I have seen a lot of Japanese movies, but I can't say which is my favorite. Most of the titles I like are the old classic films (samurai films). I like Akira Kurosawa films like Yojimbo and Seven Samurai. One of my favorite actors is Toshiro Mifune.
Have you seen "Woman in the Dunes" a novel by Kobo Abe but a film directed by Hiroshi Teshigahara? An interesting allegory of life. Or "Warm Water Under a Red Bridge"? "Ringu" is the movie upon which the American film "The Ring" was based. Japanese films can be sexual/steamy or violent, creepy and bizarre. Or sometimes, just charming like "Kikujiro."