One of the best films to come out of Japan is easily My Neighbor Totoro. It may not have been huge in the U.S. but it made a decent splash. Back there, Totoro is as popular as Disney.
The story is set with two girls who move out to the country-side in a creepy old house. They later meet with the mysterious, strange, yet lovable Totoro.
Totoro has charm and grace that most anime films never seem to capture. It's also one of the first anime that has hardly action period, yet it's really good regardless.
The Cat Bus still freaks me out though.