Other films about or related to Japan

Takashi Miike is a prolific director, who has directed over 50 films in the past two decades. He crosses genres. He directed One Missed Call (horror) and Zatoichi (Samurai). Another prolific director is Yoji Yamada, whose Yellow Handkerchief was also recently remade into a US film starring William Hurt and Kriten Stewart (of Twilight fame)

There are, of course, the various Godzilla films, which are part of the Kaiju (giant monsters) genre.

In Hollywood, there are plenty of war/anti-war films about the Japanese. Tora Tora Tora (about Japan's attack on Pearl Harbor), Pearl Harbor (of course), the Clint Eastwood-directed Flags of our Fathers and Letters from Iwo Jima.

Some other recommended Japan-related films are:

American Ninja,
American Yakuza (with Viggo Mortensen of Lord of the Rings fame),
Angel Dust (psychological thriller shot mostly in Tokyo),
The Ballad of Narayama (family tale/drama set in the late 19th? century; highly-recommended),
The Barbarian and the Geisha (which stars John Wayne),
Memoirs of a Geisha (does not star John Wayne),
Black Rain (directed by Ridley Scott of Blade Runner and Gladiator fame),
Blind Fury (loosely based on the Zatoichi films),
Bridge on the River Kwai (based on the famous bridge in Thailand; WWII story),
The Bushido Blade (with a complete disregard of Japanese-US history; a cult classic)
Code of Honour (which is about Japanese-American soldiers in WWII; a documentary)
Death Shadows (for a different view of the Samurai; based during the Edo period)
Enter the Ninja (one of the earliest Hollywood-Ninja films)
Kagemusha (based on a true story about a general and his body double)
Yojimbo (Kurosawa again; the film on which A Fistful of Dollars was based)
The Famous Sword (wartime Japanese film about the values & greatness of the Samurai)
Destroy all Monsters (a '60s film in which various Japanese monsters fight aliens!)
Empire of the Sun (based on a J.G. Ballard novel about a boy during WWII)
Heaven and Earth (rival Japanese warlords fight for the future of Japan)
The Hidden Fortress (Kurosawa again; George Lucas said he drew on this for some of his ideas for the original Star Wars)
Hiroshima Mon Amour (French film about life in Hiroshima; emphasis on a love story rather than on the impact of the bombing)
The Idiot (Dostoevsky story as envisaged by Kurosawa)
Journey of Honour (a Samurai masterpiece set in the 1600s and based on real events)
The Karate Kid 1-3 (of course)
King Rat (about Allied POWs during WWII. A classic)
The Life of Oharu (about a court lady in 17th C Kyoto)
Merry Christmas Mr Lawrence (set in a POW camp in Japan. Starring David Bowie)
Midway (starring Hollywood stars; about the Battle of Midway of WWII)
The Pillow Book (Loosely based on this)
Ran (Kurosawa's adaptation of King Lear)
Rashomon (Kurosawa again. Another classic. Looks at one even from many viewpoints)
Rebellion (Excellent film about the feudal period/feudalism in general)
Shogun (there is a film and a miniseries, both based on James Clavell's Shogun series of books. The miniseries is far superior)
Sisters of the Gion (a 1936 film that looks at the exploitation of women)
You Only Live Twice (Bond film, set mostly in Tokyo)