Rurouni Kenshin is definitely one of my favorites. Got them all on DVD. Redeemed assassins are always a great melodramatic hook.
Anything by Miyazaki (Spirited Away, Princess Mononoke, Kiki's Delivery Service, Laputa, Totoro, Nausicaa) is usually worth watching at least once.
Grave of the Fireflies makes you forget that you're watching anime with how painful and depressing it is to watch.
One "near-anime" film that I didn't see mentioned on here is
Casshern. Based on a 70's anime, this movie is live action, but screams out anime styling and intensity. I highly recommend going to their website and checking out the trailer.
Akira confused the hell out of me, and it still does. And this is from someone who actually has all the manga issues.
The first Lodoss War is great, has anyone watched the second series?