Well, it looks like I'm a bit late to help explain the distinction between different breeds of anime. Still, I'm always ready to recommend a few series, so if you don't mind getting a few more tossed your way...
Though they've already been recommended by other users, it wouldn't feel right if I didn't do my bit to push Baccano and Fate/Zero. Baccano is probably my favorite anime series to date, though you really do have to watch the dub if you can find it. Seriously, this is one of the cases where the dub completely trumps the sub.
Fate/Zero, meanwhile, was written by the same guy who wrote Madoka Magica, Gen Urobuchi. And considering your new avatar, you might be a fan of his now... To put it simply, if Madoka Magica is Urobuchi's take on the magical girl genre, then Zero is his take on shonen series. It's dark, gripping, and beautifully animated. Plus, Rider might be my favorite fictional character from any series.
Anyway, my own recommendations:
Psychopass (another written by Urobuchi)
Fullmetal Alchemist (though this one is actually still a shonen series, it's a damn good one)
JoJo's Bizarre Adventure (an anime entirely about pulling off crazy poses)
Hellsing Ultimate (probably one of the gorier series out there, in the same league as Elfen Lied)
Monster (has one of the best stories in the medium, if you ask me)
Planetes (super hard sci-fi series)
Tengen Toppa Gurren Lagann (one of the most crazy awesome series out there)
FLCL (...Yeah, I got nothing to say on this one. Just watch it.)
So yeah, that's what I've got. Once you've finished up with Madoka, I'd recommend giving these a quick look, see if the description interests you, and maybe watch an episode or two. I like to think that I have decent tastes.
*cough*Alsoyoushouldreadthis*cough* [http://www.thespectrum.net/manga_scans/?preview=manga_The-Lucifer-and-Biscuit-Hammer]