Here's a good piece of folklore from Japan, which can be found on scaryforkids.com:
(I did not make this up. I am only telling the way I remember. Also there is a movie out about it, which is called "Carved.")
A long time ago there was this samurai, and he had a beautiful wife who thought highly of herself. She was so gorgeous that all the men wanted her and the women were jealous about her looks. Well, the husband got sick of her being so self-centered that he took his sword and slit her mouth apart, calling "Who will think you're beautiful now?!" Her looks were ruined.
So now she is called the Kuchisake Onna, or Slit-mouth Woman. She carries a large pair of scissors and wears a trench coat, and a flu mask around her mouth. She commonly appears in urban areas on foggy nights, and asks mostly young people if they think she's pretty. She will then remove the mask and say "Am I pretty NOW?!" Try to run away, she'll corner and kill you. Say yes, she'll cut your mouth to make you look just like her. Say no, she'll kill you by slitting your throat. The only way to escape is to say she's average, or ask if she thinks that you are pretty. That will give you enough time to run away from her.
Other variations suggest she was in a car crash that tore her mouth apart, or that if you DO say she's pretty, she'll leave you alone. Others say that if you give her chocolate or say you have a former engagement to attend to, she will excuse herself and apologize.
Look it up on Google, you can find pictures of her and the story.