If you log into your account in the iTunes Music Store (click your Apple ID in the upper right), you will see the number of computers that are currently authorized. Although you can not see the computer serial numbers or edit them, once you have the maximum number (5) of computers authorized, a button will appear to Deauthorize All computers, effectively resetting your music rights.
[robg adds: I wasn't aware of this hidden feature, and I'm presently sitting at four machines, so I can't really test it. Kirk McElhearn told me that he's heard you can only use this feature once per year. If anyone knows for sure, please post...]

