From MacOSXHints

comes this useful hint:

macosxhints - Reset Microsoft Office personalization and ID info

A company called McGimpsey & Associates has published information regarding the remove of the Office ID for several versions of Microsoft Office. This is useful to anyone distributing licensed copies of Office in a campus or office environment, ie. as a custom Mac OS X .pkg.

Two files must be removed to clear the Office 2004 personalization:

~/Library/Preferences/Microsoft/Microsoft Office Settings (11)

/Applications/Microsoft Office 2004/Office/OfficePID

Remove those files and you'll be presented with a registration window next time you launch any Office app, allowing you to input a new name/key combo.

[robg adds: This hint does not explain how to pirate Office. When you remove these files and re-run any Office application, you'll get the registration dialog box again, allowing you to type in your name and serial number again. I actually had to go through this once at my previous job -- a user had typed their name incorrectly, and wanted to re-enter it correctly. I was thinking there would be an easier method, but in the end, we found and removed the above files. Note that the linked page also explains how to reset prior versions of Office, which have slightly different files.]