A wizard was a practitioner of magical arts. (TV: The Smugglers)
Under the alias of "Qui Quae Quod", the Third Doctor briefly passed himself off as a wizard to the residents of Devil's End, apparently holding the word to be the masculine counterpart to the "witches" familiar to the Devil's End townsfolk, (TV: The Dæmons) although the title of "wizard" could in fact be applied to a woman. (PROSE: A Honeycomb of Souls) A peasant who had been sent to 1970s London by a time eddy also believed the Third Doctor was a wizard when he saw him. (TV: Invasion of the Dinosaurs) However, after dropping the "Qui Quae Quod" disguise, the Doctor insisted to Thorpe that he was not "a magician or a wizard or anything of the sort", maintaining that his and the Master's abilities as Time Lords and men of science were entirely different from folkloric "magic". (TV: The Dæmons) Lord Quiquaequod, an alternate reality version of the Eighth Doctor, was also a wizard. (COMIC: The Glorious Dead)
On prehistoric Earth, the Fifth Doctor met a wizard called Kalid who was able to conjure realistic illusions to hypnotise people. However, Kalid was finally revealed to be The Tremas Master in disguise. (TV: Time-Flight)
In the myth of the Pandorica, as the Eleventh Doctor explained to Amy Pond, "the most feared being in all the cosmos" was sealed in the Pandorica after being tricked by a good wizard. River Song commented that she hated good wizards in fairy tales as they "always turned out to be him.", referring to the Doctor. (TV: The Pandorica Opens)
Merlin was a famous wizard associated with the legends of Camelot. Many individuals used the name at one point or another, including the Master (PROSE: The Creation of Camelot) and several incarnations of the Doctor, (TV: Battlefield, PROSE: One Fateful Knight, Legends of Camelot) as "the Merlin" was actually the official title for the astrologer of Camelot's court, rather than a personal name. (PROSE: The Creation of Camelot) One Merlin had a sister called Ganeida, who was a wizard like himself; they were both of half-demon heritage. (PROSE: A Honeycomb of Souls)
Albert Cragg, a human time traveller from the 20th century, passed himself off as "a wizard from another land" using modern technology when he travelled back to Egypt in the 14th century BC. (COMIC: Dr. Who's Time Tales)