I was thinking about this a couple of days ago - with Like buttons appearing all over the internet, Facebook has the ability to log what sites you visit, when you visit them, etc. Question is, do they? To what extent?
Of course they do. To the maximum extent they can manage. As the saying goes: if you are using a web service for free, you are not their customer, you are their product (or something like that).
The purpose of the Like button is to enable you to share stuff back to Facebook when you click on it. We anonymize all logging data collected as a byproduct of serving the Like button and other social plugins within 90 days of their collection. See https://www.facebook.com/help/?faq=186325668085084.
