Minotaur (The God Complex)

The Minotaur was a member of a species, also known as Minotaur, who had set itself up as a deity. When its subjects overthrew him, they sealed it aboard a prison ship which pulled in people for the Minotaur to feed on. As the aeons went by, the creature lost its desire to live but was unable to die because the ship was programmed to provide it with a constant food supply, and its instincts were too strong to starve itself. The Eleventh Doctor, Amy Pond, and Rory Williams encountered this creature, along with several other life forms that had been collected for its next meal. Initially believing that the creature fed on the fear of its victims, the Doctor cautioned everyone to avoid the rooms that contained their fears and to fight against those fears by holding fast to their beliefs. Eventually, only Rory and the Doctor remained unaffected by the creature: Rory because he did not strongly believe in anything, and the Doctor due to his strong will. When Amy let go of her faith in the Doctor, the food supply was cut off and the Minotaur could finally die. (DW: The God Complex)

Trivia
It may have contained some psyhic ability due to the fact that it knew the Doctor was really old and to atleast some degree to look forward to death because he had been around for so long.