Doctor Who pastiches

A number of unauthorized versions of Doctor Who and of the Doctor have appeared.

Partial list of Doctor Who pastiches

BBV Productions introduced Colin Baker as "the Stranger", originally a loose pastiche of the Doctor, who developed into a more original character. Appearing in the first three films was Nicola Bryant as Miss Brown, a pastiche of Peri Brown.
BBV also produced a comedy short film, Do You Have a Licence to Save This Planet? a parody in which Sylvester McCoy plays "The Foot Doctor". The film includes numerous references to Doctor Who as well as original alien races from the show such as Sontarans, Autons and a bastardized version of Cybermen, the Cyberons. The film poked fun at the fact that BBV and others were able to use monsters and other characters from Doctor Who, but never the Doctor himself.

BBV introduced Sylvester McCoy as "the Professor", later (for legal reasons), "the Dominie", with Sophie Aldred as "Ace", later Alice. The audios featured scripts by, among others, Robert Shearman (under a pseudonym), Mark Gatiss and Nigel Fairs.
The Wanderer or Fred, played by Nicholas Briggs in the BBV audio adventures Cyber-Hunt and Vital Signs is loosely based on the Doctor as portrayed by Briggs in the Audio Visuals fan audio series. In Cyber-Hunt, he comes up against Cyberons.
Lalla Ward and John Leeson reprised their roles as Romana and K-9, respectively, for a series of audio dramas called The Mistress and K-9. While the producers of these audios were able to licence K-9, they couldn't licence Romana, thus she was never referred to by this name. Later, when Big Finish Productions obtained a full licence to produce Doctor Who-based audio dramas, Ward was once again able to perform the character as Romana.

The Marvel Universe had Professor Gamble and his enemies the Incinerators. Later Marvel and Marvel UK stories introduced WHO, or the Weird Happenings Organization, led by Doctor Alistaire Stuart along with his sister, Brigadier Alysande Stuart. (They are obviously named after Alistair Gordon Lethbridge-Stewart.) This was originally the creation of Marvel writer and Anglophile, Chris Claremont, who, during the course of his career, incorporated several brief references to Doctor Who into his scripts.

The Wildstorm comic book The Establishment featured Mister Pharmacist, who resembled a much darker and sinister version of the Fourth Doctor. He worked alongside a team of super-secret agents based on other characters from British fantasy and adventure television series. The Establishment made many other allusions to this genre and to British pulp fiction.

Grant Morrison's The Invisibles featured surgically altered drone henchmen known as the Cyphermen.

The Doctor Who Universe itself has a pastiche version of Doctor Who, called Professor X. Bernice Summerfield briefly visited that fictional universe and met Professor X during No Future.

A number of pastiches of the Doctor have appeared, some "real" in the context of the fiction, others fictional fictional characters. A few have appeared in the Doctor Who Universe itself.

Dr. Who, an inhabitant of the Land of Fiction and/or a creation of the Doctor's own mind
Professor X, a television character very similar to the Doctor. He starred in a children's television series of the same name.

Mr. X, a puppet who traveled through time and space in his "Whatsis Box" teaching children about history. He appeared early in the Canadian version of Howdy Doody, but was removed due to parental complaints that he was "too scary".
Paradox, a heroic time travelling scientist from the American animated series Ben 10: Alien Force.
In the BBC soap opera Doctors, Seventh Doctor actor Sylvester McCoy played Graham Capelli, who had played a 1980s children's television character called the Lollipop Man. Dressed as a crossing guard, the Lollipop Man traveled through time and battled alien invaders.

Professor Justin Alphonse Gamble was a minor Marvel Universe character based on the Doctor, though not on any particular incarnation. He had stolen a time machine from the Time Variance Authority and fought the Dalek-like Incinerators.

The BBV Productions characters the Stranger and Miss Brown, played respectively by Colin Baker and Nicola Bryant, started off as a thinly-veiled version of their Doctor Who roles of the Sixth Doctor and his companion Peri Brown. (Miss Brown, however, used an English rather than American accent, to distinguish her from Peri.) Starting with the fourth adventure of the Stranger, BBV decided to explain away the Stranger as a different character, named Solomon, with an entirely different past.
An unfinished fan film, Devious, features a character referred to as "Two-and-a-Half Doctor", a partial incarnation of the Doctor between his Second and Third lives. Also featuring Jon Pertwee as the Third Doctor, the film has been in production since the mid-1990s and a 12-minute excerpt was released by BBC Video in 2009 as a bonus with the DVD of The War Games.

BBV also produced the adventures of the Professor (later called the Dominie, for legal reasons) played by Sylvester McCoy and Ace (played by Sophie Aldred) (later called Alice), as even more thinly veiled versions of the Seventh Doctor and his companion Ace. Depending on your point of view, these might count either as true adventures of the Doctor using an alias or fan fiction using the original actors.

Doctor Omega was the main character of the 1906 French science fiction novel Le Docteur Omega by Arnould Galopin. After Doctor Who nonfiction writer Jean-Marc Lofficier, discovered the character and noticed the similarities between him and the First Doctor. Lofficier and his wife Randy republished the book in an English translation, gave it a new cover similar to that of Chris Achilleos' for Doctor Who in an Exciting Adventure with the Daleks with an introduction by veteran Who writer. Terrance Dicks. Lofficier added lines suggesting that the novel told adventures of the Doctor shortly before An Unearthly Child with the Doctor having taken a brief leave of absence from his grand-daughter Susan Foreman.