You don't even have to click on the Facebook "Like" button embedded on a website for it to start tracking you – just opening a page with one will send your IP address, browser ID, and the date and time to Facebook.
This happens regardless of whether you're a Facebook member or not. However, it doesn't have to be this way. If you want to stay as unobserved as possible while you surf the net, and also don't want to be faced with constant permission queries, you can block Facebook's "Like" button with a browser extension.