The Doctor's mother

According to some accounts, the Doctor remembered having a mother. The Eighth Doctor once claimed that he was half human on his mother's side. (TV: Doctor Who) Another account said the Doctor's mother was a Time Lord. (COMIC: The Comfort of the Good) The Eighth Doctor also said that he couldn't remember if he had a mother or if he was created out of a gene-splicing machine. (PROSE: The Shadows of Avalon, Bafflement and Devotion)

Biography
The Doctor said that his mother used to sing the Zagreus nursery rhyme to him. (AUDIO: Seasons of Fear) When the Doctor was just a "small child", the Doctor's mother sat by the side of his bed and told him the story of Grandfather Paradox. (PROSE: The Gallifrey Chronicles) The Eighth Doctor relived a memory from his first incarnation where his mother watched as his father held him up as a child to see the stars. (PROSE: The Eight Doctors)

Other universes
In one universe, when the Doctor was young, his mother and father went on a trek in the mountains with him. The Doctor's father and mother owned a summer house on the other side of Kasterborous. (PROSE: The Infinity Doctors)

In the Obverse, the Doctor's mother was a mermaid. (PROSE: The Blue Angel)

Appearance
The First Doctor remembered his mother having red hair. (PROSE: A Big Hand for the Doctor) The Eighth Doctor also remembered that his mother had long red hair, and a cut-glass voice; (PROSE: The Gallifrey Chronicles) according to him, she resembled the third incarnation of Romana. (PROSE: The Ancestor Cell) At some point in life the Doctor's mother had grey hair. (COMIC: The Comfort of the Good)

Penelope Gate
Lance Parkin intended for the human Penelope Gate and the Time Lord Ulysses to be the Doctor's parents. Penelope's description matches the description of the Doctor's mother in The Gallifrey Chronicles, and, in the same story, Penelope and Ulysses are said to have a half-human son on Gallifrey. However, their son is never explicitly confirmed to be the Doctor.

The Woman
Russell T Davies has stated (in a March 2009 email reprinted in REF: Doctor Who: The Writer's Tale - The Final Chapter, pages 622-623) that the unnamed woman, implied to be a Time Lord, in The End of Time was meant to be the Doctor's mother. However, he has also said that whoever the woman is can be up to judgment, and she could be someone else. Additionally, the depiction of the Doctor's mother in The Comfort of the Good bears a striking resemblance to the Woman in both physical appearance and Gallifreyan dress.