The Doctor's ninth incarnation

By most accounts, the Doctor's ninth incarnation was the one which followed the Eighth Doctor's regeneration.

When examining the Doctor's timeline, Marnal exclaimed to Rachel that the Doctor had "three ninth incarnations". (PROSE: The Gallifrey Chronicles) The Eighth Doctor's visions of his future included a number of potential ninth bodies, (PROSE: The Tomorrow Windows) and accounts differed as to which one he eventually regenerated into. (TV: The Name of the Doctor, Doctor Who and the Time War, et al.)

Man with big ears
After the Eighth Doctor saw several visions of his future in the Tomorrow Window, a single figure solidified out of the blur: a gaunt, hawklike face that gave him a broad, welcoming grin. (PROSE: The Tomorrow Windows) According to some accounts, the Eighth Doctor regenerated into this incarnation after using the Moment to end the Last Great Time War. (PROSE: Doctor Who and the Time War, COMIC: The Forgotten) He travelled with Rose Tyler. (TV: Rose, et al.)

Warrior
By some accounts, the Eighth Doctor regenerated into an incarnation who renounced the title "Doctor" while fighting in the Last Great Time War. (TV: The Night of the Doctor) Later incarnations disavowed this version of the Doctor for breaking the promise of their shared name; (TV: The Name of the Doctor) however, this Doctor's final act was to actually save Gallifrey. (TV: The Day of the Doctor)

Others
Other possibilities included a figure in a velvet suit and eyeliner, a man with curly hair and a lopsided smile, a listless-looking man, and a pale aristocrat. (PROSE: The Tomorrow Windows)

Other possible successors to the Eighth Doctor were incarnations which the Doctor already knew lay in his future: a ginger incarnation (PROSE: The Tomorrow Windows) whose adventures intersected the Seventh Doctor's several times, (PROSE: Battlefield, Transit, Birthright, Happy Endings) and the Valeyard, who repeatedly menaced the Sixth Doctor (TV: The Mysterious Planet, AUDIO: The Brink of Death, et al.) and was described as an amalgamation of the Doctor's darker sides from between his twelfth and final incarnations. (TV: The Ultimate Foe)

One possibility was that the Eighth Doctor's successor was not even an incarnation of the Doctor, but of one of the four surviving elementals, the man with a bent nose. (PROSE: The Tomorrow Windows, The Gallifrey Chronicles)

Another possibility was that the Eighth Doctor's future included many men in pseudo-Edwardian dress as well as the First Doctor. (PROSE: The Tomorrow Windows) By one account, the old man and young girl who landed their spaceship in the junkyard at 76 Totter's Lane were Soul and Zezanne in the shape-shifting Jonah; in their amnesiac states, Zezanne believed that Soul was her grandfather. (PROSE: Sometime Never...)