Madoka Magica
Azumanga Daioh
Princess Mononoke
Angelic Layer
Video Girl Ai
Sakura Wars OVA
Outlaw Star
Akira

Sayonara Zetsubou Sensei
Cardcaptor Sakura
Whisper of the Heart
Kanon
Kiki's Delivery Service
Castle in the Sky
Kimi no Todoke
.hack//sign
Chobits
Full Metal Alchemist (I did not see it all, but I saw most of the first season and it was pretty good, intended to finish sometime)
Ouran High School Host Club (kinda the same deal, but it's for the most part a comedy anyway)
Princess Tutu
Bubblegum Crisis (saw a handful of the original OVA and thought it was pretty good, also interested in the Tokyo 2040 series)
Gankutsuou (saw some of it a while back, found the art style very unique and intriguing, but didn't give it much of a chance, will possibly try it again)
Legend of the Galactic heroes (my brother tells me nothing but good things about this show, the only thing that's really keeping me from watching it is just how long it is)
Nichijou
Nodame
Ghost in the shell
Slayers (I liked the movies based on the series, so I'd probably like the tv series as well)
Kare Kano (don't remember if I watched it all, remember the animation quality getting pretty awful towards the end. seemed pretty good too)
Maid Sama
Monster
Kino's Journey

Gurren Lagann
Neon Genesis Evangelion (watched a large portion of it, did not care for at all)
Gundam Wing (OH NO IT'S A GUND-- (dies from sword slash that wasn't even hit by))
Fist of the North Star (perhaps a bit too manly for me, but maybe I'll try it one day)
One Piece
Ranma 1/2
Inuyasha
Viewtiful Joe
Boogiepop Phantom (saw some of it at my local library a while back, wasn't very interested)
Higurashi (looks too twisted for my liking)