I don't mind regenerating health if it's
A) fitting the setting. Like Halo: CE, which I find to be the best mix of health bar and regenerating health. You have shields that regenerate and a health bar that you need to use med kits to heal with. Resistance was also pretty spiffy where you could only regenerate to the nearest quarter of your health bar at a time, and need healing pickups otherwise.
B) If it's really, really useless in combat. Like Mass Effect, or Saints Row. Sure, it recovers, but it's slow that if you try to rely on it in combat you'll be twiddling your thumbs a lot, so using healing items is really the best way to go.
C) If it's a game that's not really meant to be a challenge, just really, really fun. See Saints Row, again. it's not a particularly challenging game, and is meant for you to enjoy driving around in a stolen police car, knocking pedestrians into the sun while shooting an uzi out the side window at the cops. Or, if you're playing co-op, while your friend takes care of the ensuing cops with his choice of big sniper rifle, rocket launcher, laser-guided rocket launcher, SAW, grenades, variety of machine guns, and grenades launched out of machine guns. Oh, and the minigun. Can't forget the minigun.
In say, COD4 it doesn't make sense for you to have regenerating health. But I suppose that could be chalked up to the side effects of having a camera inserted into your head. Lost Planet did something nifty, where you have a health bar and a counter for your thermal energy. Every time you take damage, it is quickly healed using thermal energy, which is constantly decreasing anyway. Should your run out of thermal energy, you promptly start to lose health.