The problem that seems to be impacting potentially thousands of sites is that clicking on a Like button results in an error stating "The page [page URL] cannot be reached." A bug has been filed with Facebook and the developers status page indicates that the company is actively working on a solution.
This bug seems to be occurring at random -- everything from small sites to some pages on CNN.com are reporting problems. When users click on a button, a red "error" link appears and a pop-up is then displayed saying the site cannot be reached.
Users and web developers are understandably upset that their Like buttons not working properly. In just a few weeks, Facebook's Open Graph API has been installed onto hundreds of thousands of websites and is being used increasingly by publishers as a way to measure and increase traffic.
Incidentally, an error that was occurring on a few CNN.com posts was seemingly fixed by changing the button text from "Like" to "Recommend." That may be purely coincidental, but we did notice that upon making that change, the buttons that previously didn't function now work. Developers might want to give that a shot and see if the change in preference yields any improved results.
We'll keep you updated with any new information as it is released.