I only really remember the ones that I really REALLY enjoyed. I call myself a connoisseur because I don't just binge on anime in general, because a lot of it doesn't sit right on my gaijin palate. So,

Miyazaki (Howl's Moving Castle above the others, but all Miyazaki is great to me)

Cowboy Bebop, including the movie

Samurai Champloo (Essentially Cowboy Bebop in a different setting, but still amazing to watch and a GORGEOUS soundtrack)

Neon Genesis Evangelion, including the movies. (Yes I know it doesn't make a lick of sense, I don't care, it's pretty and fun)

Akira - Obvious reasons

Ghost in the Shell

All of the .hack// properties that I've seen have been really awesome

Fullmetal Alchemist is pretty good in general, some bad episodes, and Brotherhood is better than the original.

YuYu Hakusho was the tits when I was younger, not sure how it held up to time.

And lately I've been drooling over Attack on Titan.

Edit to include, seriously, go watch Attack on Titan. Strong female characters, refreshing combat techniques, really unsettling enemies/premise.