There is an important distinction however with regards to exercising the so-called "private copy rights" — at least in the case of European law, I cannot speak about other regions — which is that the source of the data you copy must be licit. Which means that your private copy right allows you to copy the ROM from a cartridge that you bought, but not copy the data from a torrent since (presumably) the uploader had no right to put it there.

Post-scriptum : read that for a better understanding of why it matters where the bytes came from, even if they are identical and should make no difference from a computer science point of view : http://ansuz.sooke.bc.ca/entry/23