An excellent book which covers this topic is Permutation City by Greg Egan (1994). If we can clone all of you (physical characteristics, brain, memories, personality) into a simulation, what are all the implications?

In it, a perfect replica of a person is scanned, and when it boots up, it continues it's existence from the time of the scan. Hacking on the model is possible, so you can avoid certain memories, update "physical" appearance, etc.

Given how prevalent virtualization has become recently, I thought it was a fairly modern book. I was surprised to find out it came out in the nineties, and not only has it held up well, it would be considered visionary even if it had been published yesterday.