In Dragon Age: Origins, your party members can’t be permanently killed, but every time they get knocked out they get a random injury which sticks with them until they get more substantial healing.
The recently released Pillars of Eternity has a system that’s like regular HP, except that you also have a much larger pool of health that takes damage at the same time. A character doesn’t suffer any penalties until their health gets low, at which point they stop being able to recover and risk actually getting killed.
Deus Ex had health for individual limbs. When you lost your legs you couldn’t stand up anymore and had to crawl around until you healed.
Cave Story has an unusual system in which killing enemies gets you little XP baubles that upgrade your currently equipped gun. When you get hit, though, you lose that XP and your gun becomes weaker.
In FTL, your ship has a hull strength which is pretty much just HP, but your systems can get hit individually, all of which have unique functions. Get hit in the weapons room, and some of your weapons go offline. Get hit in life support, and you run the risk of your crew suffocating. If your teleporter gets hit, you’d better hope you don’t have an away team that needs to be recalled. It can get really tense prioritizing which systems to repair first. Your crew functions at full strength until they die, though.
In the King’s Bounty games, your units represent a whole bunch of guys. As they take damage, some of them die and the unit’s strength falls proportionally. You have to recruit more minions to bring them back to full strength.
Way back in the Legend of Zelda, you had a special ranged attack that was only available when you were at full health. You lost it when you took any damage. It was never clear to young me whether Link was throwing his sword or it was some kind of magic blast that just looked like the sword. Throughout most of the series the games beeps at you when you’re low on health, which I think most will agree is debilitating in its annoyingness.
The Smash Brothers games work on the principle that you never get knocked out just for taking damage, but for going off the stage. The more damage you take, the further you get knocked back when you get hit. You never actually get KO’d from damage, just more likely to get taken out by a hit.
In general, I think most designers avoid punishing players too much for taking damage with good reason. Everyone loves a good comeback story, about how at your darkest moment, just on the edge of defeat you managed to pull through and snatch victory from the jaws of defeat. The more you hobble a player for taking damage, the more unlikely you make that comeback. Hobbling the player usually works alright in games with a high degree of resource management, Deus Ex or FTL, but in action oriented competitive games, most fighting games, it tends to just make defeat feel more inevitable and victory less satisfying. Maybe it’s not realistic that your fighter on the verge of defeat can swing as hard as at the beginning of the fight, but realism be damned it’s just more fun that way. The best compromise, I think, is to give a lot of visual and audio clues, things like panting or sagging shoulders, to indicate exhaustion without actually making the character weaker.