The Doctor's family

The Doctor's familial relations were numerous and paradoxical. (PROSE: Celestial Intervention - A Gallifreyan Noir) Sarah Jane Smith once referred to the Doctor's companions as their family, telling the Tenth Doctor, "You act like such a lonely man, but you've got the biggest family on Earth!" (TV: Journey's End) The Doctor chose to think of the universe as their foster family, after their parents "decided to opt out of their responsibilities." (PROSE: Beltempest)

Ancestors
According to one account, the Doctor was one of the forty-five cousins created by the Loom of the House of Lungbarrow on Gallifrey. (PROSE: Lungbarrow, Celestial Intervention - A Gallifreyan Noir) At other times, the Doctor stated that he had parents, including a Time Lord father (TV: Doctor Who, PROSE: The Infinity Doctors, Unnatural History, Matrix) and a human mother. (TV: Doctor Who, PROSE: Alien Bodies, The Infinity Doctors, Grimm Reality, Unnatural History, The Shadows of Avalon, Celestial Intervention - A Gallifreyan Noir) In a third account of the Doctor's origins, they were originally the mysterious Timeless Child, discovered and adopted by the Shobogan traveller Tecteun, who brought her child back with her to Gallifrey. (TV: The Timeless Children)

Patience taught the Doctor's grandfather, (PROSE: Cold Fusion) and the Thirteenth Doctor spoke of several grandmothers. (TV: It Takes You Away)

The Eleventh Doctor spoke of his godmother, (TV: Vincent and the Doctor) and his great-aunt Inertia. (GAME: The Mazes of Time)

Siblings
The Doctor had at least one brother, Irving Braxiatel, (PROSE: Tears of the Oracle, AUDIO: Disassembled, PROSE: ...Be Forgot, Big Bang Generation, Celestial Intervention - A Gallifreyan Noir, TV: Smith and Jones) who became an associate of the Doctor's companion Bernice Summerfield. (PROSE: Tears of the Oracle) Braxiatel was also a Cardinal of Gallifrey (AUDIO: Weapon of Choice) and was the owner of the Braxiatel Collection, (PROSE: Tears of the Oracle) which the Doctor and Romana once compared to the Louvre in Paris. (TV: City of Death) The Doctor had one niece by Irving Braxiatel, Maggie Matsumoto. (AUDIO: The Empire State)

The Thirteenth Doctor recalled once having had sisters, (TV: Arachnids in the UK) though another account indicated the Doctor never had an older sister. (PROSE: Dragonfire) Irving Braxiatel hinted that he had once lost a sister, or a daughter. (PROSE: Tears of the Oracle)

At the Eighth Doctor and Scarlette's wedding in the post-War universe, the Man with the Rosette sat at the table reserved for the Doctor's family. (PROSE: The Adventuress of Henrietta Street)

Descendants
The Doctor had, in the Tenth Doctor's own words, been "a dad" (TV: Fear Her) and "a father". (TV: The Doctor's Daughter) These children were "sons or daughters, or both." (PROSE: The Eleventh Tiger) The Twelfth Doctor claimed he had "dad skills". (TV: Listen) Clara Oswald also claimed the Doctor had once had "children". (TV: Death in Heaven)

Susan Foreman's father was a Cardinal on Gallifrey, and had a wife who died giving birth to Susan. (PROSE: Cold Fusion, Lungbarrow) It was unclear which of them was the descendant of the Doctor; however, in another universe, the Doctor's daughter was Susan's mother. (AUDIO: Auld Mortality)

The Doctor also had several grandchildren, (TV: Death in Heaven) including Susan Foreman, (TV: An Unearthly Child, et al.) John Who, and Gillian Who. (COMIC: The Klepton Parasites, PROSE: Beware the Trods!, et al.) Some accounts referred to Susan as "the Other's" granddaughter. (PROSE: Lungbarrow)

At one point, the Doctor became the adoptive father to a female Time Lord named Miranda Dawkins, whom the Eighth Doctor reared until her mid-teens. (PROSE: Father Time) Miranda later gave birth to a daughter, Zezanne, and died while trying to protect the Doctor. (PROSE: Sometime Never...)

The Doctor also had a great-grandson named Alex, the son of Susan and David Campbell. (AUDIO: An Earthly Child) Alex went on several adventures with the Eighth Doctor and backpacked around the Earth with Lucie Miller before they were both killed by the Daleks. (AUDIO: Lucie Miller, To the Death) Susan and David also had adopted children, Barbara, Ian and David Junior. (PROSE: Legacy of the Daleks)

Genetic material from the Doctor in their tenth incarnation was used to create a daughter, Jenny, via progenation. The Doctor explained to Donna Noble and Martha Jones that due to the way his DNA was processed, he was Jenny's "biological mother and father". Although initially spurning her, he soon considered Jenny his daughter and invited her to travel with him in the TARDIS. Before she could join him, however, she was shot by General Cobb. The Doctor believed Jenny to have died, and departed. (TV: The Doctor's Daughter) Unbeknownst to him, she survived and set out on her own life of adventure. (TV: The Doctor's Daughter, AUDIO: Stolen Goods, et al.)

When the Earth was relocated to the Medusa Cascade, an instantaneous biological meta-crisis was created; this meta-crisis Doctor was later was exiled by the Time Lord to an alternate universe. Technically, the meta-crisis could be considered a relative of the Doctor's. (TV: Journey's End)

Fate
Much of the Doctor's family died or went missing. (TV: The Tomb of the Cybermen, The Curse of Fenric, AUDIO: To the Death, TV: The Woman Who Fell to Earth) After the last day of the Time War, the Tenth Doctor, while telling Donna that he'd been a father before, explained that he "lost all that a long time ago along with everything else." (TV: The Doctor's Daughter) The Eleventh Doctor involuntarily reacted to Corc's accusation that he had never lost a child. (PROSE: Dark Horizons) Even after the Doctor realised that Gallifrey and the Time Lords were not destroyed at the end of the Time War, the Doctor still believed their missing children and grandchildren to be dead. (TV: Death in Heaven, The Woman Who Fell to Earth)

Affairs
The Tenth Doctor told Sally Sparrow that he was "rubbish at weddings, especially [his] own". (TV: Blink)

The First Doctor was accidentally engaged to Cameca in the 15th century when he drank cocoa with her. (TV: The Aztecs)

An earlier incarnation had been wed (PROSE: Cold Fusion) to Patience and they were said to have had a number of children and grandchildren. (PROSE: The Infinity Doctors)

After Gallifrey was destroyed in the War in Heaven, the Eighth Doctor married Scarlette in order to ceremonially tie himself to the planet Earth. (PROSE: The Adventuress of Henrietta Street)

The Tenth Doctor romanced and later married Elizabeth I. (TV: The End of Time, The Day of the Doctor, PROSE: Suspicious Minds) She later declared him an enemy after he failed to return as promised. (TV: The Shakespeare Code) The Tenth Doctor implied he had been married several times prior to Queen Elizabeth, as he remarked to Sally Sparrow about being "rubbish at weddings, especially [his] own". (TV: Blink) In his eleventh incarnation, the Doctor accidentally became engaged to Marilyn Monroe, and married her the same night in what he later claimed was not a real chapel. (TV: A Christmas Carol)

River Song often hinted that she and the Doctor had a physical relationship somewhere in her past and his future relative to the Eleventh Doctor's encounter with the Silence in Florida. (TV: Silence in the Library / Forest of the Dead, The Time of Angels / Flesh and Stone, The Pandorica Opens / The Big Bang, Day of the Moon) The Eleventh Doctor, operating a Teselecta shaped like himself, performed a "quick version" of a wedding ceremony with River because they were in the middle of a combat zone in an alternate reality. They repeatedly referred to each other as husband and wife after the ceremony. (WC: Asylum of the Daleks Prequel, TV: The Wedding of River Song, The Angels Take Manhattan, The Name of the Doctor, The Time of the Doctor, The Husbands of River Song, AUDIO: The Boundless Sea, Five Twenty-Nine, The Eye of the Storm, PROSE: Suspicious Minds)

According to Clara Oswald, by the time of the Doctor's twelfth incarnation, he had been "married four times, all deceased". (TV: Death in Heaven)

Myths
Martha Jones had believed that the Master was the Doctor's "secret brother [or something]", to which the Tenth Doctor told her that she had "been watching too much TV." (TV: The Sound of Drums)

Behind the scenes

 * Martha's belief that the Master was the Doctor's "secret brother" was the original intent for the character back in the Jon Pertwee-era, and would have been realised had Roger Delgado not passed away. This idea was reignited years later in the Peter Davison-era story Planet of Fire, with Anthony Ainley's version of the Master, before seemingly burning up, exclaiming "Won't you show mercy to your own…", never finishing the sentence. According to the DVD commentary, Fiona Cumming asked John Nathan-Turner how the line was to end, to which he replied, "brother".