The mystical cloak was given to Doctor Strange by the Ancient One after he won his first battle against Dormammu. Doctor Strange has worn the cloak throughout most of his publication history and is a key part of his arsenal.
Doctor Strange had the capability to control the cape through telepathic commands. It could fly on its own and contort itself to the will of Doctor Strange. Doctor Strange often used this to help him defeat some minions of Mordo as in Strange Tales #143.
Doctor Strange has been portrayed as wearing slightly different versions of the cloak over the years. Such as an almost identical blue cape with no powers, and different other capes in every alternate universe.
Rintrah, one of many apprentices of Dr. Strange, wore the cloak for some time. Rintrah is currently in suspended animation due to severe injury.
Strange did not wear the cloak for some time, when he lost his title of Sorcerer Supreme due to practicing dark magics. When he regained his title he regained his cloak.
In the far future of the "Guardians of the Galaxy", the cloak has been transferred to Strange's alien apprentice named Krugarr.
In the year 2061, the cloak rides with a reincarnated Doctor Strange as a new team of Avengers re-start in Malaysia after a devastating alien invasion.
In "What If...? vol. 2 #24", the Punisher wore the cloak as Strange, now little more then a spirit, gave the vigilante magical objects in a fight against an invasion from hordes of vampires.
This Punisher was then drawn into the patchwork realm of "Battleworld", and used the cloak to fight a demonic influence. It, along with the Punisher, was obliterated in a fight that destroyed several adversaries.