Shadowrun uses a condition track to keep track of damage. Any edition. The way the process works depends heavily on what edition of the game you're playing.

Any of the Storytelling games (old World of Darkness) use a similar condition track to track damage and healing.

Star Wars in its various versions have had a number of ways to handle this. In WEG's version, there was a status monitor (stunned, wounded, wounded, incapacitated, mortally wounded, orbiting Alderaan) for characters, for starships and vehicles, and for armor and suchlike. For one of the WotC versions at least, there was a division into vitality and wounds. I have no idea how the FFG version holds up.

Mutants & Masterminds have a Toughness save, and stack status effects.

Warhammer FRPG has a certain amount of hp and stuff, but usually it is a critical that'll kill ya. Or when wound fever or gangrene kicks in a while later, because you can't get good food and all the water is polluted by Chaos spores and the leg you lost sprouted tentacles and went off into the woods somewhere.