Check out the Criterion Collection, featuring many classic Japanese films with English subtitles. Great titles include Stray Dog, Heaven and Hell, Drunken Angel, Rashomon, Throne of Blood, Seven Samurai.
Look for the works of Akira Kurosawa including "Seven Samurai"; "Rashomon," which introduced Toshiro Mifune; and "Ikiru. " Hiroshi Inogaka released a trilogy of Samurai films that were highly acclaimed: "Musashi Miyamoto," "Duel at Ichijoji Temple," and "Duel at Ganryu Island"; his slightly later "Samurai Banners" starred Toshiro Mifune. Also try the original version of Ishiro Honda's "Gojiro," which became "Godzilla. "