1. The Seven Samurai (1957) Japan, bw (Kurosawa) No. 13 on the IMDB 250 - 4 awards
One of the best action films ever made, inspired many remakes and influenced all actions films that followed. The inferior Japanese film The Burma Harp got a foreign language film Oscar nomination over SS, and the award went to Fellini's La Strada
2. Departures (2008) Japan [AA] (Takita) 33 awards (39 noms) - Elegant, graceful, beautiful film, a 15 yr project for director Takita after he heard the idea from actor Masahiro Motoki [photo top] (This simply needs more total ratings at IMDB to be in their all-time top 250 - go vote! it's score would place it around 140th)
Shall We Dance? (1995) Japan (Suo) 52 awards (out of 55 nominations), won 14 out of 15 Japanese academy awards - A beautiful ballroom dance romance (This also needs more total ratings at IMDB to be in their all-time top 250)
4. The Twilight Samurai (2002) Japan ( Yamada) 37 awards (44 noms) - An anti-action film about a retired and widowed samurai now relegated to doing inventory of a wealthy landlord's food supplies and taking care of his children (This also needs more total ratings at IMDB to be in the top 250)
Ugetsu (1953) Japan, bw (Mizoguchi) 3 awards (5 noms) A haunting love story about a ceramicist trying to avoid medieval war
6. Stray Dog (1949) Japan, bw (Kurosawa) 4 awards - Early Kurosawa police procedural crime film, which caused an explosion of this genre in Japan
7. Rashomon (1954) Japan, bw [AA] (Kurosawa) No. 80 on the IMDB 250 7 awards (10 noms) - The classic about a crime seen from four viewpoints
8. Crazed Fruit (1956) Japan, bw (Kajitsu) A love triangle of two brothers and one girl
9. Grave of the Fireflies (1988) Japan (Takahata) No. 124 on the IMDB 250 3 awards - Animated, but a touching war story about children during WW2, not a kid's film
10. Samurai 1: Musashi Miyamoto (1954) Japan [AA] (Inagaki) The first of a classic samurai trilogy (The Oscar® was its only award)
11. Dersu Uzala (1975, Russia-Japan) [AA] (Kurosawa) 8 awards - classic about a Siberian guide surviving both in the wilderness and in civilization; Kurosawa's best color film to me, and his 2nd Oscar®
12. Yojimbo (1961, bw) (Kurosawa) No. 123 on the IMDB 250 - 4 awards (6 noms) - Another bw classic from the master, inspired by John Ford westerns, then remade in the west as A Fistful of Dollars by Italian Sergio Leone, the first of his spaghetti westerns with Clint Eastwood
13. Tokyo Story (1953) Japan, bw (Ozu) 2 awards - Slow but rewarding classic from another master director; for me, Ozu is an acquired taste as his films move very slowly
More worth seeing
Throne of Blood (57) (Kurosawa) - 3 awards
Floating Weeds (59) (Ozu) - no awards
Harakiri (62) aka Seppuku (Kobiyashi) - no awards
Burmese Harp (56) (Ichikawa) - 2 awards (5 noms)
Fires on the Plain (59) (Ichikawa) - 6 awards
Some of these films are rooted in the Japanese tradition of Zen Buddhism, so they are therefore culturally different than western films; they are slower, ritualistic, and more about attitudes and spirituality of life than about action. This is especially true of Departures, Tokyo Story, and The Burmese Harp, but this cultural difference permeates many other films as well.
Other fans love all Kurosawa films, but I only like the black and white ones, I find his color epics, like Ran and Kurosawa, to be long and painful to sit through, which is interesting since Seven Samurai is nearly four hours long, but it seems shorter and is riveting. It has two distinct parts: the setup and character development first half, then the action based, lengthy battle of the second half, all filmed in a driving rainstorm.
Many of these have been remade in the west. Seven Samurai was remade as the western The Magnificent Seven, and the science fiction film Battle Beyond the Stars. The British tv series The Avengers also parodied it as "The Superlative Seven" (an episode guest starring Donald Sutherland and Charlotte Rampling). Shall We Dance? was remade with Richard Gere and Jennifer Lopez, stick with the original, it's much more artistic.
Rashomon has been often copied - it's the story of a crime later recounted by the victim, the criminal, an eyewitness, and an angel (or ghost) that was watching; of course, each story is different, biased by the perspective of the each witness.
The style of Stray Dog is basically like most modern tv police shows. A rookie cop has his gun stolen on a crowded bus, which is then sold on the black market then used in violent crimes as the policeman doggedly searches for it, using clue after clue to narrow down his suspects and find the weapon.
Departures and Grave of the Fireflies are totally unique, however - each deals with death in different manners. Departures is very ritualistic, graceful, and respectful, very rooted in Zen ceremonies. Grave is a fable-like animated film about two children during WW2. I doubt neither subject will be approached in western films, because they wouldn't make the millions necessary to get them filmed. It's actually very surprising (and gratifying) that Departures won the Oscar® in 2008.
The fifth Japanese film to win an Oscar® for foreign film, Gates of Hell, is not available on dvd, so I haven't seen that one yet.