Ok, everyone has their own opinion.  Some prefer crunchy.  Some like quick resolution.  Fast paced vs. detailed blow-by-blow.  Realistic damage vs. cinematic "it's only a flesh wound."

There's no "right" answer.  But what combat system do you enjoy most?  What have you had the most fun with?  Is it genre-specific, or genre-neutral?

Personally, the most fun I've ever had was doing TFT in Junior High back in the late 70's-early 80's.  It was quick to learn and easy to understand, relatively fast-paced, and had cool little cheap counters on a hex map.  (You could upgrade to miniatures when you had the cash, but in a pinch you could just use coins, buttons, or tiddlywinks.)  It was certainly easier to learn than AD&D 1st edition (which I also played at the same time), and it seemed more intuitive than LBB Traveller (also something I played a lot at the time.)

I'm on the side of crunchy combat, but I want it to resolve quickly, too.  Ideally, I like cinematic combat - the idea that there's movement and a variety of actions. 

While many attacks may just be 'I attack with my sword, 5 damage', I like having other options like Disarm or Feint.  We give Talents that allow characters to potentially do special actions in combat.  For example, I might have 'Riposte' - that allows me to make an Attack of Opportunity if someone missed me (with a cost).  Trying to create situations that allow you to use these special abilities encourages you to create dynamic combats. 

Relative to 3.x, we allow each character to move and 'full attack' - in fact you can attack before, during, and after your move (effectively they happen simultaneously rather than in discrete phases).  This means if you have a good 10 feet in front of you, you can step up, slash them across the throat, and if you drop them keep moving another 20 feet to threaten the BBEG. 

We also do a new initiative every round.  We find that everyone acting in the same order every round creates a cadence/predictability around combat that we don't like.  If the BBEG goes last in Round 1, but they have a chance of going first in Round 2, there's a very different feel than if you are 100% certain that all of your allies will have a chance to go again before he does. 

I always end up somewhere in the mushy middle on this question, to the satisfaction of practically no one else that has a strong opinion.  But my players don't mind where I land.  So I have that going for me.

To me, there is a trade between detail, game handling time, pseudo "realism", characters being capable and characters fearing what others can do, and the feel of the pace of combat (separate from the handling time of the gaming mechanics).  To wit, the more detail and time one chases for mechanics, perversely the less fluid and anxious the combat can feel as a whole.  If nothing else, player X taking 20 seconds to resolve their mechanics is giving everyone else that much longer to think about what they are about to do.  I want to weave through all of those trades, avoiding extremes, and arriving at a set of mechanics that is "good enough" on each thing without sacrificing too much in the others. 

Since I have similar "Goldilocks" views on character customization options that feed into combat mechanics, that's effectively doubling down on my attitude.

I like swords, and axes, and hammers, etc.

I like weapons to be diverse and have different features. I dislike weapons that, judged by stats, shouldn't exist.

I like SOME realism; I do not want most swords to weight 10 pounds.

5e is bad at that, and B/X is terrible.

I like SOME crunch, but not much. Probably B/X with some fixing and critical hits would be enough for.

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Armor: I do not care that much.

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Maneuvers: I like them. Make them simple and easy. Here is what I'm playing with in my OSR minimalist:

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Combat maneuvers. Combat maneuvers (tripping, shoving, disarming, etc.) can be performed by any character. Make an attack. The target does not get a save usually, but the GM may rule that the target resisted the maneuver by exposing itself to damage, thus taking maximum damage from the attacker (or double damage on a critical hit).
Combat maneuvers (II). If you have +2 AB or more, you can split it anyway you want – as long as the split is even, you round down, and you have a minimum bonus of +1 to each roll. For example, if your AB is +5, you can attack with +2 and add +2 to damage. You can attack defensively, adding +2 to your attack roll and +2 to your AC against a single foe. You can attack five enemies at once, +1 each attack roll (in this case, the foes must be lower HD than you). You cannot take multiple attacks against a single target.

I like fast resolution of actions, without any slow look-ups.

I also like combat to flow. Not just having a few people trying to shoot/stab each other in turn until a few go down. So some variety in the moves, but also the combatants moving around the battlefield.

The chance of lethal single strikes to and from any character and over the top critical hit charts.

Depends on the system I'm playing/running, but in general I prefer quick resolution with uncomplicated mechanics. If a manuever requires 2-3 rolls from each participant, it's typically houseruled and simplified.

I also prefer flexibility over crunch. I want players to ask "Can I do X?" and get a simple yes or no answer, rather than have them pour over the rules and try to sqeak out a technicality. Again, this is going to depend on the game and the setting, since some really require air-tight tactics to work, but generally, I want to be able to adjudicate actions, not rules.

The main requirement for me is I have to get through the whole combat in a reasonable amount of time. As much as some gamers are allergic to the word "story" it's easiest to think of it in that context. How far can you really push a combat in a story before it becomes a distraction from the telling of that story? That's the upper time limit on the most complicated of combats that I would consider playable. 1E is tough to beat on this count because of some little-known features that make large-scale combat go quicker, so there's almost no limit to how much you can scale up.

Beyond that, my main turn-off is convoluted bullshit. I don't need to know yet another way to roll dice. And much like I have no interest how many frat boys can fit into a phone booth, I have even less interest in how much shit you can cram into one die roll. "This mechanic determines if you hit, when you hit, how hard you hit, whether you critical, whether you phase shift, makes up goofy complications, and scratches your balls for you. All in one roll." Hard pass.

Main turn-on is the thing that probably matters most in any game. Find the right combination of rules that are a low hurdle to clear for participation, but a high hurdle for mastery. If you're the designer of the rules, and as designer you know what the best strategies are, you system sucks. Print it up. Wipe your ass with the print out. Flush it down the toilet. Delete all your files. Then defrag your hard drive. And start over. The rules should be simple, but their implications should be beyond what you can anticipate.

I tend to measure a game's combat systems like they're a rocket and I'm computing a Power to Weight ratio, which I will abbreviate to P/W. I like crunch, but not so much that I will tolerate a system which needlessly wastes table resources like time and player effort or attention, or requires me to spend time thumbing through the book.

This is one of the key reasons I regularly recommend Savage Worlds. Perfect system? No, definitely not. But at this moment it is the undisputed champ of the industry when it comes to having a high P/W. It's also why I tend to revile percentile systems and prefer success count pool systems; player attention is a limiting factor for most of my games, and percentile is particularly bad when it comes to arithmetic, while success count pools tend to be pretty efficient in the arithmetic they require. I also don't really care for granularity, as it's generally a false sort of precision which looks good on a design doc, but doesn't actually add much to the game.

Bottom line? I do prefer crunchy combat to non-crunchy combat. But not by so much I'm willing to sacrifice the experience of players at the table. A game has to make a compelling case that it's using table time and player attention wisely.

Games where character progression means your chance to hit goes up as you increase in experience, balanced by your chance to not be hit equally goes up, leaving your hit points where they are. 

Aka, not D&D.  I don't like hitting odds going up versus lots of hit points. 

I've also noticed that a lot of my favorite games are like this.  You don't get inhumanly tougher as you level up, you get better at blocking/dodging. 

1.  Palladium series of RPGs
2.  West End Games D6 Star Wars
3.  Pocket Fantasy where hit points are fixed.  High level actually means lots of re-rolls, but so can the other guy
4.  Dungeons and Delvers Dice Pool Edition.  Max level PC is just 150% the hit points of a level-1. 
5.  Tiny-D6 series.  Hit points are fixed. 

I used to think I wanted realism, until I played a very complex system where one combatant attacked, the defender parried, then if the attacker hit, you rolled for hit location, then compared your weapon damahe to the armor on that location, then looked up a chart to see what the wound actually did to the injured party.  Oh wait...did you take i to account the amount of fatigue each combata t had?  Because it lowers your chance to hit and parry, basically making the fight take even longer.  Oh! And there's equipment damage to take into account as well. 

After an hour of all that I scrapped it and went back to D&D. I have been sticking with D&D like combat systems ever since.  It works for me so long as we can keep things moving.

I dislike combat in general. It's essentially the same as any other skill check, only with more steps, because thanks to the history of RPGs, people assume RPG = combat. Generally speaking I reward my players as much (if not more) when they handle a situation via diplomacy, stealth, or knowledge rather than fighting stuff.

Having said all that, Shadowrun 4e has some decent combat rules. PF2e had the right idea about "variable three actions" but didn't utilize it to its full extent. L5R 4e also had a pretty good combat system. No combat system that disallows "move-attack-move" is good.

Any combat system I use has to be able to run a 20 vs 20 combat quickly and easily. I don't want the limitations on a game's combat system to end up limiting the types of adventures I'm able to write.

One of my favorite combat systems is Wushu (Blackbelt Edition).  You kind of need to think like an action movie director since you get dice by describing details.  It makes for very fun uber narrative combat rounds.  One cool thing about it is that details are details, so describing set-backs, blocked attacks, or seeing that ninja in the reflection of your sword are all valid ways to build your dice pool.

It more than just Wushu marital arts action too.  I've used the system for Crimson Skies style dog fights and wizards trying to fend off an alien invasion.

This depends 100 percent on how many players are playing.  A contested combat (like GURPS or Unisystem) with specific weapon peoperties is my first choice if there are 4 or less players.  More than that, i like a bit more abstratction for speed and then we are over into Savage Worlds or DCC territory which have some flexibility/imagination allowed in resolving combat.