Bewitched sleep (incantation unknown) is a difficult spell that puts the targeted person into a deep sleep; subject is in a state almost like suspended animation and does not breathe for the duration of the spell.
The Serpent of Slytherin has been placed under a bewitched sleep within the Statue of Slytherin. So long as she sleeps, she does not age, hence allowing her to survive for a millennium, waiting for the Heir of Slytherin to reawaken her to purge the school of Muggle-borns.
Fleur Delacour tried to put her dragon into a trance at the Triwizard Tournament, but it was only partially successful, as the dragon snored and caught the hem of her robes on fire. It also may have been the spell that Dumbledore used on the hostages in the Second Task of the Triwizard Tournament.