Mickey Mouse

Mickey Mouse was an anthropomorphic mouse and an American icon.

An American icon
While giving Peri Brown a tour of Earth history, the Sixth Doctor referred to Mickey Mouse as one of the "great men" who had helped make the United States of America what they were today, to Peri's discombobulation. As they stepped out of the TARDIS, he showed her Mickey standing alongside Ronald McDonald and Steven Spielberg, all three of them eating hamburger sandwiches. (COMIC: The Incredible Doctor Who History Tour No. 7)

When Ace told Gilgamesh that all good spies wore disguises, she cited Mickey Mouse as an example. (PROSE: Timewyrm: Genesys)

Legacy
Actors costumed as Mickey and Minnie could be encountered at Disneyland. The Ninth Doctor was unimpressed with the experience and told Rose that he could take her to a place with real talking mice and ducks. (PROSE: Winner Takes All)

Mickey's likeness was also used on a number of merchandise items, especially timepieces: the Tenth Doctor revealed to Matthew Finnegan and Emily Winter that he carried a number of watches around his pockets, one of which had a Mickey Mouse design. (COMIC: Tesseract) Trix MacMillan had a Mickey Mouse alarm clock in the TARDIS which had belonged to Anji Kapoor. (PROSE: Halflife) Additionally, one of the toy trains in the Doctor's collection was a Mickey Mouse handcar. (PROSE: Model Train Set) A postcard featuring Mickey and Donald Duck could be seen stuck to the refrigerator in Rani Chandra's house. (TV: The Mark of the Berserker) One of the pins worn on her jacket by Miss Garglespike was a Mickey Mouse pin. (PROSE: The Bloodletters)

Marty Mouse, a criminal in the 82nd century, wore a costume reminiscent of Mickey Mouse. (COMIC: The Shape Shifter)

Minor references
Martha Jones had seen Mickey Mouse at Disneyland and noted that he didn't speak, but "sort of squeak[ed]". The Tenth Doctor later jokingly introduced Martha as "Martha Mouse" in Castle Extremis, to which she retaliated by introducing him as "Doctor Donald Duck". (PROSE: Martha in the Mirror)

Captain Jack Harkness later called Mickey Smith "Mickey Mouse" when they re-encountered each other on the Dalek Crucible. (TV: Journey's End)

P.R.O.B.E.'s operations were criticised by Defence Secretary Brian Williams as "looking very Mickey Mouse" after they allowed Paul Reynish to escape containment twice during the time that P.R.O.B.E. were meant to take care of his termination. (HOMEVID: When to Die)

Place within the DWU
Michael Theodore Mouse, popularly "Mickey Mouse", is one of the central characters of his own fictional universe, having first appeared in 1928 as a cartoon star in the animated short Steamboat Willie. Ace's reference to Mickey acting as a spy and disguising himself from the purpose in  Genesys is most likely a continuity reference to the seminal 1939 comic strip Mickey Mouse Outwits the Phantom Blot.

Most sources which reference Mickey Mouse within the Doctor Who universe do so owing more to Mickey's status as an "American icon" and corporate brand than as the protagonist of another science-fantasy fictional universe in his own right, and do not countenance the possibility of Mickey being real within the Doctor's universe, if only because it is well-established that Earth in the Doctor Who universe is, in the 20th century, primarily inhabited by humans, whereas Earth in Mickey's world is also home to a number of other sentient species partaking in "human" civilisation, beginning with anthropomorphic mice.

Disney Time was a 1975 TV special where Tom Baker as the Fourth Doctor introduced a variety of Disney clips, including the Mickey Mouse cartoon Clock Cleaners. The beginning of the special implied that the Doctor personally knew Mickey Mouse, whom he "had not seen in a while", though a man he talked to on the street of London only knew him, Donald Duck and Goofy as "Disney toons". This was echoed in the Ninth Doctor novel Winner Takes All, where the Doctor, infuriated with Disneyland's facsimiles, tells Rose he could take her to the home of actual talking mice and ducks.

The 1987 comic story The Incredible Doctor Who History Tour (No. 7), on the other hand, saw the Doctor citing Mickey Mouse alongside Steven Spielberg to Peri Brown as individuals involved in the modern history of the United States of America, and even showing him to her in the flesh. This (unlicensed) crossover would seem to indicate that Mickey somehow existed as a flesh-and-blood individual in N-Space itself.

Other matters
In an interview that can be found as an extra for The Three Doctors DVD, the writers wanted to name K9 "Pluto" after Mickey's famous pet sidekick, but Disney did not grant permission.