Recently, I'd borrowed a computer from someone and used my iTunes Store account to play a song on it. But I forgot to deauthorize the computer before giving it back. Unfortunately, the computer also got reformatted and reimaged in the meanwhile. However, luckily, the authorization process does not depend on anything software-specific. It's like Windows Activation; they record some information specific to the hardware on the machine. This is generally a good thing because you can sometimes reformat your machine without remembering to deauthorize and this allows you to deauthorize any time as long as it's the same physical machine.
Here's a snippet from Apple's website regarding authorization:
Make sure you deauthorize your computer before you upgrade your RAM, hard disk or other system components. If you do not deauthorize your computer before you upgrade these components, one computer may use multiple authorizations. If you find you have reached 5 authorizations due to system upgrades, you can reset your authorization count by clicking Deauthorize All in the Account Information screen.