Amnesia was the (usually temporary) loss of memory.
Instances of amnesia
Amnesia could be a common side-effect of trauma regenerations, with symptoms ranging from uncertainty about names, (TV: Castrovalva, Time and the Rani) forgetting a skill they had mastered, (TV: The Time of the Doctor) or complete memory loss. (TV: Doctor Who)
When Time Lords met their past and future selves under certain controlled circumstances, the younger versions often had their memories of the experience erased. The First and Second Doctors explicitly had their memories wiped by the other Time Lords after the first confrontation with Omega (TV: The Three Doctors, PROSE: The Empire of Glass), and the War and Tenth Doctors lost their memories of working with the Eleventh Doctor to draw up a peace treaty with the Zygons and save Gallifrey as timelines were out of sync and they would be unable to retain it. However, it was strongly implied that the Seventh Doctor always remembered the Fifth Doctor's encounter with the Ferutu from his perspective (PROSE: Cold Fusion (novel), AUDIO: Cold Fusion), and at least the first five Doctors retained clear memories of meeting the amnesic Eighth Doctor (PROSE: The Eight Doctors).
The First Doctor and Susan Foreman suffered from partial amnesia when they arrived in 1963 London, apparently caused by challenging the Time Lord rule against interfering when they left Gallifrey. (PROSE: Time and Relative) According to another account, this memory loss occurred when the Doctor stole the TARDIS and it assaulted his mind. (PROSE: Echoes of Future Past)
The First Doctor, Ian Chesterton, Barbara Wright and Susan briefly suffered from amnesia after the TARDIS' fast return switch got stuck, which would have sent it back to the creation of a solar system and resulted in its destruction. The ship crashed itself in an attempt to warn its passengers of the dangers, and a small explosion occurred in the TARDIS as the Doctor tried to correct its faulty navigation circuits, rendering all four unconscious. (TV: The Edge of Destruction)
The First Doctor force-fed an amnesia pill to William Shakespeare to ensure that he would forget the advanced technology he had downloaded into his mind. (PROSE: The Empire of Glass)
The Masters of Dorada suppressed the memories of the Second Doctor, Ben Jackson and Polly, whom they enslaved when they arrived on Dorada. (PROSE: The Dream Masters)
The victims of the War Lords suffered from post-hypnotic amnesia due to the conditioning used to make them forget what had happened to them. (TV: The War Games)
During the Third Doctor's exile on Earth, the Time Lords suppressed his knowledge of how the TARDIS worked as part of his punishment, (TV: The War Games) as well as some details of Earth's future history. (PROSE: The Devil Goblins from Neptune) They restored this knowledge when they lifted his exile. (TV: The Three Doctors)
The victims of an alien Extractor suffered from permanent amnesia. Liz Shaw suffered from temporary amnesia following a car accident after escaping the Extractor. (PROSE: The Mind Extractors)
The Fourth Doctor suffered from amnesia after being transported to Deepcity due to a flaw in the time ring. (PROSE: A Device of Death)
Alistair Gordon Lethbridge-Stewart suffered from partial amnesia from 1977 to 1983 as a result of meeting his future self; he was able to remember his time at UNIT and his immediate official colleagues, but not the Doctor or the Doctor's companions, until the Fifth Doctor reminded him of them. (TV: Mawdryn Undead)
The Viyrans erased Peri Brown's memories of being patient zero of a mutagenic virus on Grallista Social to keep knowledge of the virus secret, although they had to convince Peri of the need for this in order for her mind to accept the memory wipe. (AUDIO: Mission of the Viyrans)
The Time Lord Azmael provoked selective amnesia to the Earthling twins Romulus and Remus Sylvest by applying a green circle on their wrists, in order to make them more compliant to assist in his plans. (TV: The Twin Dilemma)
The Sixth Doctor suffered from partial amnesia after being transported to Space Station Zenobia for his trial, unable to clearly recall his last couple of trips in the TARDIS or what had happened to his companion. (TV: The Mysterious Planet)
When Jeremy Fitzoliver accidentally used the IRIS machine on himself, he caused serious mental damage to himself, leaving him totally amnesic and unable to even process new information, as well as being unable to be read by human telepaths, occasionally rambling about things he remembered from his association with UNIT only to forget them the next moment. Even after almost two decades, he never remembered anything more than that he had some association with the Brigadier, the Third Doctor, and UNIT, even adopting the name 'John Doe' out of a lack of better ideas. (PROSE: Instruments of Darkness)
Ace suffered from amnesia when the Seventh Doctor accidentally erased her memory while editing his own, but he was able to quickly undo it, (PROSE: Timewyrm: Genesys) although he accidentally gave her one of Mel's memories in the process. (PROSE: Timewyrm: Revelation)
The Panjistri supplied the Kirithons with zavát which, in addition to being their main food source, weakened their resistance to telepathic suggestion, allowing the Panjistri to suppress certain memories and even the Kirithons' awareness that they should have those memories in the first place. (PROSE: Timewyrm: Apocalypse)
The Time Scaphe crew lost their memories after their ship collided with the TARDIS, but regained them after Ace told them the name of their home world, Gallifrey. The TARDIS took the Doctor's memories to keep them safe from the Process, but later returned them to save itself from destruction. (PROSE: Cat's Cradle: Time's Crucible)
The Seventh Doctor and the people who had consumed the essence of the Celestial Toymaker gave themselves electroshock therapy to suppress their memories of the Toymaker in an attempt to destroy him. (AUDIO: The Magic Mousetrap)
The Seventh Doctor briefly suffered from amnesia when he was thawed out after being frozen in ice for millions of years. (AUDIO: Frozen Time)
The Master suffered from amnesia while on Perfugium as the Doctor's deal with Death caused him to revert to the persona he would have had if Death had not marked him as her champion. (AUDIO: Master)
On Erratoon, the robot constables punished lawbreakers by removing their memories. Ace suffered from this fate, and although the Seventh Doctor said he could restore her lost memories using the TARDIS, she wondered if there were some memories which she would never get back, knowing that if there were, she'd never know it. (AUDIO: The Prisoner's Dilemma)
Chris Cwej suffered from amnesia while on Ardethe. (PROSE: Deadfall)
The Eighth Doctor suffered from amnesia after falling into the Master's trap, requiring him to be guided by Rassilon to regain his memories by visiting and mentally linking with his previous seven selves. As he met each past self, he regained their memories up to the point when he met his past self, starting to remember their futures once he reached his third incarnation and regaining all his memories once he met his seventh self. (PROSE: The Eight Doctors)
The Eighth Doctor, Charley Pollard and Gideon Crane suffered from amnesia after the TARDIS crashlanded in Malebolgia, the TARDIS's damaged telepathic circuits dividing the Doctor's mind between Gideon and "Zebediah Doe" and nearly erasing Charley's mind. (AUDIO: Minuet in Hell)
The Eighth Doctor suffered from amnesia after the brain-worm attacked him in the Cube. (AUDIO: Something Inside)
The Eighth Doctor suffered from amnesia after being forced to destroy Gallifrey. (PROSE: The Ancestor Cell) This was initially attributed to trauma, but was later established as the Doctor erasing his own memory to create room for him to store the compressed Matrix in his subconscious. (PROSE: The Gallifrey Chronicles)
The Eighth Doctor suffered from amnesia while on Espero, but his memories were just suppressed and quickly restored. (PROSE: Halflife)
Madeleine Fairweather suffered from amnesia from 15 January 1942 until shortly before her death on 1 January 2008, believing herself to be Charlotte Pollard as an unintended side-effect of the Doctor reprogramming the Cyber-Planner while it was linked to Madeline's mind. During the same crisis, contact with the neural worm left the Doctor with his memories of the last few hours lost, with the result that he forgot about his confrontation with the Cybermen on the SS Batavia and the chain of events that led to him and Charley being separated. (AUDIO: The Girl Who Never Was)
The Ninth Doctor and Rose Tyler suffered from partial amnesia after being transported to Satellite Five, requiring a few moments to remember how they had arrived in their new positions. (TV: Bad Wolf)
The Tenth Doctor erased Donna Noble's memories of their time together to prevent her mind from burning with the Time Lord knowledge she had gained from a biological meta-crisis. (TV: Journey's End)
The staff of Torchwood Three often employed a drug called retcon to induce amnesia about recent events and prevent the existence of aliens being made public. (TV: Everything Changes)
Tricky Van Baalen lost his memory in a salvaging accident, prompting his family to lie and tell him that he was an android as part of a strange joke. (TV: Journey to the Centre of the TARDIS)
Emily Blandish suffered from amnesia after being hit on the head by a Dæmon. (PROSE: Child of Time)
Iris Wildthyme lost most of her memories when Panda smashed the crystal containing them. (AUDIO: Wildthyme at Large)
In order to protect themselves from becoming the Hybrid, the Twelfth Doctor and Clara Oswald exposed themselves to a tool that would erase the memories one of them had of the other; this left the Doctor with all memory of Clara lost, and although he was able to piece together some details about her name and what they had done together, he was unable to recall what she looked like even when directly talking to Clara. (TV: Hell Bent)
After the Twelfth Doctor and Bill Potts returned to St Luke's University in the TARDIS, the Doctor contemplated erasing Bill's memories of the adventure to prevent her from telling anyone else who he actually was. At the last minute, though, he decided against it. (TV: The Pilot)
As partly mechanical life-forms, Daleks could suffer from memory loss if the appropriate cybernetic components were damaged. When the Dalek that would become the High Priest of the Elite crash-landed on Florana in the distant past, it initially had trouble remembering the Doctor and the TARDIS when it was disconnected from its usual casing, the casing too damaged to sustain the Dalek on its own for long, although it soon identified both when it was returned to its casing for a short time. (AUDIO: The Elite)
When the Eighth Doctor fled the starship Theseus with a group of human survivors and crash-landed on a jungle planet with a damaged Dalek, he was able to convince the battered Dalek that its name was 'Dal' and that it was the humans' ally, Dal using its sensors to help the Doctor guide the refugees to a temporal safe zone established on the planet by the Time Lords, although Dal was destroyed before the Doctor could determine if he had been able to convince Dal to change on its own. (AUDIO: Echoes of War)
When Oswin Oswald accessed the Daleks' cyber-network, she was able to delete all knowledge of the Doctor from all Daleks, although they eventually remembered him again during the Siege of Trenzalore when the Daleks hacked the records of the Church and learned about the Doctor from those. (TV: Asylum of the Daleks, The Time of the Doctor)