Make Tech Easier recently posted a walkthrough for doing this with Google Analytics that doesn't involve registering an FB application. I'm actually not sure why that step is even there(in John's answer); it seems not to be for simply tracking the likes, but so that you can use the Facebook Insights tool in addition. If you want that, fine, but I had no call for it.
Try Facebook Analytics: http://fa.baldsoft.com/
It's a free tool, enabling you to define list of URLs and then you get all the necessary statistics. If your web runs under WordPress, it's even easier, because it can read URLs directly from WP database.