Smile.

The Kuchisake-Onna; what she is and how to deal with her. 

She's an example of Japanese folkloric spirits and monsters called yokai, and she's interesting (apart from being an appealingly deranged story) because she was an example of a piece of folklore being invented in contemporary times. She seems to have appeared first of all in elementary schools in the Nagasaki Prefecture in the 1970s, and caused a genuine panic that spread through Japan.

In some versions she is mutilated by a jealous and violent husband, but this is the first version I heard.