Updated 25th April 2012: since writing this post, it seems that Google removed the ability to use your Analytics id to track published Google Docs, which means this post probably isn’t much use to you now.
Browsing this morning, I discovered that you can track views of your published Google Docs using your Google Analytics account.
A published Google Doc is one that you have chosen to openly share with anyone on the web.
To switch on tracking of your published Docs, go into your Google Docs account, choose Settings then the Editing tab.
Select the checkbox next to Use Google Analytics to track the number of visits to your published documents and paste in your Google Analytics tracking code:
Views of all documents published from this account will now appear in your Analytics reports.
How to publish a document
To publish a Google Doc, go to Share > Publish as a web page:
Next choose Publish document:
Limitations
Note that this feature currently tracks published documents only. At the time of writing, tracking isn’t available for spreadsheets or presentations.