@solfege
Good anime in general (animes that even those, who don't like anime, find great):
Death Note
Full Metal Alchemist Brotherhood (no words needed. Just watch, if you haven't)
Claymore
Clannad (+ Clannad after story)
Steins;Gate (guess you know it already)
Cowboy Bebop (kinda relaxed style. Easy to watch and kinda mysterious)
Samurai Champloo (basically like Cowboy Bebop (a very unique, relaxed style), but in edo. +historical facts)
Avatar the last airbender (it's rather for children, but the wise words said by General Iroh are really getting to the core)
Gurren Lagann (Somewhat turns to shit after the first half. You'll know why when you watch it. The first half really is a must-watch though.)
Hellsing
Toradora (funny romance)
Spice and Wolf (can't remember much anymore, but it had some pretty good dialogues, which I mostly didn't understand back when I watched it
)
Some of my personal favourites:
Gintama
Elfenlied
Higurashi no Naku koro ni + kai
And there are some anime's that people say are great but I haven't seen yet, that's why I name them seperately
Psycho-pass
Ghost in the shell (there are many different series, so I don't know which one is good)
Code Geass
Neon Genesis Evangelion
Berserk (I read the manga though and it's freaking awesome)