Initially, Tintin & Asterix in school (with occasional doses of Lucky Luke and Papyrus). Also Archie Comics.
Later, Batman and the rest of the DC Universe (as a direct result of the influence of the Dini/Timmverse cartoons, which had occasionally-printed tie-in comics at the kids' level, which were generally excellently done and highly recommended, by the way) and thus thence to Vertigo and their other acquired/spinoff imprints by extension, and some Marvel Comics as a result of the various X-Men cartoons, though to this day, I'm still fonder of DC as superhero universes go.
Nowadays, quite a lot of stuff, probably not as varied as I think it is, but I'm willing to try anything ranging from superheroes to manga to bandes déssinées to slice-of-life thinly-veiled autobiographical comics and litfic-styled graphic novels. I especially like non-fiction-ish works such as Jim Ottaviani's GT Labs comics on science and scientists, the various Cartoon Guides done by Larry Gonick and Manga Guides done by No Starch Press and Hill & Wang's recent offerings of history and biographies, and I like Classics Illustrated types of adaptations as well.
In terms of lasting influence, I'd say that the original Batman: The Animated Series and its spinoffs through to Justice League Unlimited had a major impact on how I view these things and probably some of my social and personal attitudes regarding certain forms of human interaction.
Asterix was definitely responsible for my love of Ancient Rome, Greece, and Egypt and subsequently reading as much as I could from the school library about their histories and mythologies, and probably then also moving onto other cultures' histories (not so much mythologies, which I kind of lost interest in). I have a certain fondness for Neil Gaiman & Mike Carey's depiction of Lucifer Morningstar, which is pretty much how I picture any mention of him now. And between them, I think that Alan Moore's various comics and Kurt Busiek's Astro City are my definitive view of how superheroes ought to logically work.