I'm a huge geek, I'll be here a while.
It's a tie between Ghost in the Shell: Stand Alone Complex and Cowboy Bebop, with FLCL and Evangelion close behind.
I think I should say it now, I'm a huge Production I.G. fanboy, I enjoyed IGPX. I'll follow anything related to these two series: Ghost in the Shell -- as in I own both movies, seen both series, read the mangas, waiting for Solid State Society, etc. and the Blood: The Last Vampire line -- the novels, the tv series based on the movie, that horrible, horrible Blood: 200(2)0.
My favorite series:
It's a tie between Ghost in the Shell: Stand Alone Complex and Cowboy Bebop. With Neon Genesis Evangelion and FLCL right behind that. It's sad, I've watched FLCL so many times I can more or less quote it on command. And I actually understood most, if not all, of it. Lots of sex-stuffs.
I enjoyed: Blood+ -- some of the best openings I've ever seen
s'true --, Black Lagoon Ergo Proxy, Samurai Champloo, Eureka Seven, Trigun, Hellsing, Naruto--Shippuden is really, really good--, Bleach, Outlaw Star, Berserk, Last Exile, The Melancholy of Suzumiya Haruhi, Paranoia Agent, Code Geass -- most Gundam I dislike, but I hold a special place in my heart for the 08th MS Team and the original Gundam series, Azumanga Daioh, Serial Experiments Lain, I'm digging Code Geass, Death Note, D.Gray-man, Blue Submarine no.6. Shit, I'll be here for a while. You get the picture. I've watched a lot. You can blame Toonami for that. Full Metal Alchemist was good, but ugh, the fan-boys-girls annoy me a lot. Same with most animes.
As for movies:
Both Ghost in the Shell movies, some Miyazaki films, Blood: The Last Vampire, End of Evangelion, the Cowboy Bebop movie, erm...man, Paprika is going to be awesome.
I actually prefer some dubs to the original voices. Animes like Ghost in the Shell: SAC and Cowboy Bebop have very good dubs, with actors who sound close enough to the original to make it work while still making the characters their own. I mean, the Major's English voice actor is, in my opinion, superior to the original voice actor because man, she's commanding. And Cowboy Bebop, that's just an amazing dub, isn't it? I like it when teenagers sound like teenagers, you know? Renton from the Eureka Seven dub actually sounds like a teenager, and not a little girl. That's why I prefer dub Shinji to the original one, he doesn't sound like a girl.