False Memories are Common [...]

Memories are not stored the way an event is stored in a video or audio file. For something to be remembered, it must be recreated. Furthermore, each time we remember something, we alter our memory of it. In the case of remembering events, the more we remember an event, the more we are likely to have distorted it. Surprisingly, the most-remembered events can sometimes be the least reliable.°

The psychologist Jean Piaget had a particularly interesting false memory. He believed he was the victim of an attempted kidnapping:

… one of my first memories would date, if it were true, from my second year. I can still see, most clearly, the following scene, in which I believed until I was about fifteen. I was sitting in my pram, which my nurse was pushing in the Champs Elysees, when a man tried to kidnap me. I was held in by the strap fastened round me while my nurse bravely tried to stand between me and the thief. She received various scratches, and I can still see vaguely those on her face. … When I was about fifteen, my parent received a letter from my former nurse … she wanted to confess her past faults, and in particular to return the watch she had been given as a reward. … She had made up the whole story. … I, therefore, must have heard, as a child, the account of this story, which my parents believed, and projected into the past in the form of a visual memory. (Source)

False identification of criminals from victim and eyewitness testimony presents a similar problem (Link)

Reconsolidation theory provides insight into why this happens. See Engram Lifecycle