Agent86 - this works fine for 95/98 and maybe 2000/NT, but probably not for XP because of the copy protection features. Maybe one could get away with it if you used an identical HDD and changed the volume ID to be the same as the original disk (and then maybe not).
There are a couple of utilities out there that allow you to change the volume ID of FAT or NTFS HDDs - search for "change volume ID" on Google.