Mythological creatures that feed on fear?

Answer 1

I haven't heard this in mythology however I can think of two instances where it is used:

1. The comic book The Specter
2. A star-trek (original) episode.

EDIT: And the obvious, Dementors (kinda)

EDIT: Lethifolds are the original name for demetors, though they have been documented in mythology for thousands of years. Closely related to shadow people, these creatures feed off fear and life energy, especially while their victims sleep. They are sometimes referred as nightmare cloaks.

Answer 2

I think like in HARRY POTTER AND THE PRISONER OF AZKABAN, a boggart is a creature that feeds and imitates your worst fears.