Matt Cutts of Google reassures users and conspiracy-theorists in his recent blog post at http://www.mattcutts.com/blog/chrome-privacy/
Google's browser, Chrome, was released early September 2008, moving out of the Beta stage in mid-December. Upon its release, I began using Google Chrome, and it soon became my preferred browser. Early trouble with Google's own services such as Gmail were quickly resolved. I can count the sites I use that won't work with Chrome on one hand.
As with many other software applications, you can turn off the option to send crash information to developers. In Chrome, click on the wrench icon, choose Options, then the Under the Hood tab. Uncheck the option for usage stats and crash reports to be sent to Google if you are worried about what they will see. I have yet to see Chrome crash, despite my habits of having 30 tabs open at once.