I have played with three health systems that I think work pretty well:
1. Halo 1 and Halo: Reach. This was mentioned before, but I think its good to have partial regeneration, but also health packs. In Reach especially, I liked how your health could essentially be rounded up to the nearest quarter or so, and you had shields, so that you would definitely feel the effects of consecutive combat, but it wouldn't leave you with those annoying scenarios of being stuck in a fight with 1 health and no way to get it back.
2. Resident Evil 4. I loved the herbs and health sprays. In fact, I loved everything about RE4, but the health combined with the inventory system really was great. You could compensate for a lack of skill by having an abundance of health items, but supplies were ultimately limited, and so was your capacity to carry. You would also have to make decisions between ammo, guns, and health. I won't mention Resident evil 5, because that game took the inventory system I loved and murdered it...
3. World of Warcraft/TF2. You have a health bar that, in WoW at least, is capable of recharging itself, but very, very slowly. The process can be sped up through items, like food or bandages, as well as potions or healing spells in combat. Team Fortress 2 actually is somewhat similar to this, in that medics can heal you, you can pick up health packs, or, in some cases, use class specific weapons or items to regain health, but at a cost.
I will say that I appreciated recharging health when it first started out, just because games always used health packs before then and it got a bit old. Now, however, we once again see the industry largely showing no creative spark and just using the most common techniques.
Recharging health can be good, but you need to be creative with and critical of it, rather than just making the same old system that has been used in nearly every fps since 2004.