Last of the Time Lords

In several of their incarnations, the Doctor considered themselves to be "the Last of the Time Lords".

History
When the War Doctor was preparing to use the Moment to end the Time War, the sentient weapon warned him that to do so would result in "no more" Time Lords and Daleks, and that his punishment would be to survive. (TV: The Day of the Doctor)

After taking Rose Tyler to see the destruction of Earth, the Ninth Doctor confided to her that he was the last of the Time Lords and that his planet had burnt, as hers did, in a war. (TV: The End of the World)

Encountering the Metaltron, which he believed to be the last surviving Dalek, the Doctor revealed that, save the two of them, both the Daleks and the Time Lords were wiped out at the end of the Last Great Time War. In reference to the Doctor, the Dalek gloated that "the coward survived". Ultimately, the Dalek chose to self-destruct after being "contaminated" by Rose's human DNA. As such, the Doctor deemed that the war was over; as the "only one left", he had won. When Rose suggested that some Time Lords might have survived as the Dalek did, the Doctor claimed that he would know if they had, that it felt like there was no-one. (TV: Dalek)

By reading Adam Mitchell's mind via his infospike, the Jagrafess and the Editor learnt that the Doctor was the last of the Time Lords. (TV: The Long Game)

When Jeanne-Antoinette Poisson presented King of France Louis XV to the Tenth Doctor, he introduced himself as the Lord of Time. (TV: The Girl in the Fireplace) The Beast, who claimed to have lived before the universe, knew the Doctor as "the killer of his own kind". (TV: The Satan Pit)

Saying goodbye to Rose in Pete's World, the Doctor assured her that he would be back to his "same old life" as last of the Time Lords. (TV: Doomsday)

The Face of Boe, whilst acknowledging that the Doctor was the last of his kind, told him that he was not alone, much to his shock. The Doctor later admitted to Martha Jones that he was the last of the Time Lords and that his people were all lost in the Last Great Time War against the Daleks. (TV: Gridlock)

The Family of Blood knew the Doctor to be the last of the Time Lords, whom they understood to be a "wise and ancient race". (TV: Human Nature)

On Malcassairo, the Doctor introduced himself as the last of the Time Lords to Professor Yana and Chantho, the latter of whom related as she believed herself to be the last Malmooth. The Doctor was humbled to know that, at the end of the universe, neither Yana nor Chantho recognised the name Time Lord. After Martha found a biodata module, a device which she knew could hold the essence of a Time Lord, on Yana's person, Jack Harkness suggested that Yana could be a Time Lord, that the Doctor "might not be the last one", though the Doctor was hesitant to accept this. Martha recalled the Face of Boe's words, and the Doctor came to realise that he was referring to Yana, who soon revealed he was the human disguise of, under a Chameleon Arch. (TV: Utopia) The ensuing confrontation eventually led to the death of in a new incarnation, who refused to regenerate despite the Doctor's pleas, knowing that there was "no one else". (TV: Last of the Time Lords)

General Staal of the Tenth Sontaran Battle Fleet, who was aware of legends of the Last Great Time War, knew the Doctor to be the last of the Time Lords, and savoured the prospect of him dying in the Sontaran invasion of Earth. (TV: The Sontaran Stratagem)

On the surface of Mars in 2059, the Doctor was preparing to leave the crew of Bowie Base One to their historically established fate when he remembered that he was the last of the Time Lords. With this knowledge, he returned to the base to change history, coming to believe that the Laws of Time were his alone and deeming himself Time Lord Victorious until he was challenged by Adelaide Brooke. (TV: The Waters of Mars)

Having made arrangements for his resurrection prior to his death, the Master returned and was confronted by the Doctor, only for both to be embroiled in the Final Sanction initiated by, who had been made aware of a prophecy identifying the Doctor and the Master as the "two survivors", to facilitate the escape and survival of Gallifrey beyond the final day of the Time War. This plan was stopped by the Doctor, whilst the Master returned to the Time War as he attacked Rassilon, leaving the Doctor alone once again. (TV: The End of Time)

The newly established New Dalek Paradigm recognised the Eleventh Doctor as the last of the Time Lords and so deemed that the Daleks were the winners of the Time War, striving towards mastery over space and time only to be continually thwarted by the lone Time Lord. They eventually learnt of Gallifrey's survival during the Siege of Trenzalore. (PROSE: Dalek: The Astounding Untold History of the Greatest Enemies of the Universe)

The Eleventh Doctor observed that Alaya, a Silurian, was using the Klempari defence when she claimed to be the last of her kind under interrogation. The Doctor explained that, being the last of his species, he knew how it "[sat] in a heart", warning her not to insult him. (TV: The Hungry Earth)

As part of a ploy to acquire control of the Doctor's TARDIS, the Claw Shansheeth claimed to Sarah Jane Smith claimed to have found the body of the Doctor, the last Time Lord. In reality, the Doctor was alive and well. (TV: Death of the Doctor)

When House noted his killing of hundreds of Time Lords in an attempt to intimidate the Doctor, the Doctor retorted that he had killed all of them. In addition to himself, the last Time Lord, the Doctor claimed his TARDIS to be the last TARDIS, and that there would be no more after them. (TV: The Doctor's Wife)

Even after the Eleventh Doctor teamed up with several of his past and future regenerations to preserve Gallifrey in a pocket universe, (TV: The Day of the Doctor) with the Time Lords managing to return to the universe, albeit hiding in fear at the end of the time continuum with nothing anywhere near their old power, (TV: Hell Bent) the Twelfth Doctor continued to hold himself to be the "Last of the Time Lords", a title which Clara Oswald applied to the Doctor as the equivalent to Robin Hood's "Prince of Thieves". (TV: Robot of Sherwood)

Meanwhile, left Gallifrey and, (TV: Death in Heaven) upon learning of the Eleventh Doctor's apparent death at the hands of River Song, met with his recorded killer, to whom she presented herself as the "Last of the Time Lords", which she claimed also made her the best one and the winner as the others had "all [gotten] themselves killed". (AUDIO: The Bekdel Test)

After reuniting with Missy, (TV: Death in Heaven) and discovering that Gallifrey was now "hiding" at the end of the universe, the Twelfth Doctor introduced Missy to Bill Potts as "the other Last of the Time Lords". (TV: The Lie of the Land)

Behind the scenes

 * In Tony Blair Regenerates, the regenerated Tony Blair, played by David Tennant, presents his "Last of the Time Lords hand gesture" in an address to the people of Britain.