An impromptu Birds of a Feather (BoF) session given by Dave Misell at the SPA Conference admirally demonstrated what happens behind your back when you visit a website. Key to the demonstration was showing (very simply) how much data is passed between sites using cookies and how much data is retained (for considerable length of time in some cases) between site visits.
The session used the Paros proxy server with Firefox which easily showed the web transactions when entering a simple URL (I won't disclose the URLs used in the demonstration, suffice to say that the sites were well-known). Using Paros, it is easy to see how much information is passed via cookies. Stopping cookies results in the same information being passed via URL (although this is more obvious since the data appears in some form in the address bar). In many cases the same data is passed to a number if websites regardless of whether the data is appropriate or useful to the receiving website.
Although it is possible to see the information being sent to a website, it is not possible to determine what is done with the data by the receiving site. In most cases the data is used to trace a journey through website (so that the 'user experience' can be improved) which is totally transparent to the user since these are performed server side.
So is it possible to stop the information being transferred? Not easily, but choose your sites carefully. There is some legislation in the EU which has tightened up the exchange of information through websites, particulalry to third parties, without the express permission of the user. Unfortunatley this legislation is dependent on where the website is hosted, which isn't always obvious from a simple URL. There is always 'education' which applies to both the end user and also to the developers of the site, and there are some good courses now which can help (e.g. ethical hacking and MSc in Information Security at Royal Holloway College in London) increase awareness.