You can, but it's not legal, at least not in the United States. It's never really been litigated, but a reading of law would seem to say it's not legal. There's no "personal use" or "personal backup" clause in the law. It's a copy, and copying is not OK outside of the "fair use" bounderies outlined in section 117 (there's also some provisions for libraries and archives, but those don't apply to individuals).
Legality is really tangential to the point, however. The question is that for any given work, whether that's a book, piece of music, game, etc, do you "own" that work seperate from the physical media you purchased it on. Can you obtain a ROM, a copy of the book or a copy of the record in question legally in perpetuity because you bought it in one form once?