The immortals from the webcomic El Goonish Shive do something like this to avoid insanity, passing only important memories into their new lives. It tends to lead to panic (due to half-remembering important things) or unwanted obligations in their next life.

It would be helpful, if still dealing with a human brain, to forget things in order to remain sane. Simulated brains which have the ability to forget removed end up acting pretty much exactly like schizophrenics brains.