Sigh. It is so sad that I know this website exists, but, according to
tardis.wikia.com/wiki/The_Doctor
After Gallifrey was destroyed in the Second War in Heaven, the Eighth Doctor (Paul McGann) married Scarlette in order to ceremonially tie himself to the planet Earth. (PROSE: The Adventuress of Henrietta Street)
The Tenth Doctor (David Tennant) romanced and later married Elizabeth I. (TV: The End of Time, The Day of the Doctor) 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 (Matt Smith), 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) A Teselecta version of the Eleventh Doctor with him hiding inside married her in an alternate timeline shortly before his "death". Later in their individual timelines, they spoke as if they considered themselves husband and wife. (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)
According to Clara Oswald, by the time of the Doctor's twelfth incarnation, the Doctor had been "married four times, all deceased." (TV: Death in Heaven)
So, there's four - Scarlette, Elizabeth I, Marilyn Monroe (maybe) and River Song. Plus, he started with his granddaughter Susan, so presumably there was a TimeLady wife before he stole the Tardis. Five? Or is Scarlette discounted because it was only in a book and not the TV series (there are all sorts of arguments about what is Doctor canon and what is not).