I think some games can narratively justify regenerating health (or partially regenerating health), and when you actually do that it's fine.
Like in Mass Effect 3, you have shields and health. When your shields are depleted your health goes down. Your shields regen, your health does not. This is a great system.
In Deus Ex: Human Revolution you are a freaking cyborg, when you get hurt all the crazy technology in your body heals you.
But if you're just like a normal dude with a gun, your health shouldn't regenerate. But if you're a normal dude with a gun, you really shouldn't survive multiple gunshot wounds anyway.