"health" is an abstraction anyway. Tailor the health system to the game, I say.
Personally, I reckon that regenerating health removes some of the challenge from the game task of surviving, and should only be saved for when the bad guys all have a pretty decent chance of killing you one-on-one in a fair fight.
Basically, you should either be fragile in the short-term but capable of regenerating to full health fairly quickly, or tough in the short-term but reliant on external influences to restore your health.
One thing I'd quite like to experiment with would be a hybrid "tiered" system of damage.
Let's say you have your health bar which is green. You can take three types of damage:
Stun damage, which is represented by a section of your health bar turning blue.
Wound damage, which is represented by a section of your health bar turning red.
Life damage, which shortens your life bar.
Each type of damage counts from the far left of the hitpoint zone taken up by the next more serious type. So, if you've taken two Life damage, three wound damage and seven stun damage, then from right to left you have a small black zone, a slightly larger red zone, and a much larger blue zone, then it's green all the rest of the way.
Different weapons have different damage profiles. A tazer does huge amounts of stun but barely any wound and no life damage, for example, whereas a burn from a jet of steam is more wound than stun or life, and a sword does lots of life and wound, but not a lot of stun.
Stun damage regenerates quickly, Wound damage regenerates slowly, Life damage can only be restored by medkits, or spells, or whatever.
when your stun damage bottoms out you suffer minor penalties - your vision's a little blurry, your aim wavers. When your wound damage bottoms out you suffer major penalties - can't hear, can barely see, terrible aim. When your life damage bottoms out, you die.
Oh, and you make the bar VISIBLE.
you could even apply the system per body part, Deus Ex style.