The ability to control what we remember could have enormous implications, ranging from programming trauma victims to eliminate painful memories to strengthening our ability to retain certain types of information. “In the case of truly traumatic experiences, it's necessary to prevent the intrusive memories of those traumas from dominating your day-to-day life,” Dr. Anderson adds. “People who experience persistent reminders, flashbacks and nightmares are very troubled by these things, and it can be debilitating. There is value in reducing the influence of those things on your everyday thoughts.”

Forgetting is an important function of the brain:

http://www.nature.com/neuro/journal/vaop/ncurrent/full/nn.3973.html

Interestingly, remembering can trigger forgetting:

Conversely, participants' memory of the hat grew weaker, and they became increasingly unable to distinguish which picture they had first been shown when given the choice between two images. The fact that one memory became more vivid while the other grew less clear demonstrated that we have the ability to diminish the power of certain thoughts.

“Remembering can cause forgetting,” explains one of the study’s researchers, Dr. Michael C Anderson, who has worked on a number of suppression theory papers during his career. “It's a form of active forgetting that people aren't necessarily aware of. The patterns of the way we use our memories can shape what remains accessible and what doesn't.”

“Forgetting arises when other competing traces interfere with retrieval and inhibitory control mechanisms are engaged to suppress the distraction they cause,” the paper reads. Dr. Anderson called the results surprising, and said they “could tell us more about selective memory and even self-deception.”