Hayao Miyazaki's movies are awesome:
Howl's Moving Castle, Spirited Away, My Neighbor Totoro, Porco Rosso, Castle in the Sky, Valley of the Wind, Princess Mononoke are some of his best movies (in my opinion)
I also enjoyed watching:
Paprika, The Cat Returns, Grave of the Fireflies
and then there's the real action movies:
Nobody Knows (one of my favorite movies of all time)
GO
Shinobi
Death Note (three movies)
and I just have to mention a few other asian movies even though they're not japanese they are definitely worth watching:
House of Flying Daggers - Chinese
Curse of the Golden Flower - Chinese
Sympathy for Mr. Vengeance - Korean
Lady Vengeance - Korean
Old Boy - Korean
Bin Jip - Korean
I could go on forever, but these are some of my favorites
