Let me preface this by saying that I don't *hate* regenerating health.
I prefer health packs. They make games, in my opinion, more intense. You have to actually put some thought into your actions. When you engage an enemy you need to actually think about getting the upper hand so that you minimize the damage you take. If you run into a room guns blazing without a single care in the world for your health pool, then end up with 2HP and no armor right before a boss fight... well, good luck. That boss fight is going to be a hell of a rollercoaster ride.
I can totally understand why some players might not like that. They may not like having another resource to manage. They may not like having to think about tactics when they'd rather just run around squeezing the trigger until all the mean things fall down. Maybe they just don't like the potential risk of making a mistake then getting stuck, right after saving, with too little health to progress. All legitimate reasons. Just not reasons that I *personally* agree with.
I admit I do enjoy a number of games that feature regenerating health. I loved Modern Warfare and Modern Warfare 2. Though it isn't out yet, I'm sure I'll have a lot of fun with Deus Ex: Human Revolution (regardless of whether or not it's equal or better than the health-pack-and-soy-food-featuring original Deus Ex). My only main gripe with it is that I never feel like there are any consequences to my tactical decisions. If I make a mistake... whatever. Just hide behind a chest-high wall or something until my character squeegees the cherry Kool-Aid off his or her eyes. In Modern Warfare 2 if I fall from a great height I get to hear the disgusting crunch of my leg bones snapping, my screen goes red, then I continue sprinting at full speed without skipping a beat. In the original Deus Ex, if I fall from a great height, I completely crush my legs and get to crawl my way toward the next objective like that Green Army Guy that no one likes. Does regenerating health keep up a fast pace in the game? Yeah. But does it add any sort of difficulty to the game or tactical thought to the game? No. That's my main problem with it. It makes games easier and more mindless. In something like Modern Warfare which plays like a fast-paced adaptation of a Tom Clancy story as envisioned by Michael Bay with an infinite budget for pyrotechnics it works. You play the game for the shoot-outs and pretty explosions, not to think. It's a summer popcorn flick in the trappings of a video game. But for anything deeper than that... regenerating health just doesn't work for me.