Baku appears in many guises in Japanese Mythology and folklore. There are many references to a creature resembling a tapir. To ask for Baku's protection, one can either chant "Baku kurae" or "Baku kue" -- "eat it up tapir" -- immediately upon waking from a bad dream (as memebomb reports above), or place a written petition to Baku under one's pillow before sleep. A statue, picture or shrine in one's sleeping quarters might also be handy. Direct experience with a four-year-old plagued by bad dreams, and a little plush elephant named Baku, suggests that the psychic mechanisms at work here are effective.
There is some speculation that the Baku legend originates in China; this makes plenty of sense: real Malaysian tapirs actually live in Southeast Asia.
One description has Baku with spines on its back, a trunk like an elephant, tusks, sharp pointy teeth, and a mane like a lion. Some say Baku has a cow's tail, and rhino eyes. The trunk seems to be Baku's most important feature: it occurs in most of the visual representations, including netsuke, and temple ornamentation.
Even the creators of Pokemon have tapped into the Baku myth in their game/card/movie/junk/marketing/mind-poisoning product. Two of them: Drowzee and Hypno have the familiar tapir-like trunk and use their psychic abilities to put opponents to sleep. Hypno even "survives by putting its prey to sleep and consuming their dreams."