I would second Attack on Titan, Code Geass and FMA, all good stuff. Bleach was Ok for me until about epesode 70-ish I think, everything after that should be chained up and thrown off a bridge.
If we are taking just general recommendations my list would probably include these:
Cowboy Bebop - Best damn show to come out of an anime studio.
Berserk - A dark bloody beast of a show with few rivals. The manga is even better.
Full Metal Panic - Best Mech series IMO. Three seasons, all different, all good.
Gunbuster OVA's - The ending of this show gets me every time. I've never seen anything capped off better.
One Piece - Get past the unconventional style and sillyness and there is a subtle genious at work behind a good dose of wonder and adventure.
Gurren Lagann - High energy giant robot stuff. Another great ending here.
School Rumble - Really funny, dub and sub.
Tora Dora - Funny slice of life romantic stuff. Don't usually go for these much but this one worked for me.
Some random honorable mentions:
Hajime no Ippo
Samurai X
5cm per second
Fate/Zero
Detroit Metal City
Ghost in the shell (movie)
Black Jack
Black Lagoon
Beck