
It depends. The problem with doing as you state is that unless the mother board in the computer you are moving the drive to is exactly like the computer you are moving it from, then you will have conflicts with the mobo drivers that are installed on the hard drive during the initial install of computer "A". In addition, Windows will scream and pitch a fit because other hardware (sound or graphics cards, CD/DVD, modems, etc.) is trying to use drivers that are not correct for them. Now, if the operating system happens to be WinXP then you will have even more difficulties because the authentication process WinXP utilizes will detect different hardware parameters which will cause you to have to do a clean install (or at the very least) a repair install and obtain a new activation code from Microsoft.
Hope this helps.
Kilowatt