Haibane Renmei, - a non action suspense drama thats pretty (the artwork is done by Yoshitobe Abe the guy who did Lain)
Angelic Layer- a girly clamp action show
Chobits- hilarious with dirty humor
Excel Saga- SO HILARIOUS YOU WILL BE LAUGHING REALLY HARD EACH EPISODE
Bleach- I could not get into Naruto but Bleach is an awesome action show and each episode is up and running on youtube. In matter of fact almost all of these can be watched there.
Gunsmith Cats is another awesome anime thats action packed with hots girls with guns
As far as movies, I am a huge miyazaki fan:
* NausicaƤ of the Valley of the Wind, 1984 film
* Laputa: Castle in the Sky, 1986 film
* My Neighbor Totoro, 1988 film
* Kiki's Delivery Service, 1989 film
* Porco Rosso, 1992 film
* Princess Mononoke, 1997 film
* Spirited Away, 2001 film (winner, Academy Award for Best Animated Feature, 2002)
* Howl's Moving Castle, 2004 (nominee, Academy Award for Best Animated Feature, 2005)
My taste in anime is pretty kid1e with romantic comedies tossed in here or there.
Good Luck :3