Too many, here are some.
Evangelion.
In chronological order: Original series; manga; GirlfriendOf Steel2 (a pleasant intermezzo); Death/Rebirth; End of Evangelion; Re-Take (an excellent doujin series with plausible ending, but NSFW), Movies: RebuildOfEvangelion: 1.0 You're (not) alone/2.0 You can (not) advance/, waiting for 3.0: Q(uickening).
Shinji Ikari Raising Project manga is brainless comedy fanservice crap.
Cowboy Bebop: original series, Knocking on Heavens door. Gotta love the style and jazz/blues soundtrack by Yoko Kanno and The Seatbelts.
Welcome to the NHK! could be quite ironic. It's a comedy series with good depth.
Azumanga, Great Teacher Onizuka, School Rumble, RozenMaiden(desss...heh...must restrain myself...), Yukikaze, Area88 and Macross/Robotech for some degree of dogfight (wishing there was AceCombat anime)
For splatter AND action, i recommend Hellsing OVA, Black Lagoon, Highschool of the Dead.
Postapocalyptic setting? Desert Punk, Trigun, Fist of the North Star, the last is splatteraction.
Akira was quite philosophical. (also, SouthPark parodied it in the Trapper Keeper episode)
The dystopian style and atmosphere reminded me also somewhat on Wings of Honneamise from GAINAX.