Anything Satoshi Kon, Makoto Shinkai or Mamoru Oshii for starters =)
Gankutsuo, Kino's Journey, Haibane Henmei, Samurai Champloo, Noir, Wolf's rain and Twelve kingdoms!
Now on to the reasons.
Satoshi Kon - Millenium Actress, Perfect Blue and Paranoia Agent are master pieces. They are great stories that deserve several viewings, as you can always notice something new every time you do.
Makoto Shinkai is beautyful and poetic 5 cm per second is melodramatic, but is difficult not to be touched by it / Voices of a distant star also have a very interesting setting. Great romantic stories.
Mamoru Oshii well, ghost in the shell is a revolution in scifi. In any medium. Patlabor is also a great movie.
Gankutsuo is Gonzo at its best! It's the anime adaptation of The count of Monte Cristo with some of the most beautiful animation. The sound track is also epic.
Kino's Journey, Haibane Henmei - laid back series. The first is the episodic accounts of Kino's adventures as she travels through the world. Haibane henmei is well, absurdly hard to classify, but well worth seeing.
Samurai Champloo, Noir, Wolf's rain - these are stylish, great technically (animation, sound, music) and very fun. The first is samurai's with Hip hop, despite what you may think at the first time, it actually blended these two almost opposite concepts well. Noir is your typical girl with guns series, fun to watch. Wolf's Rain is your futuristic fantasy with some post armageddon settings.
Twelve kingdoms - What can is my favorite of all time!
It's your traditional cape and sword tale, told the chinese way. Everything about it is perfect except one thing. It hints on a story arc that unfortunately was never animated =(