Michelangelo

Michelangelo was a 16th century human artist. The Doctor described him as a whiner but also seemed to be friendly with him, once calling him "Mikey." (TV: Vincent and the Doctor, WC: The War of Art)

Biography
In 1508, Michelangelo began working on the Sistine Chapel. Michaelangelo was afraid of heights. The Doctor, who was present at the time, told him that he should not have taken the job. (PROSE: Managra, TV: Vincent and the Doctor)

At another point, he did a portrait of the Doctor. (DWM: Changes) Momus abducted him for its dinner party while he had a model in his studio. (WC: The Lonely Computer)

An android copy of Michelangelo containing his memories was placed in the Paloma Centre. The Eleventh Doctor used his sonic screwdriver to control it into attacking the invading Arucha. The android moaned about attacking the group of Arucha, asking if he had to. The Doctor told him he had to. (WC: The War of Art)

According to one account, the Tenth Doctor claimed that he had never met Michaelangelo. (PROSE: The Stone Rose)

On his travels, the Monk, a renegade Time Lord, acquired a sculpture by Michelangelo which had been lost to history. Lucie Miller threatened to break it if he did not return her to Blackpool in the early 21st century. The Monk instead materialised his TARDIS in the Deimos moonbase in the 23rd century and threw her out. The sculpture remained intact. (AUDIO: The Resurrection of Mars)