This started out as a reply to Diego’s best. superheroes. ever. post.
Early on I was into primarily Marvel stuff: Fantastic Four (huge!), X-Men, Spider-Man, some of the team stuff, Power Man and Iron Fist, even (shudder) ROM. (What was I thinking...) Later I started to get a little more discriminating and discovered some new stuff. And that's where I found the interesting stuff is a little murkier.
Frank Miller's Daredevil started out just like everything else because he was only doing art. But once he took over writing duties it really picked up. The whole Elektra/Vanessa/Bullseye storyline was very non-Marvel for the time (early 80s), when everyone was mutant crazy. Who's a good guy? Who's a bad guy? Why does the Kingpin care enough about his wife to wipe out carefully laid political ambitions? Good stuff. He came back for a short (four or five-issue) stint a few years later for writing and it was clear which was more important. I'd probably group Elektra's later adventures in here as well.
Baron and Rude's Nexus was also heavy stuff, and just plain gorgeous. (I still think Steve Rude draws the best lips in the business...) Most of the time comic books deal with redemption just long enough for the hero to avenge someone. This was a series-long arc with all kinds of bumps and dives along the way.
There is no denying the appeal of the X-Men, especially to teenagers outside the main group. I think Michael Chabon's description of this appeal hits it on the head. I also agree with Diego on Wolverine, although I think some of the others could have done with the same expanded writing attention that his popularity brought on.
Matt Wagner wrote and drew Mage, which featured a wonderful hero in Kevin Matchstick. Normal guy who finds out he's King Arthur, who was really the embodiment of The Hero. I hope he's able to finish the story -- it's probably one of the few comics I'd spend the money on today, and even then I might wait for the graphic novel. His Grendel could also be fantastic.
Mike Grell's Jon Sable got old after five years or so, but the mercenary with a sometimes heart of gold story worked pretty well. Plus it was occasionally really funny.
For some reason I always thought Moon Knight was pretty cool. Not real deep, just cool. More are bouncing around in my head, but it's getting late...