Forty-Fifth Doctor

Incarnations of the Doctor
Widely accepted
Others / unplaced incarnations
More ambiguous

According to one account, the Forty-Fifth Doctor died in River Song's arms on a battlefield, telling her that she had yet to have many more adventures with his earlier selves.

However, what he had failed to tell River was that, knowing she was destined to be uploaded to the Library, but not wishing her to be "lonely", the Doctor had arranged to upload his mind into an artificial moon that would orbit the Library forever, which became known as the Doctor Moon. From then on, the Doctor's mind took on a new avatar, "Doctor Moon", within the simulated world of the Library's hard drive. (NOTVALID: Showrunner Showdown)

Behind the scenes

Doctor Moon. (TV: Silence in the Library)

• Doctor Moon does in fact appear, played by Colin Salmon, in Silence in the Library and Forest of the Dead, where he meets River Song, who remains unaware of his true identity.
• The 45th Doctor and his story, referred as the "Very Last Scene in Doctor Who", was thought up by Steven Moffat in 2008 during the writing of Silence in the Library and Forest of the Dead. Though Moffat admitted that the idea would likely never make it to screen, it interestingly suggests that, whether he knew it or not, Colin Salmon technically played the 45th Doctor (or, rather, a post-mortem Doctor) on televised Doctor Who.
• In a 2013 interview with SFX, Moffat mentioned the concept of a 45th Doctor again, this time while explaining the inspiration behind the War Doctor:

"Why not a mayfly Doctor, who exists for one show only? I'd often thought about that. Would it be weird in the run of the series to have the 45th Doctor turn up and be played by Johnny Depp or someone? Would that be a cool thing to do?".Steven Moffat

• The numbered forms of the designations of the various incarnations of the Doctor are usually given in literal form (e.g. "First Doctor" rather than "1st Doctor"). The 45th Doctor, whose name has yet to be spelled "Forty-Fifth Doctor" in any official source, is thus an unusual exception to this rule.