My wish to have traffic stats for user generated content hosted by Google is partly fulfilled. Google Docs has a new option to track published documents using Google Analytics. You need to go to the Settings page, enable the tracking option and add a Google Analytics profile ID. It's not clear whether you need to create a new profile or use an existing one, but both options might work.
After publishing a document, you'll see a small message: "Tracking visitor traffic with Google Analytics."
The screenshot below shows the source code of a published document: the first Google Analytics tracking code is used by Google, while the second tracking code is associated with your account.
The other hosted Google service that allows you to add Google Analytics code is Project Hosting. It's also easy to add the tracking code if you develop iGoogle gadgets.