If you like anime with a good story line I'd recommend
Basilisk : Kouga Ninpou Chou, lots of action, story of vengence, multiple twists, strange powers, etc.
Ima Sokoni Iru Boku (Now and then, here and there) Don't be put off by the childish look of this anime, it's actually one of the most violent/sad/beautiful anime I've ever seen.
Chrno Crusade : the end is just so so sad and the rest of the anime so so good.
Azumanga Daiho : just so silly very funny
Samurai Champloo : A medley of different genre by the same director who made Cowboy Beebop
Elfen Lied : a tad bit violent and gore but great anime.
Movies :
Tokyo Godfathers
Old times favourite :
Maison Ikkoku : a love story full of misunderstandings
Hana Yori Dango : same as above
Evangelion
Escaflowne
