The only place I have found where volume labels and ids can be important is in some Linux distributions (determining where a filesystem should be mounted). I've never heard of it being used as a copy-protection mechanism for games (but that's a technology that I am not particularly familiar with).
All the games on my computer use a serial number, sometimes in conjunction with Internet verification, that is stored in the registry. But that doesn't mean that other techniques don't exist.
Perhaps if you say what games you had problems with someone more knowledgeable may have the answer. I've never come across a case where a disk image didn't restore everything to how it had been.