What information does Google receive?
By default, Google Desktop Search collects a limited amount of non-personal information from your computer and sends it to Google. This includes summary information, such as the number of searches you do and the time it takes for you to see your results, and application reports we'll use to make the program better. You can opt out of sending this information during the installation process or from the application preferences at any time.
Personally identifying information, such as your name or address, will not be sent to Google without your explicit permission.
How we use unique application numbers, cookies and related information.
Your copy of Google Desktop Search includes a unique application number. When you install Google Desktop Search, this number and a message indicating whether the installation succeeded is sent back to Google so that we can make the software work better. Additionally, when Google Desktop Search automatically checks to see if a new version is available, the current version number and the unique application number are sent to Google. If you choose to send us non-personal information about your use of Google Desktop Search, the unique application number with this non-personal information also helps us understand how you use Google Desktop Search so that we can make it work better.
The unique application number is required for Google Desktop Search to work and cannot be disabled.
http://desktop.google.com/privacypolicy.html