[Maila Munster]

Noroi: The Curse (2005), directed by Kōji Shiraishi.

This movie is in a form of a documentary and presents the story of Masafumi Kobayashi, a Japanese journalist and paranormal investigator. He researches and records seemingly unrelated mysterious events and people. Soon things get complicated and Kobayashi discovers that the common feature of these strange events is the word "Kagutaba".
I don't want to attach any spoilers so I'll just say that it's definitely not a typical Asian horror. I think that this one requires patience as the action develops slowly and there are plenty of threads to follow, but if you decide to watch it, you'll get fair amount of suspense and terror.

A Slit-Mouthed Woman (Kuchisake-onna) (2007), directed by Kōji Shiraishi.

It is said that this movie is based on the Japanese urban legend known as Kuchisake-onna, and it presents a story about a series of child abduction caused by a ghost of a woman with a mutilated face.
From what I know it's far from the original legend of Kuchisake-onna and I think that the potential that this character definitely has, wasn't fully exploited. It was predictable and the presentation was quite lousy, although the concept was great IMO.