My favs:
RAN
Historical, Serious & Sad.
Death Note
Amusing & Entertaining if you like the general death note idea.
Battle Royal
Has become a modern classic/cult favourite.
Chakushin ari
Of one two Japanese horror film I really liked, most I just do not get at all, usually prefer Korean ones.
The other is about a sort of haunted house with a doll maker and a mysterious ghostly girl in red, that I can't remember enough about to find the name of it