From Muppet Wiki

The Fairy Godperson is the resident wish-granting fairy of Sesame Street. His performer and appearance are generally consistent, but his name and specific powers are not. Like Lecture Lady or Mr. Gameshow, his name in dialogue is tailored to his function on an episode-to-episode basis.

His earliest appearance was in Season 29 as Wolfgang's Fairy Godperson. He appeared again as the Jacket Fairy in two episodes (Episode 3858 and Episode 3974), the Bubble Fairy in Episode 3877, the Dog Fairy in an episode from Season 33, and as Elmo's Fairy Godperson in Episode 4080. In the latter, he grants Elmo's wish of being a bird. He carries with him a cellular wand which has recorded a number of instances in which Elmo has made the wish. After Elmo has had his fun, he summons his Fairy Godperson again to change him back into a monster.

His most recent appearance was in Episode 4128, appearing this time with a tall stack of hair, as the Hairy Godperson. He appears when Zoe wishes she had longer hair, like Rapunzel, and grants her wish with the aid of his magic curling iron.

He has an upcoming appearance in the new Sesame Street Dinosaurs direct-to-DVD movie as some kind of dinosaur fairy. (source)