The Legendary Tengu
One common statue at various Japanese temples is the Tengu. It is defined by its characteristically long nose, and round face often with a beard that gives it the appearance of an elderly man.
The earliest Tengu however were origingally depicted with a beak, likening it to a bird of prey. In fact, if you go to the temples at Mt.Takao in the west extremity of Tokyo, you can see both interpretations of the Tengu standing tall next to one another.
I have heard in some popular folklore (mostly from Japanese video games), that the Tengu's long nose is highly sought after, and defeating one to take the nose is a quest of a hero, as the nose can be used for a sort of cure-all remedy.