Originally Posted by Azar
The only bad thing about starting with Bebop is that very little, if nothing else out there, is better. But it's my absolute favorite and should definitely be among the first things you watch. Here's a nice list
Cowboy Bebop - (Action, Drama, Comedy, Romance, the whole nine yards.)
Neon Genesis Evangelion - (Deep, thought-provoking, though angst ridden mecha series.)
RahXephon - (Evangelion done right. Better animation, less angst, more focus on plot and character development.)
Trigun - (Good action scenes, comedy, and a surprisingly in-depth plotline.)
FLCL - (Absolutely insane, with awesome animation, some funny moments, and some touching scenes.)
Berserk - (A war series in a medieval setting, but with most of the focus on character development. Big swords.)
Excel Saga - (Inspired lunacy.)