero/Smart Hero/Tough Hero might be better as an add-on for a game that didn't already have ability scores covering the same areas, or at least in combination with a stat generation method for race/class like that of 13th Age). Specific abilities might work better if they break the original number scale but have more range in the new system - for instance a 'Celerity' power is less unbalancing in a game that already has multiple actions, or ability damage mechanics in a game with larger ability ranges. If a 'specific ability' is something that breaks relatively commonly in the original system (e.g. armour or hit points have scales that don't work) the subsystem is a good candidate for hacking. The ideal I guess would be for a pair-up to fix complementary problems in both systems (a synergy where two wrongs making a right).

Problems are likely to occur if adding bits of a system that bring a lot of design constraints (e.g. if transplanting White Wolf priority grid to a new game, you now need 9 attributes rated 1-5; if using One Roll Engine hit locations, you now need to use match-counting as part of your core mechanic; see post #118 on constrained design spaces). If a transplanted sub-system is an alternative solution to a problem that the original design already solved, it has to be better than the original, for the joining to be useful. There are likely to be problems if design goals of the games are in conflict - if they operate at different abstraction levels, or if they have contradictory assumptions (e.g. old school lethality vs. complex and lengthy chargen/builds), if a random-roll power or lifepath system is welded onto point-buy and imbalances it. Major changes can alter the relative importance of attributes and so unbalance point-buy. Another common mistake might be to convert a non-skill-based magic system to skill based (random factor or attribute modifier shifts what characters can do and may break the system, particularly combined with a change in core mechanic).

Cynical Note: Note that commercial new editions are as oft as not driven by a desire to sell books/make more money as by legitimate need for rules changes, so can include much random revision for revisions' sake. New editions can also include rewriting for better organization, without necessarily much rules change (AD&D 1E vs. 2E being as much about reorganization as anything else, or the republishing of Dragon Warriors as a single hardback rather than 6 novel-sized books).

Using non-RPGs as subsystems
Another odd idea is to use a different (non-RPG) game as a 'subsystem' in an RPG, for instance:
-the Crappy Birthday cardgame as a Gamma World junk generator  http://www.rpg.net/reviews/archive/16/16212.phtml
-Fiasco as a random character background generator/seeder pre-game (cf. JonWake's thread).
-somewhat awkwardly playing out fully, a game that occurs in an RPG (for instance, the City of Terrors module for T&T includes a scenario where you play poker with NPCs, by playing poker)

Miscellaneous links
List of significant changes between Shadowrun editions: http://tgdmb.com/viewtopic.php?t=55798

Specific possibly-vaguely-useful hybridizing ideas:
-The Fantasy Trip + Dragon Age stunts: Briefly suggested by a thread here.
(Since TFT uses 3d6-roll-under, doubles gives stunt points = to whatever was rolled on the double works pretty easily.  Another elaboration that could work is that since TFT sometimes uses 4d6 roll under, a character could deliberately choose to make a 4/DEX roll (i.e. make their roll harder) to increase their chance of doubles. Possible downsides: since TFT is tactics-heavy, have to be careful not to make options too random.
Would fit better with  'blackjack' assumptions i.e. higher is better as long as you roll-under, since lower scores have lower doubles (while a '3' or '4' are always doubles, they're only double-1).
I'd also mention at this point that Dragon Age's 'stunt point' system would be an especially kickass addition to a martial-arts focussed game.
*DCC + 5E backgrounds: DCC has only a limited skill system and one from anywhere else could be grafted on (e.g. Basic General skills for instance); 5E could potentially work better since because of the character funnel (4 characters of whom one gets to survive) something fast is preferable, 5E working here since its the one background. To move to a 5E skill system completely, add extra skills (from the 5E list) upon attaining 1st level. Well, I think this could work.
*Palladium + Alternity ability checks: straight d20 roll under is hard with Palladium since scores can be higher than 20 fairly often; adding a task difficulty penalty (-d6 to -d20) could let these work. Again Palladium doesn't have an ability check system, so adding one from elsewhere is useful.
Another option for an ability-check system might be that of HERO: roll under [8 +1/5th of stat] on 3d6. Formula could also be tweaked slightly e.g. [7+1/3rd of stat] on 3d6.
*Gamma World (or Mutant Epoch) mutations + Rifts: would require conversion. Rifts theoretically has muties, but mutant rules are limited and using the Mutant rules from heroes unlimited gives mutants that are more super-powered (Altered Physical Structure etc. - like X-men). A GW mutant could convert over as say a Vagabond OCC for skills, or choose any scholars and adventurers class. Or characters might be allowed to trade in a successful Psionics roll for (say) d3 mutations. Note that cybernetics might be able to eliminate some defect mutations by replacing the defective parts (though a beginning character usually can't afford this, short of transitioning to the Borg OCC).

ORE+ ?: Potentially ORE's system for hit location could be good match for another dice-pool system when used with damage dice only, rather than to-hit dice - this seems to avoid most of the tricky issues with difficulty varying too much, autosuccess at >10d, etc.). It could potentially even be added as a supplemental system in a game that uses e.g. just a pool of d6s for damage like D6 system or even a houseruled GURPS - use the total for damage as normal but the most common individual roll could determine a location (e.g. = left leg, 2 = right leg, 3=torso, 4=l. arm, 5 = r. arm, 6 = head).
To be genuinely useful the 'host' system also needs hit location to be worth calculating, however.


Edits - 28/6/15 Invulnerable note; 5/10/15 - AFF note. 10/10/15- extra hybridization ideas. 16/10/15 Shadowrun note. 25/10/2015 ORE note

New Subtopic - Character Conversion Between Systems

Iteration - converting specific characters between editions: a desire to let existing characters remain similar can slow down change (influencing a new editions' design / content). Sometimes rules changes to fix problems will specifically shut down 'builds' designed to take advantage of loopholes, so optimized characters tend to be hit hardest by edition changes. Rules (or specific GMs) may 'grandfather' certain characters, letting them continue to use particular rules. Where rebalancing occurs via 're-costing' items rather than altering their functioning, characters might just change their point value or level; that generally works fine for NPCs, at least.
In some cases abilities that were 'built in' initially, might be turned into add-ons that are sold separately. (An interesting case of that for example is "Tome" D&D variant's 'Seeker of the Lost Wizard Traditions', which has a variety of weird special abilities designed to make 3E spells work like 2E spells; this includes lightning bolts reflecting, fireballs that expand, uncapped damage dice, spell ranges that are further outdoors, and harvesting of monster body parts).
New iterations might alter cost-accounting to either simplify and make accounting more straightforward, or add more options. Converting characters to a 'streamlined' system might cause some things like skill values to change when they're forced to conform (e.g. if skills go from exact percentiles to ranks that are +10% each, a skill at +7% has to become either 0 ranks or 1); going the other way a character might transfer exactly, although as for 2E/3E D&D conversion risks being made 'suboptimal' as other options appear that make them less comparatively efficient.


System conversion between wholly different systems becomes particularly tricky when systems have different default assumptions/setups that can't be bridged easily:
*level-based systems like d20 have combat ability set to level - if they work, anyway - which makes characters hard to convert if they are built with points and specialized for some non-combat niche - the best starship designer in the galaxy is an NPC that might need protecting in a point-based system, but in a level-based system would be a high-level character.
*cinematic vs. realistic or high-lethality: e.g. Palladium MDC thingies convert badly to Savage Worlds, where exploding damage rolls intentionally make most characters 'up, down, or off the table'.
*balanced vs. unbalanced: a random-roll, ad-hoc-advantage/disadvantage character converted to point buy/a unified feat or advantage system, may find a huge number of points sucked out of them to pay for/duplicate what were previously virtually nearly free abilities, more than said abilities are actually worth since the abilities are probably generated randomly rather than assigned in an optimized fashion. For instance, a character might have a rolled ambidexterity but not be specifically (or usually) a TWF character.

There can also be problems with one-value vs. two-value systems (a character suddenly needs a high base stat to be good at something), or where something that's independent suddenly is reset to a derived value that can't be easily constructed that way (values might be averaged, or some details might end up overlooked).

Sometimes games have wildly different opinions on how difficult something is, particularly on more minor details. Character durability can differ markedly between 'realistic' and 'cinematic' systems (as noted in Dragon #165 conversion guide below). Languages can differ a lot also e.g. a Gamma World 2E character will usually know 3 languages initially (Common, area language, cryptic alliance language) and can speak up to [1/2 INT so about 5 at Int 10]; a Tunnels and Trolls character needs Int 17 to have 5 languages. A 3E D&D character has extra languages equal to 'speak language' skill ranks so could easily learn 20 languages, a 5E character will know 2-4 (2 for race, up to 2 more for background) and usually has to burn feats to pick up any extra. Within D&D, 2E characters tended to have fewer special abilities than 3E characters; a character can be converted 2e-to-3e relatively easily gaining abilities, whereas backporting 3E-to-2E, some feats might be particular class or 'kit' abilities and so, with a higher barrier to entry and so exact abilities requiring implausible amounts of multiclassing or multiple kits or DIY classes. A few 3E wizard feats were 'only' spells in 2E e.g. Enchant an Item, Vocalize, perhaps Lower Resistance; that could be argued to be almost equivalent given higher difficult in finding spells, fewer spell slots, etc. in 2E.

Something that can be interesting is that different systems' different levels of detail in some areas, can result in game mechanical information simply becoming 'colour' (detailed to less detailed), or needing to be created. For example some game systems have personality mechanics and some don't: a 3E D&D character converted to 5E needs bonds, flaws, ideals etc. to be created (out of how the player envisages the character based on actual play).
Conversion may be a misnomer really - 'translation' might be a better word since its not necessarily a purely mathematical process but also needs to consider context in trying to find something that means the same rather than being purely equivalent.
Another particularly difficult issue is the different 'playstyle' of different games, which might mean that a characters' actions in how they're played (for instance, how gung-ho they are in combat) can change from neutral to very suboptimal, or at least would be so unless the character's actual statistics were changed to make them tougher.

Conversion Resources - Dragon #165 has a primer on converting published adventures between systems - this includes details on various dice rolling mechanics and recommends converting characters by taking probabilities e.g. of stats and mapping it to an equivalent number.
There are actually a couple of alternative probabilities that can be mapped through: either the probability of rolling an attribute score itself, or the probability of task success with a given score. #165 is primarily the first - this works OK for stats in 'random roll' systems, although in modern times where stats are more often point-bought it becomes more difficult. Another article here shows an example of the other approach (for FUDGE to d20) where the task dice probabilities are roughly converted to give ranges.

'The Armoury' published an interesting Conversion book between assorted early 90s systems, which assigned systems letter codes for interconversion, noting which stat equated to what. The table format used here is also interesting for its compactness.
Functions of a stat expanding through editions - could cause an effect in older versions to give weird side effects (one 2E Advanced Fighting Fantasy character I had, a dwarf warrior, did an old Fighting Fantasy adventure where they lost an eye, which according to the text causes -1 to permanent Skill. In 2E-AFF rules, the skill drop reduced their Armour use skill rating and so prevented them from wearing their current armour).

A couple of d20-ports of early gamebooks included 'Golden D20's Bronze' which added a feat that could grant a Luck attribute, or Myriador's d20 adaptation of Fighting Fantasy which added a Luck score. These were probably a bad idea in that it adds extra complexity by duplicating a Luck score that existed for simplicity - replacing an array of saving throw numbers and generating variation in damage amounts - though Myriador's also acts as a spendable strategic resource).

Adventure conversion between systems: this may involve character conversion, as well as task-resolutions being altered, expected resources being more or less available (for example, even an edition change altering how available/powerful 'create water' is might invalidate the desert-survival part of a desert adventure). Specific monsters might be more or less powerful. Assumed lethality can differ between systems and a highly lethal game may give more instant-death situations not even involving game mechanics. Situations where one roll can stop the adventure may be OK in games with 'luck points', bennies, etc. but might need tweaks in other systems. Combats involving lots of combatants vary in difficulty depending on how difficult the system makes that - splitting defensive actions for example. Typically this works in favour of the monsters though some games it might actually favour the PCs (combats in a DCC 'funnel' adventure for 16 PCs might suddenly become easy in Tunnels and Trolls, instead of a bloodbath).

In old-school circles, one thing of interest conversion-wise is the FLAILSNAILS articles, intended to promote use of D&D x.x to whatever other vaguely related systems - suggesting you could run a Swords & Wizardry adventure with (say) a DCC character, AD&D 2E character, BECMI character and Pathfinder character. Conversion specifics are largely up to the GM.
http://jrients.blogspot.com.au/2011/08/flailsnails-conventions.html

You could probably swap all but the first one with the catch-all terms "iteration" and "appropriation" and maybe even "adaptation."

Iteration would be editions and clones.

Appropriation would be good both for "magpie" and hybrids.

Adaptation would be emulation of a non-RPG in RPG form. Both for licensed properties and for war-game to RPG transitions (chainmail to D&D, Warhammer to various Warhammer RPGs, or Iron Kingdoms D20 to Warmachine to the new Iron Kingdoms).