I'm really not a fan of action/super heroes so I never really bothered with comics, after I was recommended I Kill Giants I began to take the medium a little more seriously. It's not at all what you'd expect, the story follows a social outcast with a highly overactive imagination. It does have it's share of teen angst as you'd expect but as the pieces come together the story becomes increasingly tragic.
Perhaps the best graphic novel I've read is Dave Mckean's cages, it's about a painter who moves into an apartment next to a Jazz performer and a retired author. It critically examines creativity and the arts and for some reason, religion. Apart from the surreal story and characters perhaps the most interesting aspect of novel is the visuals, whose style changes dramatically throughout the novel from highly detailed paintings to photography to chaotic line drawings, a technique used to portray a night out with the dialogue becoming harder and harder to decipher and the lines becoming more erratic, bleeding into the surrounding panels. Definitely something to pick up if you're interested in the arts.