Most of my American comic collections are superheroes:
Iron Man
Spider-Man
Batman
Fantastic Four
The Tick
Teen Titans
X-Men
But I've got like two or three non-superhero ones such as Bone. Bone (for those of you uncultured bastards who don't know) is a fantasy series by Jeff Smith about three cartoon-looking characters getting kicked out of their village and end up in a battle between the humans and the rat creatures. Very good stuff. It has some "OH SH!T!" moments and some funny moments. I also read a few Star Wars books, but nothing that lacks Boba or Jango Fett.
But typically if I'm going to buy American, then it's usually got a super powered person in it...or someone who fights using technology (Batman or Iron Man.)
And I've got quite a collection of manga. About 120 volumes. Mostly what's referred to as "Shonen," which appeals to the younger male audience...I've got a series about bounty hunters, a series about American Football, etc.
Mostly I read action related comics, both American and Japanese. My excuse is that if I wanted something deep, I'd pick up a novel. Comics/manga being a visual medium, I want something to happen.
Dresden Files, though I prefer the novels, fit my criteria, except I really don't pick up many comic adaptions of books or movies. I made an exception because I like The Dresden Files enough.
Edit: I'd like to say: most of what I've read of Fantastic Four and X-men is the Ultimate line.