Temporal dissolution

Temporal erasure was the removal of an object or individual from time and space, as though they had never existed. This was a risk in changing history, (TV: In the Forest of the Night) sometimes as a result of the butterfly effect, (TV: Thin Ice) or otherwise due to unrestrained interference in the timelines during a large-scale conflict such as the Last Great Time War. (AUDIO: The Starship of Theseus)

One could be erased from time by a time field, (TV: Flesh and Stone) or by technology used by the Time Lords. (TV: The War Games, PROSE: Engines of War) The Time Lords sometimes made a habit of "deleting" whole species from history, as a quick solution. (AUDIO: Fugitive in Time)

In some cases, time travellers could remember an individual even after they had been wiped from history, though the Eleventh Doctor explained to Amy Pond that she would not remember Rory Williams, as he was intimately linked to her own personal history. (TV: Cold Blood) On other occasions, the Doctor retained his memories of a previous timeline at least for a short while, while no one else did. Eventually, the Eighth Doctor's recollections of those erased from time in the Last Great Time War slipped away. (AUDIO: The Starship of Theseus, One Life)

Last Great Time War
During the Last Great Time War, changes in reality caused Sheena to be renamed to Emma, then to Louise before disappearing from time entirely. (AUDIO: The Starship of Theseus)

Soon afterwards, Quarren, a Time Lord with a special ability to change reality with his thoughts, erased himself from time, and even the Eighth Doctor and his new companion Bliss soon enough could not remember him. Nevertheless, without even knowing why, the Doctor felt compelled to check up on Rupa Maguire, Quarren's wife. (AUDIO: One Life)

In an attempt to end the Time War, used the Heavenly Paradigm to alter the timelines, but inadvertently instead changed various planets' histories, largely for the worse. Among these worlds was Chelfrey, once a famed recreational planet, which ceased to exist as a direct result of the Master's actions. (AUDIO: The Heavenly Paradigm)

Post-Time War
After failing in her first attempt to ensure that her father did not die alone, Rose Tyler and the Ninth Doctor travelled back to a point just prior to his death in 1987, precariously close to their past selves. When Rose saved her father from the car that killed him, the past Doctor and Rose disappeared from existence. (TV: Father's Day)

Time Lords
Tried for his crimes by the Time Lords, the War Lord was dematerialised out of existence along with his subordinate War Lords. (TV: The War Games) In an alternate universe, the War Lord was accidentally dematerialised out of existence before the Time Lords could finish telling him that he would be dematerialised. (AUDIO: Exile)

The De-mat Gun was capable of wiping its targets from time and space. During the Sontaran invasion of Gallifrey, the Fourth Doctor used the gun to eliminate Commander Stor and his unit of Sontarans. The De-mat gun was supposed to be forbidden knowledge, the existence of the gun known to all Time Lords who viewed it with horror. (TV: The Invasion of Time)

During the Last Great Time War, Rassilon wielded a gauntlet which possessed the ability to remove individuals from history. (PROSE: Engines of War) He used this power against the Partisan, reducing her to dust. He later intended to use his gauntlet against both and the Tenth Doctor, but ultimately failed to kill either. (TV: The End of Time)

Time field
Amy Pond's mother and father, Tabetha and Augustus Pond, were erased by the crack in her house. (TV: The Big Bang)

Aboard the Byzanitum, a crack erased several clerics of the Church. In quick succession, Crispin, Phillip, Pedro and Marco all came into contact with the crack and disappeared. Though the clerics were oblivious to what was going on, their memories of their lost colleagues being erased with them, Amy was able to remember them, having travelled through time. Soon after, the Eleventh Doctor used the ship's gravity to send the Weeping Angels, led by Angel Bob, falling into the crack. (TV: Flesh and Stone)

Shortly following his death at the hands of Restac, Rory Williams was erased from history when his corpse was consumed by the crack in the Silurian city. As Rory was a part of Amy's personal history, she quickly lost her memory of him. (TV: Cold Blood) However, Rory would later return as an Auton. (TV: The Pandorica Opens)

It was ultimately realised that the cracks in time had been caused by the destruction of the Doctor's TARDIS, which led to a Total Event Collapse. As the Doctor warned, this would cause every star to supernova at every moment in history, resulting in the entire universe never having existed. Further than that, a Cyber-Leader claimed that "all universes will be deleted." (TV: The Pandorica Opens) As the eye of the storm, Earth remained for a time, with the explosion of the TARDIS taking the place of the Sun. In addition stone after images of members of the Alliance persisted, such as the Stone Daleks. In 1996 of the alternate timeline, the Eleventh Doctor used the Pandorica to reboot the universe in what he called Big Bang Two. As a result, Rory was restored to human form while Amy's parents returned as well. (TV: The Big Bang)

Other references
When a solar flare threatened to destroy the Earth in the 2010s, the Twelfth Doctor explained to Clara Oswald that the many futures of Earth that they had witnessed through their prior travels through time would be erased should Earth be destroyed at this point. (TV: In the Forest of the Night)