
Serial Experiment Lain - This is what started it all for me, it is to this day, and always will remain my biggest fantasy
Cowboy Bebop - This is totally cyberpunk, an award winner, and a classic to many
Ghost in the Shell - When I was fourteen, I was really big into philosophy. You know, the kind of stuff that makes you question existence, life, free thought, and purpose
Akira - I know a lot of people don't share my opinion on this one. It really didn't age very well, but I think the characters were very well developed. They were all individuals and not your usual canned archetypes.
Ergo Proxy - A very artistic series, that in my opinion challenges the original Matrix
Noein - With a smashing introduction, and a very existential conclusion, this is a must watch.
OutlawStar - While not as strong a series as those listed above, Gene Starwind becomes a real hero towards the end of the series.
Armitage III - You have to really take a few steps back before watching this one. Don't try to judge the characters, or how believable the situation might be. Instead understand the setting, and watch the story. There are two follow up films, I've only seen Poly Matrix.
Blue Submarine N.6 - Can't not recommend this one. It's a great film.
And this is where the genre fades ...
I'm always on a lookout for more, but most of it ends up being filler, unambitious, and unsatisfying. Anyways, this is by no means my all time favorites, I just tried focusing on one genre.