Meh, depends on the game itself, its story, context, etc.
I thought it was alright in Halo, but would have been unfitting in STALKER games, and I loved STALKER games the way they were. Then again no regeneration in Halo would have felt strange... dunno. It was alright anyway (with those two examples, and more). I like challenge, but not frustration. I don't want a simulation either. I do NOT want to have to crawl and bleeding out until death if I get shot by one freaking bullet... BUT... if I play a simulation "game" and that happens then that's fine I would have asked for it.
But... say Halo again, would it need to be like that? Would Halo need to have those energy weapons turned "more plausible" and after one or two shots Master Chief goes down? No, why? Because it doesn't fit, it's an action game, take it with a grain of salt (then again play it on Legendary and that can happen, anyone recalls the Jackal Snipers in Halo 2 on Legendary? One shot, dead). Really, not all games need to have "this and that" (simulation or action). The games need to be the way developers wanted them to be (I mean game-play mechanisms here, not necessarily the story). The "down side" to that is of course the risk to be a bad game, but that ain't a big deal is it? There's risks for everything out there.
Just give me a middle in there somewhere, some games can be good with health regeneration, some wouldn't be. Some games might be good even if not a simulation but still challenging (still, I wouldn't want one bullet to kill me unless it IS a simulation game). I don't mind dying and having to try a few times, and that's they key (for me). If I die say... 3 or 4 times and I've spent 1 hour trying to save some hostage from the same freaking room but each time he(she) would die instantly from a bullet to the head because I need lightning-fast reflexes then I might as well just train for that in real life and realize it ain't for me.
Anyway, point is there (speaking for myself if anything), it just depends on the game. There's one thing I don't really like anymore though, and I agree with those who say it needs to go away in favor of other "damage/death" mechanisms, and that is the Health Packs... man that's old. Ironically they are in Halo and there's regeneration anyway, although I know, there's actual health bars below that shield regeneration which I always tend to call health regeneration, even though I know it's really just "shield" regeneration.