I know I might be in the minority, but I will definitely recommend Midnight Nation. The premise is that a cop from Los Angeles tries to track down some criminals committing brutal crimes, and when he finally confronts them, they attack him, but instead of killing him they steal his soul. Without a soul, he fades into sort of an alternate world, the Midnight Nation, where all the uncared for or forgotten people of the world go. It's a world of dilapidation and near-hopelessness, and anyone who goes there literally disappears from the real world.
The main character has a chance, however, to reclaim his soul, and make it back to the real world. In order to get his soul back, however, he has to go to New York, far across the country. He has a year to accomplish this, but since the only machines in this other world are broken and can't work, he has to travel on foot.
It's loosely based on Christian lore, but the author is not Christian himself, so he takes a fair share of liberties. Regardless, it's still a very moving and very well-written series. It's on issue 11 right now, out of a total of 12.
I also suggest you take a look at Kabuki, written and illustrated by David Mack. Later issues are actually painted in watercolor, and it has some of the most gorgeous art of any comic I've read. It's a bit cerebral and non-traditional, but it focuses on one main character, a woman who works for a law-enforcement agency in Japan. All of the agents of the agency wear masks from Noh plays (a style of Japanese play), and the main character wears a Kabuki mask. Because of the intense symbolism of having to always wear a mask, the story mostly involves tracing Kabuki's internal thoughts as she has to deal with the assignments the agency gives her, which she increasingly begins to feel are wrong. It's an odd premise, but is pulled off very well.
Finally, you can't go wrong with manga. Well, you can, but not if you get good stuff. There is about a thousand times more manga coming out of Japan as there are comics in the US, so your chances of finding something that you like are much higher. Plus the art, though often a little unorthodox by Western standards, is consistently high quality. It seems bizarre to me that a lot of comic companies in the US settle for crappy art for many of their books, but in Japan, manga is so much a staple of the society that there is no shortage of skilled artists to illustrate their comics.
Ryan "RangerWickett" Nock
p.s., Avoid the D&D: In the Shadow of Dragons comic like the plague. No offense to those here who work on it, but I think the art is poorly done, the story cliched, and the characters emotionally bland.