For sheer style: Noir, Lain, Boogiepop Phantom.
For action: Noir, Blood, Slayers.
For sci-fi goodness: Lain, Cowboy Bebop.
For humor: Slayers, Dragon Half.
For music: Noir, Lain, Cowboy Bebop, Revolutionary Girl Utena.
Noir and Lain are definitely the most influential for me, but generally I...