All the popular ones +
Dennou Coil (probably the most creative anime I've come across)
Eve no Jikan
BECK: Mongolian Chop Squad
Eureka 7 (folks hate on this one, not sure why)
Street Fighter
Avatar (BEST EVER!)
Boondocks
Rurouni Kenshin
GITS: SAC
Genshiken
HunterXHunter
Fooly Cooly
But the anime that's stuck with me the most after all these years?
Serial Experiments Lain

Animes I mean to watch:
Welcome to the NHK
Baccano
Darker than Black
Wolf's Rain
and a ton of others... but it's been a while since I watched some animes
Mangas that should be animes:
Vinland Saga (This would instantly be one of the best animes, ever.)
Otoyomegatari
Holyland
Eternal Sabbath
Solanin
Yotsuba to!
Planetes (An anime that actually follows the manga this time)
Personant
Island