What is the genre of The Three Little Pigs?

In the strict definitions of traditional literature, it would be a fable (a story with a moral lesson).

All of the animal characters act like people, which teaches a lesson to be passed on through generations. It is a folk tale, not a fairy tale, because there is no magic.

It can also be considered a "nursery rhyme tale" for the rhyming conversation of the Wolf and pigs when he wants them to let him eat them:

Wolf: "Little pig, little pig, let me in."

Pig: "Not by the hair of my chinny-chinny-chin."

Wolf : Then I'll huff...and I'll puff... and I'll blow your house in!"