Here are some that I liked:
The Book of Five Rings - a good insight into some aspects of the Japanese psyche, written by the most famous Samurai, Miyamoto Musashi, a bit like the "Art of War" by Sun Tzu.
Memoirs of a Geisha - both the book and film, follows the life of a fictional geisha in the old capital of Kyoto around the time of WW II.
Shōgun - by James Clavell, both the book and t.v. miniseries, loosely based of the rise Tokugawa Ieyasu, the greatest Shōgun, through the eyes of the English sailor, also loosely based on a real person.
My Neighbor Totoro - a charming animated film from the legendary Hayao Miyazaki, gives a good artistic view of 1950s Japanese countryside and folk culture/nuances, an all around fun film.
Sonatine - an award-winning film about a Tokyo-based Yakuza who is sent down to Okinawa to "sort out some things", interesting insight into the Yakuza and their culture in the 1990s, also shows some of the cultural differences of parts of Japan i.e. Tokyo vs Okinawa.