Risk 2: Tracking cookies
Use your browser's security or privacy settings to reject third-party cookies -- that is, cookies that originate from sources other than the site you're on.
Blocking all cookies can be problematic if you want specific sites to remember your log-in info or preferences. Blocking third-party cookies, on the other hand, won't inconvenience you on most sites but will take your privacy up a notch.
Note that blocking new third-party cookies won't actually get rid of the ones that are already on your system. So to be thorough, you can use your browser's security/privacy settings to either delete all of your current cookies at once -- which means you'll have to re-enter log-in information or preferences at certain sites (but only once) -- or look through your cookies file and manually delete those that aren't from sites whose cookies you want to keep.
However, some services -- notably Doubleclick -- have been able to install cookies even with third-party cookies blocked. You can opt out of Doubleclick's cookies by, ironically, installing an opt-out cookie. But if you clear your cookies file at any time, you might also delete the opt-out cookie. Google provides tools and instructions for making your opt-out preferences permanent in Firefox, Internet Explorer, Chrome and Safari.
Another option is to take advantage of your browser's "private browsing" feature. The most recent versions of Firefox, Safari, IE, Opera and Chrome all offer private browsing sessions -- sometimes called "InPrivate" or "incognito" browsing -- that purge cookies and passwords when you close the browser, and also erase your Web history and browser cache.
The only challenge is remembering to select private browsing before you begin a sensitive search.
This will make a huge number of sites unusable, but it will make it much more difficult to track your online behavior. Note that you can add exceptions for sites you trust using the "Trusted Sites" list in IE8 (on the Security tab under Internet Options) or by clicking the NoScript toolbar icon and selecting "Allow" for sites you wish to accept scripting from to restore functionality.