In the case of Nintendo, this is what they have to say:
Originally Posted by The Back Page of any Nintendo game manual from the last several years
Copying of any video game for any Nintendo system is illegal and is strictly prohibited by domestic and international intellectual property laws. "Back-up" or "archival" copies are not authorized and are not necessary to protect your software. Violators will be prosecuted.
Nintendo's official policy is that ROMS are illegal, regardless of if you 'own' the game or not. I'm fairly sure this can extend to all systems, software and music. You don't own the software, you only own the right to use it.
The irony of this law is that whilst Nintendo have a problem with you emulating their games via copies or back-ups, strictly speaking this doesn't apply to original copies. In short you can run it off the CD/DVD, but just not off a ROM dump...