I mostly watch what my brother watches and don't read much manga. I watched One Piece but stopped for a long time and am not caught up though I have seen past the Marineford Arc so know about some big spoilers.

I liked what little of Bleach I saw at the beginning.
Trigun
Neon Genesis Evangelion
Mahou Shoujo Madoka Magica
Stein's;Gate
Many Gundam series, G, Wing, Seed, 08th MS Team, 00.
Fullmetal Alchemist
Gurren Lagann
Soul Eater
Shingeki no Kyojin
Star Driver

I know there are more, but meh.

Currently into Kuroko's Basketball, and watching the Monogatari series.

EDIT: I did used to read a bit of manga before, Chobits, Magical Knight Rayearth, Culdcept are some of my favorites.