In a new study, published in the Journal of Psychiatric Research, the drug propranolol is used along with therapy to "dampen" memories of trauma victims. They treated 19 accident or rape victims for ten days, during which the patients were asked to describe their memories of the traumatic event that had happened 10 years earlier. Some patients were given the drug, while others were given a placebo.

A week later, they found that patients given the drug showed fewer signs of stress when recalling their trauma.

Similar research led by Professor Joseph LeDoux has been carried out at New York University on rats; scientists were able to remove a specific memory from the brains of rats while leaving the rest of the animals' memories intact. An amnesia drug called U0126 was administered.

The rats were trained to associate two musical tones with a mild electrical shock so that when they heard either of the tones they would brace themselves for a shock.

The researchers then gave half the rats the drug when playing one of the musical tones.

After the treatment, the rats that had been given the drug no longer associated that particular tone with an imminent shock but still braced themselves upon hearing the second tone, demonstrating only one memory had been deleted.

Science fiction fans have a number of associations with the idea of banishing unwanted memories. In the 2004 film Eternal Sunshine of the Spotless Mind, Kate Winslet and Jim Carrey play lovers who have a falling out. Winslet's character goes to a company called Lacuna, Inc. to have her memories of the relationship removed.

(Jim Carrey gets spotless)

In the film, the process involves showing the person a memento of the relationship and then encouraging them to bring up specific memories while an electric shock is given. Not to give away the film, but this technique does not work as planned.

Here's a memory you might have repressed. In the classic Star Trek episode Requiem for Methuselah, Jim Kirk becomes enamored of Rayna, a beautiful woman who turns out to be an android created by a five thousand year old man who calls himself Flint, who was also Leonardo DaVinci and Shakespeare (among many others) during the course of his long life. Flint wants Rayna for himself, Kirk wants her, she loves them both, her circuits overload resulting in her death, and Kirk is devastated.

(Rayna and Flint)

Finally, Spock saves the day by applying a little-known property of the Vulcan mind-meld, which is that he can make Kirk forget about his sorrows and return to duty.

Philip K. Dick was one of the first to make use of this idea. In his 1966 short story We Can Remember It For You Wholesale he writes about selectively erasing memories:

Someone, probably at a government military-sciences lab, erased his conscious memories; all he knew was that going to Mars meant something special to him, and so did being a secret agent...
(Read more about erasing memories)

In related stories, see how researchers have developed a technique that Detects False Memories; also, read about how you can Hack Your Own Reality - The Virtual Way to have better memories than the ones you actually have.