Memories were the mental record of a lifeform's past experiences.
A man is the sum of his memories, you know. A Time Lord even more so.
The Fifth and Sixth Doctors both noted that memories from before their second regeneration were vague. (PROSE: Cold Fusion, COMIC: The World Shapers) According to Madame Xing, by the time the Eighth Doctor visited her, his memory had been interfered with on thirty-seven separate occasions, with eight of them still uncorrected. (PROSE: Halflife)
Clara Oswald read the Doctor's name in The History of the Time War. When that timeline was later averted, however, she had no memory of it. (TV: Journey to the Centre of the TARDIS) The telepathic circuits of a dead TARDIS retrieved some of those lost memories. (TV: The Name of the Doctor)
Retcon was a drug used by Torchwood to remove memories of the organisation and/or alien encounters from witnesses. (TV: Everything Changes, Adam, They Keep Killing Suzie, Meat, Something Borrowed, COMIC: Shrouded) The drug was also used by other individuals and organisations, notably the mayor of the trap street, Ashildr. (TV: Face the Raven)
Because their time streams were out of sync, the War Doctor and the Tenth Doctor couldn't retain memories of saving Gallifrey along with the Eleventh Doctor. (TV: The Day of the Doctor) Because he could not remember the true outcome of the war, the Doctor suppressed their memories of their war incarnation, not acknowledging him as an incarnation. (TV: The Name of the Doctor) As a result of Missy existing alongside him on the Mondasian colony ship, the Master was unable to retain his memories of his time there, his successor not even being able to fully recall the regeneration that had birthed her. (TV: World Enough and Time, The Doctor Falls)
In order to prevent Clara Oswald from dying, the Twelfth Doctor tried to use a neural block to erase himself from her memories. Upon learning of his plan, Clara reversed the polarity of the device and the Doctor lost his memories of her instead. (TV: Hell Bent) The Doctor's memories were restored near the end of his life when a glass avatar of Bill Potts allowed him to see her once more. (TV: Twice Upon a Time)
After Bill Potts's encounter with a puddle of sentient oil in the form of her friend Heather, the Twelfth Doctor intended to wipe her memories of the event. Bill realised his intentions and pleaded him not to. Eventually she gave in but before he could go through with it, she told him to imagine how it would feel if someone did it to him. The Doctor, perhaps remembering how Clara Oswald distorted his own memories, reconsidered his actions and allowed Bill to remember. (TV: The Pilot)
Iris Wildthyme once placed her memories within the Memory Crystal, which was then sought after by many higher powers who wanted to claim her memories for their nefarious needs. Iris also likened her memory to that of an elephant's. (AUDIO: Wildthyme at Large)
The Silents were genetically engineered so that people would lose their memories of them when they turned away. (TV: The Time of the Doctor) Through the usage of an Eye Drive, people could counteract this effect and retain their memories of the Silents. (TV: The Wedding of River Song) The Doctor later exploited this to make information that the Inforarium sold about him memory-proof. (HOMEVID: The Inforarium)
Within the Dalek casing, the cortex vault catalogued all the memories of the Dalek mutant and suppressed those that may cause the Dalek to stop feeling xenophobic hatred. (TV: Into the Dalek) When the Daleks of the Dalek Asylum's intensive care ward cornered the Eleventh Doctor, Oswin Oswald deleted all the memories of the Doctor from the Dalek pathweb. (TV: Asylum of the Daleks) This gap in their memories caused the war machine of the New Dalek Paradigm to grind to a halt as the Parliament of the Daleks debated the identity of their now unknown foe. When they turned Tasha Lem into a Dalek puppet during the Siege of Trenzalore, her own memories of the Doctor were uploaded to the pathweb, allowing the Daleks to regain their memories of their foe. The return of the memories drove the Prime Minister of the Daleks insane. (TV: The Time of the Doctor; PROSE: The Astounding Untold History of the Greatest Enemies of the Universe)