Jan Svankmajer: Czech director who was supposedly a big influence on the Quay Brothers- uses stop-motion (think that's the right term) animation within the films, mixed with child-hood nightmarish tales. Just seen Little Otik and Conspirators of Pleasure (both recommended) and heard that Alice and Faust were also worth seeing.
Faust more so than Alice.
Takashi Miike: Visitor Q is one of the most unsettling movies I've seen in a while- lots of violence (including a teenager beating his mother) plus incest and necrophilia (the later of which provides an especially disturbing yet somehow funny scene). I've heard that another film of his, Audition, is even more graphic.
I thought Visitor Q was an almost complete misfire, interesting only for inverting the usual that outsider-family subgenre (Teoreme, Boudou Saved from Drowning). Didn't care much for Fudoh either. Much better--and conveniently both just released on US DVD though I haven't seen those--are City of Lost Souls and Dead or Alive which rework yakuza/crime films through culture clashes (and anybody who says they expected the ending of Dead or Alive is a liar). Way way over the top is the flabbergasting Ichi the Killer, even in the slightly censored Hong Kong DVD. Audition is good in a what-is-reality way like Polanski's Repulsion but not quite as "unwatchable" as its reputation. I'm hoping to get around soon to Happiness of the Katakuris, Miike's musical remake of a Korean film (no really). Other current Japanese directors worth checking out are films by Kiyoshi Kurosawa (especially Cure which I think is one of the best films of the 90s), Sogo Ishii (Angel Dust is pretty easy to find but don't pass up the dark satire Crazy Family), Sabu (the peculiar DANGAN Runner) and Shunji Iwai. Shinya Tsukamoto is well-respected but has always seemed pretty trite to me. I'd guess all Zornlisters already know about Seijun Suzuki and Takeshi Kitano. And I'd rate Hayao Miyazaki as one of the best filmmakers anywhere. LT