Fall of the Eleventh

The Eleventh Doctor, having expended the 12-regeneration life cycle beginning with the First Doctor, was enabled to undergo what he called "regeneration number thirteen" into the Twelfth Doctor after being provided with additional regeneration energy by the Time Lords at the end of the Siege of Trenzalore. (TV: The Time of the Doctor) This event was prophesied as the Fall of the Eleventh by Dorium Maldovar. (TV: The Wedding of River Song)

However, in a timeline viewed by the Doctor earlier from his perspective, the Doctor was seen to have finally died, with their TARDIS growing its exterior dimensions and acting as his grave. (TV: The Name of the Doctor)

No more regenerations?
Accounts differed as to whether the Eleventh Doctor was, in fact, physically capable of regenerating further, regardless of Time Lord intervention.

At some point after undergoing his siphoned regeneration, (TV: The Stolen Earth/Journey's End) the Tenth Doctor met Jackson Lake, a man who believed himself to be the Doctor after picking up a Cyberman infostamp. Before discovering this fact, the Doctor speculated Jackson to be either his successor or the "next one along". (TV: The Next Doctor)

Other accounts set after the siphoned regeneration indicated the Tenth Doctor's awareness that he only had one regeneration remaining. In a meeting between himself and the Twelfth Doctor, he assumed his successor to be his next and final incarnation. (COMIC: Vortex Butterflies) In a meeting in an aborted timeline between himself and his two immediate successors, the Tenth Doctor was skeptical of the Twelfth Doctor's identity, believing that he couldn't exist. (COMIC: Four Doctors)

Anticipation
According to one account, the Tremas Master claimed that the Valeyard was the Doctor's "penultimate reincarnation… somewhere between [their] twelfth and thirteenth regenerations". (PROSE: The Ultimate Foe)

After being contaminated with Judas tree poison, the Eleventh Doctor suggested that he should regenerate only for the TARDIS' voice interface to point out that his regenerative ability was "disabled". (TV: Let's Kill Hitler) Whilst faking his death at Lake Silencio, the Teselecta in the form of the Doctor gave the appearance of a regeneration which was interrupted by the intended assassin, River Song. A future version of River Song, as part of the ruse, claimed to Amy Pond and Rory Williams that the Doctor was killed "in the middle of his regeneration cycle" and so could not make it to "the next one". (TV: The Impossible Astronaut, The Wedding of River Song) On Hedgewick's World of Wonders, the Doctor threatened to use regeneration to hold off Mr Clever from taking over his mind. (TV: Nightmare in Silver)