An exciting mechanic I do not see in enough games is a state between fully capable and dead. Some games weaken the player as injuries accumulate, but most follow the trope codifier in letting you (and your enemies) operate at full power with 1 hit point and instantly die to the next falling leaf. For this post, I am less interested in gradual weakening than a transitional dying state. This is variously known as dying, downed, unconscious, “fight for your life,” bleeding out, second wind, etc.
There are two common implementations. One is “defeat an enemy to self-rez.” You are not just going out in a blaze of glory, you are re-lighting your torch. The biology of that is curious, since you seem to gain a lot of health from shooting people in the face, but these are often worlds where many things improve through shooting people in the face. This mechanic keeps a player from losing 99% of the way to victory, although that just pushes back the threshold; you will surely rally if you are downed by an enemy you can kill with your next hit, but now you get a similar effect from enemies who have 1 hit point left when you finish bleeding out.
The second implementation is to let friends revive you easily while downed. This is a great thing, and it rewards group play without requiring it (although some content virtually requires it). I can help my buddy up; it’s pro-social. Games may vary on whether anyone can help you up or only a healer character (similar to a normal rez).
Finishing off downed foes/players is sometimes available. In some games, you have X seconds between 0 hit points and death; in others, you have Y additional hit points. If hit points, the enemy can probably keep attacking to take someone out fully. In either case, an enemy might be able to coup de grace the dying the same way an ally could help him/her up. This is usually combined with a vulnerability mechanic, more for balance than realism; while lining up the beheading, you expose yourself, possibly because you are taking the time to be awesome and showy. (This makes less sense for a thief character who is slitting a throat, although maybe he is over-exposed while hunching over the body. This makes lots of sense for a necromancer who finishes foes by sucking souls from bodies.)
I cannot tell you how many times I have traded grenades or rockets with the enemy and died because my attack finished first, whereas I would be instantly revived if my explosion happened 0.005 seconds after theirs. You just lie there, alone and helpless, wishing that enemies would attack so you could kill one. Your game has brought you to an odd place if, when you are bleeding to death, you desperately long for attacks by bandits and savage dogs.
Because of this, fights against large targets in games with this mechanic will almost always include smaller foes that support the boss, usually with endless respawn. These are necessary for your survival, not additional threats. The boss has 100,000 hit points; his minions have 100 hit points. When the boss knocks you down, you are meant to kill part of his support team to pick yourself back up. Part of your planning is keeping that potential revive on-tap without having it become more of a threat, since it is also still doing full damage if you leave it with 1 hit point.
Guild Wars 2 adds the very sane variation that you can heal yourself (slowly) if you are downed and not taking damage. No more bleeding to death because you won the fight while an attack was resolving! It does, however, make environmental hazards and hallways full of traps problematic to design. They are either non-threatening or effectively one-shots from which recovery is impossible. GW2 also gives characters a whole ‘nother set of skills for the downed state and builds some mechanics around it like the necromancer’s death shroud.
As with so many things in our MMO world, Dungeons and Dragons blazed a trail. Most editions of the game have an unconscious state between 0 hit points and dead. Most of those have you slowly bleeding to death unless a friend heals or bandages you. The old standard is “death at -10 hit points,” but some rule sets give you a huge pool of hit points before dying (absent coup de grace) or had odd rules for being exactly at 0. At least one edition lets you still act while dying, instead of immediately going unconscious, although you damage yourself with the strain. I do not recall any D&D versions that let you rally by defeating a foe.
I like the pro-social aspect. I like the way it lets you recover from the brink of defeat. I like that it makes that brink into a game mechanic. I do not like the way it forces designers to add trash swarms to boss fights.