Rumpelstiltskin was the persona adopted by a non-corporeal species who traveled from the Gamma Quadrant through the Bajoran wormhole and had taken a position in the plasma fields near the Denorios belt, where they read as elevated thoron emissions in 2369.
That year, this Rumpelstiltskin persona was taken from the imagination of Miles O'Brien.
He, along with two other's in the imagined personas of Buck Bokai and Jadzia Dax later converged in the replimat to discuss their findings, only to be confused by the irony of their results.
Following the crew's realization that their own imaginations were responsible for the events that transpired on the station, the crew was finally able to return things back to normal. After returning to his office, Bokai revealed himself to Benjamin Sisko, explaining their actions, stating that they were "on an extended mission exploring the galaxy. Awhile back, we followed one of your ships through that "hole in space" out there. We've been watching you, trying to figure out the rules of your game." (DS9: "If Wishes Were Horses")
This alien portrayal of Rumpelstiltskin was played by Michael John Anderson.