Beard
A beard was a form of hair growth on one's face. They were often shortened to just thick upper lip hair known as a moustache.
The Master often wore one (TV: Terror of the Autons et al.) known as a goatee. (COMIC: The Judas Goatee) It led to the Fifth Doctor asking the Tenth if he "still had that rubbish beard". The Tenth Doctor replied that he had a wife instead. (TV: Time Crash) When the Twelfth Doctor reencountered the Master in his "Harold Saxon" incarnation, he had grown a beard. (TV: World Enough and Time)
Charles Dickens had one when he met the Ninth Doctor and Rose. (TV: The Unquiet Dead)
The Doctor first grew a beard in his fifth incarnation when he spent over a year stuck in Victorian London, as people thought he was too young to take seriously without it, (AUDIO: The Haunting of Thomas Brewster) but he apparently shaved it off once he resumed his travels. He grew a beard once again when he was aged a relative year while travelling through a time distortion field to escape a high-security prison. (AUDIO: Doing Time) While staying in the house on Henrietta Street in his eighth incarnation, the Doctor briefly grew a neat goatee beard, intended to test if he could change as well as the wider universe; he claimed to have worked out how to transform himself into a creature of pure light by adapting his self-biology, but estimated that it would take three thousand years of concentration, so growing a beard was easier. (PROSE: The Adventuress of Henrietta Street) He only kept the beard for a short time before he shaved it off. (PROSE: Mad Dogs and Englishmen, Hope) The incarnation known as the War Doctor grew a beard on a full-time basis. (TV: The Name of the Doctor, The Day of the Doctor) The Eleventh Doctor would grow a beard when held in captivity for significant periods of time. (TV: Day of the Moon, The Wedding of River Song) An alternate Twelfth Doctor wore one, too. (COMIC: Four Doctors)
In a Kantrofarri-induced shared dream, Santa Claus had a beard when he met the Twelfth Doctor. According to Wolf, he initially grew the beard as a disguise, but "people have picked up on it". (TV: Last Christmas) Indeed, even the Roboforms, who took the form of robot Santas, had beards. (TV: The Christmas Invasion, The Runaway Bride)
Owen Harper likened his partial resurrection to Jesus Christ "but without the beard". He immediately realised "shit, I'm never gonna have a beard" but denied wanting one. (TV: A Day in the Death)
Varun Singh had one grown due to the practice of Kesh in Sikhism. (TV: For Tonight We Might Die, The Coach with the Dragon Tattoo, Brave-ish Heart)