It's a compelling enough idea that Eternal Sunshine of the Spotless Mind built its entire plot around it: selecting and erasing certain memories from the human brain.
After all, we all have a skeleton or two in our closet, and an idiocy or two thousand in our past that we'd like to just wipe off the record. Wouldn't you, if given the chance, choose to erase from your mind that one time in eighth grade that you got hammered on spiked punch and tried to grope your math teacher on the dance floor?
One boy's drunken error was the greatest night of Mr. Jameson's life.
The Sci-Fi Solution:
Well, soon you can! Science has been tinkering with the memory parts of the human brain for quite some time, for reasons that range from potential military applications to curing Alzheimer's disease to "because they can." In fact, some successful lab tests on memory alteration have already been made.
"We found our car keys! Thank you, science!"
"But Cracked," you say, "surely that means nothing? Some wacky doctors playing with lab rats are light years away from any actual, tangible results on humans." Good thing, then, that one Dr. Merel Kindt and her team from Amsterdam University -- Amsterdam having no shortage of people with memories of the "Oh fuck, what did I do last night?" variety -- have already performed memory drug tests on human subjects.
Their project has dealt exclusively with dampening bad memories. Naturally, scientists being scientists, they first artificially created said memories with a slightly serial killer-y method of electric shocks and pictures of spiders, but still -- they managed to tamper that very specific fear-memory back into obscurity, so it's probably OK.
"What a curious little creat- OH MY GOD, IT'S GOT MY HAND!"