Planet (An Unearthly Child)

The original home planet of the Doctor and Susan (TV: "An Unearthly Child") was unclear due to the Doctor's shifting timelines and alterations to their biodata, thus giving the planet many potential identities. (PROSE: Unnatural History)

The Doctor's home planet was as distant as a night star, (TV: "Rider from Shang-Tu") although generally similar to Earth. (TV: "A Desperate Venture") However, some accounts actually identified the Doctor's home planet as Earth, (PROSE: The Dream Masters, The Lair of Zarbi Supremo) while many later accounts identified it as Gallifrey. (TV: The Time Warrior, Gridlock, etc.)

Susan, upon travelling with Marco Polo, felt that she had had many homes. (TV: "The Roof of the World")

Other realities
In a parallel universe, Martin Bannister was uncertain whether or not to make it explicit that Doctor Who and Susan Who came from Venus in the 49th century. (AUDIO: Deadline)

Behind the scenes
The unnamed planet in the 49th century, the home of Dr. Who and Susan, was first mentioned in The Pilot Episode, where it was explicitly mentioned as the origin of the characters; in the the televised story, this line is less specific. The First and Second Doctors' eras contained several vague allusions to the Doctor's home, typically inferring that he and Susan were simply humans from another planet, until the "Time Lord" backstory was established in TV: The War Games and developed in the Third Doctor's era.

Since then, despite the Doctor having numerous origins being an accepted and oft-mentioned part of the character's backstory, this origin has been very rarely referenced, with the only two references to it outside of the First and Second Doctor's eras being PROSE: Unnatural History and PROSE: Escape Velocity (though the planet was referenced in AUDIO: Deadline, which isn't set in the "main" Doctor Who universe), even then only entertaining it as a possibility as opposed to directly confirming it as a backstory. Other stories, such as PROSE: Doctor Who in an Exciting Adventure with the Daleks usually play with the general idea, albeit a different take upon it.

One of Anthony Coburn's early scripts would have established that Susan had been a princess on her home planet, which would have been different than Doctor Who's world. Thereafter, Susan was envisioned as a fugitive from the Doctor's home planet. Coburn later altered the character to be the Doctor's granddaughter, to avoid having a biologically unrelated female teenager travelling with an old man.

In the 1964 Doctor Who television story The Sensorites, Susan's description of her home planet was reminiscent of Venus, albeit with a science-fiction spin. However, this planet cannot be Venus as in Marco Polo, which was broadcast earlier in 1964, had Susan explicitly say that her home planet was as far away as a night star. However, Venus being the home of the Doctor and Susan was referenced in the 2003 Big Finish Unbound audio drama Deadline, although this story was set in a parallel universe where the Doctor was only fictional. Regardless, Susan's description of her home planet having orange skies at night with silver trees was later retroactively applied to Gallifrey, becoming part of the well known design as seen in the post-2005 of Doctor Who, although Gallifrey's skies were typically depicted as being orange, even during the day.

In the unaired 1960s audio drama Journey into Time starring Peter Cushing, that version of the Doctor mentions that his civilisation was actually Earth, but three thousand years in Mike's future (who came from the mid-twentieth century).

A behind the scenes note on the Second Doctor had this to say about his origin: "He is the eternal fugitive with a horrifying fear of the past horrors he has endured. (These horrors were experienced during the galactic war and account for his flight from his own planet.)"

- 49th century on the Fringes of War, Nate Bumber's Tumblr