Caligula

Caligula, an emperor of the Roman Empire during the 1st century, was one of the individuals that Momus the Wise pulled out of time to help lead the people of Planet 12 of the Ridion Alliance into a new age of enlightenment. The Tenth Doctor noted that he wasn't as bad as he was portrayed in I, Claudius. (PROSE: The Lonely Computer)

The male version of Iris Wildthyme (who was in actuality a simulation created by her TARDIS) and "his" companion Panda attended a party thrown by Caligula. However, Panda claimed that the real Iris would never be associated with a madman like him, no matter how good the party was. (AUDIO: The Two Irises)

Lucie Miller encountered Caligula during her travels with the Monk. She later told the Eighth Doctor that he was "well bonkers" and claimed that the Sensorites were "not as much of a laugh." (AUDIO: The Resurrection of Mars)

Caligula once tried to throw the Doctor to the lions as he did not like the cut of his trousers. (AUDIO: The Labyrinth of Buda Castle)

Behind the scenes
Caligula was portrayed by John Hurt in the BBC's 1976 adaptation of I, Claudius and by John Simm in the 2004 miniseries Imperium Nerone.