Nightmare On Elm Street and Hellraiser are my two personal favorites of this sub-genera of horror. I like Saw too, but I consider it a different kind of horror movie, so I think it should probably have been omitted from this.
I will say that Michael Meyers has never been fully defined, but there is a cult and supernatural angle involved there eventually, even though they never fully explain it. Basically he's not just a murderous sociopath he's some kind of "evil one" so to speak. It's been a while though.
Also I'm not sure if I'd define Jason as a "Zombie" per se, he's more of a manifestation of a curse of vengeance. What they do with him varies from movie to movie, but at one point they wind up having him possessing people and everything when he loses his body. The only thing is we generally don't see him reform, regenerate, or whatever else probably because they never thought it through that much especially to begin with, however I think the key to the whole thing was Mrs. Voorhees and her curse, more than Jason being out for revenge on his own.
That said someone does need to sit down and create a new super-slasher for the current generation. I mean the classics are what they are, but I think it's a sad state of affairs when horror buffs keep talking about the same old campy franchises which haven't even seen any new material for quite a while... except maybe crappy reboot attempts by people who didn't quite get it. Rob Zombie really needs to focus on doing his own stuff.