Comment by wahern
Closer to the truth is that the brain never completely forgets something, in the sense that there are always vestiges left over, even after the ability to recall or instantly draw upon it is long gone. Studies show, for example, that after one has "forgotten" a language, they're quicker to pick up it again later on compared to someone without that prior experience; how quickly being time dependent, but more quickly nonetheless.
OTOH, IME the quickest way to truly forget something is to overwrite it. Photographs being a notorious example, where looking at photographs can overwrite your own personal episodic memory of an event. I don't know how much research exists exploring this phenomenon, though, but AFAIU there are studies at least showing that the mere act of recalling can reshape memories. So, ironically, perhaps the best way not to forget is to not remember.
Left unstated in the above is that we can categorize different types of memory--episodic, semantic, implicit, etc--based on how they seem to operate. Generalizations (like the above ;) can be misleading.