Just some of my favorites that I haven't seen here yet:
John Constantine (Hellblazer) -- He's a pretty fascinating character in that he's always trying to do what he thinks is best, but he lives in a world where the "best" option often entails having to screw over everyone he knows and loves. It makes for an extremely dark, oppressing atmosphere
Morpheus (The Sandman) -- This character really shows why Neil Gaiman is considered such a brilliant author. He's created a character whose motives seem entirely alien at times, but still manage to make sense. This leads to stories that are unpredictable without seeming contrived, and makes his very presence terrifying because of the sheer power he holds and the inability to discern quite how he'd react to a given situation.
Atomic Robo (Atomic Robo) -- This character encompasses everything that is good about Brian Clevinger's writing in one metallic body.
Klaus Wulfenbach (Girl Genius) -- Girl Genius was technically a print comic before it went on the web, so I'm going to count it. He's a brilliant subversion of the "evil dictator" cliché, to the point where you're rooting for his success as often as not.
Othar Trygvassen, GENTLEMAN ADVENTURER! (Girl Genius, again) -- Girl Genius loves to play against clichés, but not in the way everyone would expect an author to. Othar has every quality that makes up a classic adventure hero -- he's campy, grandiose, loved by all, able to inexplicably escape certain death, and fights the oppressive authorities for the common people. He's also completely insane.