Google now allows you to see some of the information they have collected on your from your various accounts (e.g., Gmail , Picasa, etc.). The announcement is available at: http://googleblog.blogspot.com/2009/11/transparency-choice-and-control-now.html and the dashboard view is available at http://www/google.com/dashboard (you need to log in with your Google username and password to see your data.)
I took a look, and I have to say that I was expecting to see more. What I did see, and what the New York Times Bits blog also noted, is that most of the information that is listed on the dashboard is simply the kind of humdrum stuff you already know about your account. For example, how many pictures you have stored in your Picasa Web Album and how many emails you have stored in Gmail. I guess I was expecting something more along the lines of "this dude is 40, male, and here's the last web site he visited," but there is nothing like that to be found in Dashboard.
The Bits blog entry also quotes John Simpson of Consumer Watchdog who says essentially that the information in Dashboard is the info linked to your name, but the real dirt is in the information linked to your IP address, which Google is not revealing for now.