Anime for beginners
Dragon Ball
Dragon Ball Z
Dual!
Gatekeepers
Slayers
Street Fighter: Alpha the Movie
Street Fighter 2V
Street Fighter: The Animated Movie
Any of the various Gundam series
Oh! My Goddess
Anime for the advanced
Ranma 1/2
Evangelion
Escaflowne
Serial Experiments Lain
Video Girl Ai
Rurouni Kenshin
Trigun
Martian Successor Nadesico
Initial D
Vampire Hunter D: Bloodlust
Anime for girls
Sailor Moon
Cardcaptors (Cardcaptor Sakura)
Fushigi Yugi
Ayashi No Ceres
My personal favorite anime
1. Ranma 1/2
2. I’s
3. Evangelion
4. Love Hina
5. Dual!