The system works well in most games it's used in, and I enjoy it in some, but not in others. I don't mind an in-universe explanation like a special super-soldier suit or something, so long as the healing isn't too quick as to make the game easy. Crysis is a nice example, where since you're out in the jungle it doesn't really make sense to stumble upon health kits every few seconds, and your shield power is also used to fuel other special abilities you have. On the other hand, it's completely unwarranted in a game like Call of Duty 4. I don't mind a mild health regeneration, but in that game you literally go from near-dead to just fine in the span of about five seconds. It's ridiculous. I think you should be able to sustain a hit or two before healing up, but a "critical" hit should permanently lower your movement speed, accuracy, etc., similar to Rainbow Six. It would encourage a more realistic sort of play-style with better use of cover and leaning, something I think needs to be emphasised a bit more in the gameplay - there just isn't enough risk to standing in the open. Additionally, Modern Warfare is mostly focused on squad combat. Give the team a medic who can heal you up if you're critically wounded, but make it take several seconds.
I think Far Cry 2 deals with player health really nicely compared to most games, and does a good job of providing health regeneration without it being overpowered. Your health bar is split into segments, which each will refill up to a certain point. You can heal at any point if you have a syrette in your inventory, but they can be limited and will run out in more intense firefights if you're not careful. Critical damage requires a long healing animation to play out, which leaves you very exposed to enemy fire. Having a buddy rescue you on death is pretty cool, too. Overall, probably one of the best health systems I've seen in a game recently. It works well, keeps things flowing quickly, adds a good sense of risk/reward to combat, and leaves you just mortal enough so that you can't go running around like a headless chicken, but can still soak up a reasonable amount of damage. It's also fairly realistic, especially when on higher difficulties you can't take too many direct hits.