This is the list.
These are the classics.
These are my favorites.


Cowboy Bebop - bounty hunters of the future. comedy and drama as well as action. Great soundtrack.
Trigun - comedic dystopian world and one heck of a protagonist.
Haibane Renmei - somewhat dramatic but paints a vivid possible afterlife.
Excel Saga - insane sci-fi comedy centering around some truly messed up characters.
Now and Then, Here and There - very thick dramatics in a dystopian parallel world.
Ghost in the Shell - future sci-fi centering on a cyborg protagonist.
Oban, Star-Racers - futuristic ship racing to win the ultimate prize.
Azumanga Daioh - quite a funny bunch of quirky schoolgirls.
Aeon Flux - a future assassin gets killed repeatedly and a story develops from there.
Di Gi Charat - lighthearted and messed-up alien antics of a game store mascot.
Hare Nochi Guu - omg what is Guu exactly? that's what Hare would like to know.
Rurouni Kenshin - often funny but action-oriented tale of a samurai who gave up killing.
IRIA - Zeiram the Animation - future bounty hunter encounters unkillable monster.
Evangelion - organic mecha pilots face the ongoing threat of alien 'angels' in Tokyo-3.
Millenium Actress - the story of the life of an actress chasing a lost love.
Metropolis - future politicial robot film by none other than the creator of Astro Boy, Osamu Tezuka.
Battle Angel - adaptation of the GUNNM manga, which I would suggest reading.
Kino's Journey: the Beautiful World - occasionally philosophical journey of a girl and her talking motorcycle.

That's it for now. I will expand this further, gradually.