When I look under the General tab of System Properties, I see the following:

"Registered to:

<My name>
<Company>
XXXXX-XXX-XXXXXXX-XXXXX"

My question is, what is this 20-character number?

It's an ID code for the disc used to install Windows on the machine. It's not the "CD key" which you have to enter during the installation, but it IS a unique ID 'name' for the specific install disc that you have.

In other words, it's a publically viewable unique ID for your Windows installation.

Thank you for the info.

Are there any other ways of uniquely identifying an installation of Windows? Possibly identifiers that would change from installation to installation even using the same Windows XP CD?

To clarify, is there a method of uniquely identifying a computer that would no longer work after Windows was reinstalled?

The only thing that would provide you with a different ID is a different key. All copies of, say, Windows XP Pro SP2 have exactly the same files(file names, file versions etc). The only thing that sets them apart is the installation ID, which is generated using the CD Key used to install Windows. Hence, you could install Windows on 2 machines with the same key, they would have the same installation ID.
Why wouldnt a computer work after reinstalling Windows?

Do you mean a way for users to identify a particular PC, in order to aid with a Incident Report system.

If you do, my advise would be to label the PCs, for asset tracking, and use the same for the Computer Name. (You can change the computer name, to something of your liking, from that menu).

That way, each system can be accessed via its name, for accessing remotely their Harddrives, or remote control; SMS, VNC.... and the user can tell you the PC name, by the asset tracking label.

That is the system we use, and it works well. I would advise it for all medium / large businesses.