I might be a bit conservative in my taste but I really love most Akira Kurosawa's movies, the favorites being Seven Samurai and Rashomon. Kenji Mizoguchi is another favorite although his themes at least in the 50's are maybe too consistently about prostitution and woman's position in Japanese society. That doesn't make his movies any worse. Besides them Masaki Kobayashi's Harakiri might be the all time second best samurai movie ever. It has a very thought provoking story, hypnotic cinematography, great acting by Tatsuya Nakadai and others, very athmospheric music by Toru Takemitsu and great sword fights.
Of the bit more modern movies I like Takashi Miike's Audition and Happiness of Katakuris, Shinobu Yaguchi's My Secret Chache, Takeshi Kitano's Hana-bi and Sonatine, Yoji Yamada's Twilight Samurai, Hirokazu Kore-eda's Nobody Knows and Naoe Gozu's Falling into The Evening, which sadly isn't released on DVD anywhere but in Japan. I've seen it several times on a worn out VHS cassette and I really love its melancholic athmosphere.
I think Hayao Miyazaki's Laputa - Castle in the Sky is still my all time favorite anime movie and one of the best movies in general. The action and humor is Miyazaki at his best and I really like the innocent and simple relationship between Pazu and Sheeta. I also like all the rest of his movies. I think either Princess Mononoke or Nausicaä of the Valley of Wind is his second best movie. Akira is usually criticized as too confusing and I also thought that way when I first saw it but it has grown in to me. The plot makes a bit more sense after you've read the manga but even if you haven't can't help loving the extremely detailed, expressive and smooth animation and unique soundtrack. Super Dimension Fortress Macross - Do you remember love? and The Girl Who Leapt Through Time are also great.