I have searched for the answer to the above question but cannot find a direct answer.
I am about to sell my PC and would hate it if my backup would not restore on a new system.
I am using the standard Windows 7 backup procedure.
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I know from experience that the non-image backups restore well on other hardware, and I would be EXTREMELY surprised if you couldn't do that with the image backups as well. However, before you sell your computer with the old hard drive, you should be CERTAIN you have securely wiped the hard drive; see this list of programs that can securely wipe your data.
Note that the story at the top of the list was nowhere near as bad as it could be: in the story that precedes the list, somebody gets embarrassed. You could get actually your identity stolen if you don't wipe your drive securely: people keep credit card information, passwords, and other sensitive information on your computers, and anybody you sell the computer to can read these unless you either keep the drive or you make certain that you securely wipe it.