Well in an FPS, you could have the following indicators of injury:
1) Injured player view gets dizzy and has trouble seeing clearly, and needs to retreat from the action, for the view to settle down.
2) Walking/Running has a limping effect. Even the occasional fall, where the player has to pick themselves up
3) Player has trouble holding up weapons, drops heavier weapons, fumbles with reloading.
4) Player hand models (the ones holding up the guns) could show various levels of pain like bleeding fingers.
4) Use sound for an exaggerated heartbeat (or rumble on a console)
How would it relate to gameplay? These would be your health indicators. Current battle scars mean nothing, because it's your health meter that tells you how the character really is. When health can be displayed without the use of a health bar, then it makes the game more cinematic and frees up room on the screen. For similar reasons, very few game screenshots show the in-game menu.
A simple example of how this would enhance games, would be if the players could have "in game injuries" :
A player participates in a major battle and instead of merely dying, they "badly injure" a shoulder, an arm, or a leg. Over some time in the game world that major injury would slowly heal, and until then - that player wouldn't be able to run as fast, or wield heavy weapons.
This doesn't have to be a particular major event of the game, just any random battle in a game, where for whatever reason the player performs poorly, or tries to kill everyone in a situation where they should use stealth.
This situation also leads to deeper gameplay situations when NPCs are involved:
Imagine Half-Life 2 episode 1, where you had suffered an ingame major injury and had to depend on Alyx to protect you. There's a way of allowing a player to feel emotions for an NPC.
Or if Alyx could sustain an injury like that, if you didn't help her during fights.
Think of Half-Life 1, where the hero starts out as someone with very limited weapons experience.
In the beginning, firing a handgun should be similar to one's first time firing a handgun. Holding a heavy weapon should be difficult for him. Holding it steady should be a challenge, that over time goes away, as the character becomes stronger. Improved graphics and physics allow that to happen. The "evolution" of the main character from "average Joe in a bad circumstance" to hero is better realized this way.
And how would those directly relate to the gameplay? I don't want to play a game just to see battle scars "improve" over the course of fighting. It's like...watching paint dry.
Edit: And to add about the health indicator thing, I think I agree with some posters that it won't be obvious enough, especially (and particularly) when playing an FPS. Looking at the reflection of yourself in the lake just to see your health status? Isn't that a bit