Look into Negima. There are two series (live action doesn't count) and some OVAs and they're very distinct but alike enough to be recognizable. If you want more light-hearted stuff with focus on school life and awkward semi-romance, go with Negima!. If you would rather see artistic magical combat between bits of pure comedic lunacy, Negima!? is your series. A word of warning about Negima: If you watch it dubbed, be patient with Negi's voice. I swear you'll get used to it and the rest of the cast does really well.
GAINAX=great. Plain and simple. Neon Genesis Evangelion, FLCL, Gurren Lagann. Find. Watch. Love.
If you're looking for pure comedy, try Lucky Star (though you may need to do homework to get a lot of it and very little actually happens in it. Seriously, you can use it as background noise while playing a game and not miss anything) and Keroro Gunsou, known in English as Sgt. Frog.
The Tenchi Muyo! series are harem comedy classics.
Cowboy Bebop and Samurai Champloo should not be missed if you love action, comedy and an ultra-cool atmosphere.
Other various recommendations are Love Hina, Desert Punk, Trigun, Hellsing, Outlaw Star, Azumanga Daioh, VanDread, Crayon Shin-chan, Burst Angel, FullMetal Alchemist (which I don't think is related to Full Metal Panic), Ichigo 100% and Chocotto Sister.
You might dabble in Dragon Ball. Just dabble, enough that if someone who's really into anime asks if you've seen it, they won't ridicule you, but that about it. Its maybe ten pounds of awesome in an OVER NINE THOUSAAAAAND pound sack.
For head tripping brainplay, Paranoia Agent, Higurashi: When They Cry, and the Melancholy of Haruhi Suzumiya will twist your ideas of how anime works. Careful of the 8th episode.
Higurashi will twist your ideas and stomach. Its a high quality series in art, story-telling and acting. Among the best I've seen. But unless you're at the very least okay with gore, I would say no on that one. It isn't that violent as anime goes, but when it is, its quite frankly fucked up. Kids and crows. All I'm sayin'.