The Doctor (The Brain of Morbius)

Eight incarnations of the Doctor before the First Doctor were seen during the Fourth Doctor's mindbending contest with Morbius before the mechanism broke down. (TV: The Brain of Morbius, PROSE: Doctor Who and the Brain of Morbius, PROSE: Cold Fusion, AUDIO: Cold Fusion)

Biography
When describing his "renewal" process to Ben and Polly, the Doctor implies that he might have renewed himself in the past; before opening a trunk which contained relics from his previous incarnation(s), including Saladin's ornamental dagger, a large earring he used to wear, a solid gold-like thick bracelet with odd pictures and Cameca's jade brooch.(PROSE: The Power of The Daleks)

When Polly Wright, Ben Jackson, and Jamie McCrimmon found a shaving mirror on the control console of the second control room in the Doctor's TARDIS, Polly and Ben speculated that the room may have been used by a bearded incarnation of the Doctor from a time before either of the Doctors they were familiar with. (PROSE: Something at the Door)

The fourth Doctor states to Romana, probably in jest, that Time Lords have 90 lives and that he got through about 130. (TV: The Creature from the Pit)

When the Seventh Doctor transformed himself into a human named John Smith he removed almost all of his memories, although he was unable to remove the ones from before he was born. "Verity" kept these memories out of John Smith's head. (PROSE: Human Nature)

The eleventh Doctor says to Clyde that he can change 507 times. (TV: Death of the Doctor)

Behind the scenes

 * A previous (TV: The Three Doctors) and later stories would suggest that William Hartnell's Doctor was, in fact, the earliest. (TV: The Five Doctors, The Time of the Doctor)
 * The original rehearsal script by Whitaker for TV: The Power of the Daleks (then known as The Destiny of Doctor Who) states that the Doctor renewed before and that last time he was wearing a metal bracelet stored in a drawer of the console, described in the John Peel novelisation. (DWMSE 4)
 * PROSE: Lungbarrow, also stating the Hartnell incarnation to be the first, proposed a possible solution: following persecution from Rassilon, a Time Lord founder threw himself into a Loom to be resurrected, and the Doctor had many of his memories. The novel hints, but not explicitely states, that the mindbending contest faces are from The Other and not the Doctor.
 * Philip Hinchcliffe, producer of TV: The Brain of Morbius and himself appeared as one of the faces, stated on the faces: "We tried to get famous actors for the faces of the Doctor. But because no one would volunteer, we had to use backroom boys. And it is true to say that I attempted to imply that William Hartnell was not the first Doctor." They all wore stock costumes.(REF: In-Vision #12: The Brain of Morbius, A History of the Universe) Hinchcliffe reconfirmed it in REF: Classic Who: The Hinchcliffe Years. Hincliffe stated again in REF: A Day with Philip Hinchcliffe, that the original intention of the faces were to represent previous incarnations of the Doctor, but fans of the time chose to ignore this but still pick up on the "thirteen incarnations" limit four serials later. He went on to say that no matter how many Who fans say these are "mind battle faces" or "past incarnations of Morbius" doesn't matter, followed by him stating the fact that he played the Doctor.
 * Co-writer Terrance Dicks stated "I have no idea who the faces in the Mind Battle were. You would have to ask Bob." (REF: In-Vision #12: The Brain of Morbius) He confirms the event of the episode wiht the unkown faces appearing after the Doctor's ones while Morbius mocks him in his novelisation PROSE: Doctor Who and the Brain of Morbius but in PROSE: Junior Doctor Who and the Brain of Morbius he does not mention the unkown faces at all.
 * Script-editor and uncredited co-writer Robert Holmes, as well as one of the faces, confirmed Hincliffe's account: "We don't know which one Hartnell was, whether he was the first or not. In the phantasmagoric scene where they are mind-wrestling, we see the Doctor forced back through a number of regenerations." (REF: In-Vision #12: The Brain of Morbius) He would later introduce the idea of a twelve regeneration limit in TV: The Deadly Assassin. Assuming that the last face shown was the true first incarnation of the Doctor, that would have meant that the Fifth Doctor had no regenerations left. In Holmes' story TV: The Caves of Androzani, the Doctor said before his regeneration, "Is this death?" and "It feels different this time."
 * REF: Doctor Who The Handbook: The Fourth Doctor states that the faces are of Morbius after showing those of the Doctor, opposing how the episode showed Morbius, then the Doctor and then the debated faces.
 * The faces included directors Christopher Barry and Douglas Camfield, script editor Robert Holmes, production unit manager George Gallaccio, producer Philip Hinchcliffe, writer Robert Banks Stewart, and production assistants Chris Baker and Graeme Harper.
 * Lance Parkin, author of the novel Cold Fusion, confirmed that Patience's newly-regenerated husband, leaving ambiguous whether it were the Doctor's own memory, was intended to specifically be the Douglas Camfield Doctor (REF: AHistory); in an earlier draft of the novel The Infinity Doctors, Patience's husband would have been the Robert Banks Stewart Doctor.