Spend some time browsing through the Anonymizer proxy or Lucent Personalized Web Assistant, which screen out your identifying information before it reaches webservers. Are there sites you feel more comfortable visiting anonymously?
Find your cookies file to see who's been feeding your browser. Search for Netscape's file cookies.txt or the Internet Explorer folders \windows\cookies or \windows\Temporary Internet Files.
Turn on cookie warnings for a day to see how many sites are offering these treats. If you're baffled by the number of menu items you have to go through to make this choice, visit the Junkbusters site or Cookie Central for browser-specific instructions. Notice that cookies are enabled by default on a new browser.
Run a few searches on your favorite search engine (try Yahoo, AltaVista, or Excite) to see what targeted advertising you get. Browse Amazon for a book and watch its recommendations.