This is all for the US.
Having a backup of a game that you own is legal, as Lostelle said, but modifying that ROM in anyway is not. For a non-ROMHacking example, you may back up your... we'll go with Sims 3. You can back up your Sims 3 (that you physically own), and as long as that backup is an exact copy then you're in the clear. That's perfectly legal. What is illegal is modifying that backup in any way (you might want to remove the DRM on it, for example. That's illegal.) The law on that is supposed to act as a deterrent for deleting DRM (as far as I know, that was its intent), but it technically catches ROMHackers too, since we're modifying backup ROMs to create our hacks.