Robinson's requiem was a "sort of" FPS. It was more a survival simulator. You were the survivor of a spaceship crash and had to build spears and bows, hunt your food, cook it, etc... It was well-known for its very complex damage system. In fact it looked more like a mediacl simulation : you could see your character's body and read several information about blood pressure, temperature, etc... you could die of a dozen diseases, had a wide range of medical items (if you could find them) you could repair bones, even cut a member ( an interesting feat being cutting both of your arm without any help :-) )

It didn't make it a good game, there were quite a few flaws IMHO. But if you want to see a complex health system, you could give it a go. It is abandonware by now.

A good reason to put no healthbar and a complex medical simulation would be, in my opinion, to force the player to stop, hide, find a shelter, drop the gun and examine his/her status, make the necessary healing and then go back in battle. It is clearly inadequate for a fast-paced Quake3-like game, but for an anxiety-driven, atmosphere-heavy FPS (WWII simulator anyone ?) it could add quite a bit of immersion.