Much agreement with FLCL as one of the all time best.
Here are some of my favorite animes:
Lucky Star (my absolute all-time favorite; notice avatar&sig)
Loveless (Includes shounen-ai and shoujo-ai, so if you don't like that, stay away)
.hack//<insert series or movie here>
The Melancholy of Haruhi Suzumiya (Mix of FLCL and Lucky Star)
Kanon 2006
Ouran High School
And as far as anime movies go, almost anything by Miyazaki (creator of Spirited Away and Princess Mononoke) is amazing, especially Castle in the Sky and The Cat Returns.