We need to have three permanent sticky threads: Asian film, anime, and comic recommendations.
Ahem. At any rate, a few brief recommendations:
God of Cookery - Earlier Stephen Chow comedy about shaolin cooking madness. Freakin' awesome.
Ping Pong - Japanese manga adaptation about teen agnst, sport, and the glory of ping pong, all with an element of the fantsatic. This film is universally loved, I shit you not.
Tampopo - Urban cowboys meet ramen stands and absurdist vignettes in the most amazing film about food you will ever see. Brilliant, touching, and very, very funny. WARNING: Under no circumstances should you watch this film while hungry. Any of Juzo Itami's other films are well worth watching, particularly the comic attacks of the yakuza that got him killed. Minbo (aka The Gentle Art of Japanese Extortion) is particularly amusing, as are the Taxing Woman films.
Cure and Pulse - Kiyoshi Kurosawa (no relation) makes amazing contemporary horror films. Cure is a serial killer flick with a bizzare, horrific twist. Pulse mixes social commentary with haunting visuals and a quietly apocolyptic ending. I can't recommend these enough.
Graveyard of Honor (1975) - The quinessential yakaza film, courtesy of Kinji (Battle Royale) Fukasaku. This is the bleak, incredibly violent true story of a gangster who was out of control and utterly without honor, even by the standards of his fellows. The rest of Fukasaku's yakuza films (particularly five-film epic The Yakuza Papers or Street Mobster) are also highly recommended. Takahashi (Audition) Miike's recent remake, Shin Graveyard of Honor, is also quite good, though somewhat more subdued.
Branded to Kill - Seijun Suzuki's absurdist yakuza masterpiece, which got him kicked out of the studio system. The Number 3 killer in Japan does battle to become the Number 1 Killer before someone else gets him first. Stunning visuals, a terrific jazz soundtrack, femme fatales, rice huffing, and an extended finale that must be seen to be appreciated. See also: Any other Suzuki film; Criterion recently released Youth of the Beast and Fighting Elegy in R1.
After Life - Hirokazu Koreeda's quietly humorous meditation on death. As assorted group of the recently deceased find themselves in a somewhat run-down retreat where the beauracrats of the afterlife inform them that they will spend the next week determining their most important memories, filming them, and then living in them forever. Very funny, very touching, and guaranteed to make you think.
Absolutely anything by Akira Kurosawa - If you haven't seen Rashomon or The Seven Samurai, what the hell are you waiting for? If you have, try some of his non-samurai work like The Lower Depths or High and Low.
Okay, so those are virtually all Japanese recommendations. I'll second the recommendation for The Tale Of Two Sisters (which I thought wrapped itself up quite neatly), a beautifully shot Korean horror film.
FnordChan