Since you didn't limit this to animation...let's dust off some cult classics shall we?
Gozu, mind bending horror:
Hausu, surreal comedy horror:
Burning, it's technically a short Japanese story adapted to movie by a Korean director, it has as much in common as Oldboy with it's comic, but it's also just as good.
Haruki Murakami has a really distinctive writing style that makes daily life feel kinda magical, the movie really captures that despite how different it is from the source material.
Suicide Club, Not really much of a obscure movie, but it's a cult classic and has some deep shit under all the gore.
The Neighbor No. 13, really amazing Japanese horror movie that i feel gets overshadowed by Ichi the killer sometimes since they share similar concepts.
Ichi the Killer, while i prefer Gozu from Takeshi Mike, this is definetly the movie that made him famous overseas.
Man, i wonder what the fuck happened to Japanese movies, there used to be so much cool shit, now it's mostly Live Action movies that look like cosplay fan films.
I feel like the modern Korean movies are like what Japanese ones used to be.