The Doctor's final incarnation

By some accounts, the Doctor eventually reached their final incarnation, and then subsequently met their death.

Knowledge of the final Doctor
The Master told the Sixth Doctor that the Valeyard was "an amalgamation of the darker sides of your nature, somewhere between your twelfth and final incarnation". (TV: The Ultimate Foe) This phrasing would be repeated by the Seventh Doctor (PROSE: Matrix) and A Brief History of Time Lords. (PROSE: A Brief History of Time Lords)

When Ruath used a Time Scoop to view the Doctor's time stream, she advanced the viewer to the Doctor's final face. After remarking "So that's what you become! Well, that's no good to me.", she shifted the Time Scoop to the Fifth Doctor, who she thought would be easier to manipulate. (PROSE: Goth Opera)

The Doctor's thirteenth incarnation
By various accounts, the Doctor's final incarnation was the thirteenth of their original life cycle.

By one account, said that the Valeyard came from between the Doctor's twelfth and thirteenth incarnations. (PROSE: The Ultimate Foe)

When Ace entered the Doctor's mind, she saw that the Doctor's mind had space for thirteen total selves, with the incarnations beyond the Seventh Doctor still being Watchers yet to be molded into distinct incarnations, including the final thirteenth incarnation. (PROSE:  Revelation)

The Eleventh Doctor was the final regeneration of the Doctor's original life cycle, (TV: The Time of the Doctor) and had his final death in a timeline in which he never received a new regeneration cycle. (TV: The Name of the Doctor, The Time of the Doctor)

Later incarnation
The Eleventh Doctor was saved from his death by the granting of a new regeneration cycle, leading to the Doctor surviving beyond his original life cycle. (TV: The Time of the Doctor)

The Valeyard believed that the Doctor's final incarnation could only be postponed, not averted. By his account, the Valeyard had "splintered" from the Doctor before his final incarnation as a causal imbalance, meaning he only had one life and could not regenerate. As such, Bernice Summerfield did not consider him to be a true incarnation of the Doctor, saying that he was a twisted little fragment that "just fell off the back of a lorry". (AUDIO: Every Dark Thought)

Behind the scenes

 * Paul Cornell, who mentioned the Doctor's final incarnation in several of his stories, wrote a depiction of the Doctor's final life in his short story The Last Doctor.
 * Craig Hinton's Doctor Who lore indicated that the Doctor's thirteenth and final incarnation would survive after death as the Red Guardian.