Yeah, I watch it. A lot. (around 200 TV series and movies).
So, my recommendations would be:
Neon Genesis Evangelion - probably the deepest piece of art I've ever watched. Everyone should see it.
Ghost In The Shell is great as well.
Watanabe's series - Cowboy Bebop and Samurai Champloo - crazy ass action and likable characters
Planetes - amazing realistic sci-fi
The Melancholy of Haruhi Suzumiya - nice sci-fi comedy
Tengen Toppa Gurren Lagann - epic, just EPIC
Redline - badass racing with great visuals
Code Geass and Deathnote - lots and lots of interesting twists
Princess Mononoke - best Miyazaki movie in my opinion
The Girl Who Leapt Through Time and 5 Centimeters per Second - for those who love drama and romance.
Dennou Coil - sci-fi with light atmosphere and interesting setting
...And of course fucking K-On! with cute girls doing cute things; haters gonna hate.