Helldriver (2010) - Yoshihiro Nishimura

HellDriver is a 2010 Japanese splatter film directed by Yoshihiro Nishimura. It stars Yumiko Hara and Eihi Shiina, and was written by Nishimura and Daichi Nagisa.
A meteorite crashes into Japan, releasing a toxic ash that turns the northern half of the country into bloodthirsty zombies. Some time later, with the north now walled off from the rest of Japan, a young woman (Hara) is charged with leading a group of ragtag soldiers into the infected region to kill the "zombie queen" (Shiina) - who also happens to be her homicidal mother.

Shout outs to A-H-M for links


Trailer

Zoo (2005) - Masaki Adachi, Ryu Kaneda

Zoo is a collection of 5 short movies of varying genres.

Kazari and Yoko - Kazari and Yoko are twins living with their mother, although, one of the twins is abused by their mother. The story follows Yoko, in her attempts to survive her ever raging mothers efforts to get rid of her.

Seven Rooms - Two siblings wake up in an empty room, only to find a locked, large steel door, 2 slices of bread and a sewage stream. They find out they are not alone and their time is growing short.

So-Far - The story follows a young boy, who begins to loose sight of his parents after their relationship heads downhill.

Hidamari No Shi - A short animated story about an android learning the cycles of life and death.

Zoo - Follows a photographer and his extremes actions after the break up with with his girlfriend

Some of the best, and highest quality Japanese short films.
Shout outs to A-H-M for providing links. be sure to check those guys out.