Anything in particular that you're looking for?
In case of Japanese films I've just seen The Returner (I think we were talking about it at the City Beach Meet) and Versus. I'm thinking about picking up Battle Royale, Shiri, and Ichi the Killer next.
Woo woo...now you're talking. Yeah, all those you mentioned plus other Asian films like 2009 Lost Memories, Wonderful Days, Avalon, Princess Blade, Gen X & Y Cops, My Wife is a Ganster I & II, My Sassy Girl, Suicide Club, Volcano High, etc.
Regarding anime I'm so out of the loop on the new stuff...but older stuff I'd be interested like Patlabor TV (my 2nd fave mecha show after Macross), KOR, Maison Ikkoku, Nadesico, Dual, Sakura Diaries, OMG, Votoms, Berserk, Excel Saga, Full Metal Panic, Sakura Wars, etc.
How many movies do you typically get to rent per month?