The Doctor, according to several accounts, had a father.
The Doctor's father often discussed wars, great projects, and big things that had to be taken care of with his friends, such as Mr Saldaamir. When the Doctor was "barely a loomling", he let a cobblemouse loose in the great hall of the House of Lungbarrow and it scattered his father's plans and notes in the air, which made him very angry. (PROSE: Unnatural History) The Eighth Doctor recalled his original incarnation lying in the grass as they watched a meteor storm together. (TV: Doctor Who) The Seventh Doctor had a flashback to a time when his father had his arm across the Doctor's shoulders as together they watched a Gallifreyan dawn. (PROSE: Matrix) The Eighth Doctor relived a memory from his first incarnation where his father held him up as a child to see the stars. (PROSE: The Eight Doctors)
A version of history existed where the Time Lords banned all mention of the Doctor's father's name for consorting with aliens, and one where he got every record of himself deleted from the files. (PROSE: Unnatural History)
Other universes Edit
The Doctor's father was also friends with Savar before he went on his mission to find Omega. The Doctor's father chose to stay behind on Gallifrey rather than attempt to rescue Omega from the black hole he was trapped in.
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. The Doctor's father was still on Gallifrey when the Doctor had children, and stood at his side while he lost a chess match to Savar.
Later references Edit
The Eighth Doctor said that he was immortal on his father's side. The sentient quantum field of the planet Albert later told the Doctor that there was a reality where he knew his father's face. (PROSE: Grimm Reality)
When Quintus asked the Tenth Doctor not to tell his dad Lobus Caecilius that he showed the Doctor where Lucius Petrus Dextrus lived, the Doctor responded, "Only if you don't tell mine." (TV: The Fires of Pompeii)
The Master, holding the Tenth Doctor and Wilfred Mott prisoner, commented, "Your dad's still kicking up a fuss," when Wilfred protested in defence of the Doctor, he replied that he would be proud if he was. Later, the Doctor told Wilfred that he would be proud if he was his father. (TV: The End of Time)