Most favorite of all time: A Knight's Tale

Close seconds: Fifth Element, Matrix

Favorite Anime series: RoboTECH

Other excellent films and anime:

Ghost and the Darkness

Real Genius

One Crazy Summer

Dune

Bubblegum Crisis (series)

The Studio Ghibli Collection of Anime (6 DVD set, 2 movies each), including:

Nausicaä of the Valley of Wind

Kiki's Delivery Service

My Neighbor Totoro