"Connect via Facebook" — these words are coated on over a million websites nowadays, but Facebook Connect poses a risk of leaking personally identifiable information to those third parties. If you're not convinced Facebook Connect is safe, then turn off the flow of personal data to those websites!
Brian Kennish, an engineer at Google, has developed an extension for the Google Chrome web browser, called "Facebook Disconnect". This extension blocks all traffic from third-party sites to Facebook servers when browsing the web via Chrome. You will still be able to access your Facebook account itself, so for those of you who want to get rid of Facebook completely, check out some of the more drastic options.
To use Facebook Disconnect, simply download and install the extension, available here.
"Although I'm an engineer at Google on the Chromium project, the work here is entirely my own and in no way endorsed by Google."
For those of you who don't use Google Chrome, there's another option— Adblock Plus.
"Annoyed by adverts? Troubled by tracking? Bothered by banners? Install Adblock Plus now to regain control of the internet and change the way that you view the web. You can also choose from over forty filter subscriptions to automatically configure the add-on for purposes ranging from removing online advertising to blocking all known malware domains."
Here's an overview with complete instructions from ProCasts, showing how it works, how to install it, uninstalling it and how to get help: