There are several great ones, but Serial Experiments Lain wins this handily. It's absolutely beautiful. Here's the video, and a link to the full acoustic version (which is somehow even better).
http://www.youtube.com/watch?v=r6t-rqR2GoU
Narutaru has the single greatest troll opening in history. The actual story is basically pokemon meets Neon Genesis. The opening even managed to get the show past the sensors in a few countries. The manga is much better though:
Honorable mentions go to Ghost in the Shell and Elfen Lied, for their gorgeous soundtracks, and Samurai Champloo, for its gorgeous animation.