[wampus]

If the button image is hosted on Facebook's servers (and it commonly is), they have a log of your request for it, including the page it was on (from the "Referer" header). This request is sent when you load the page, without the need to click on the button. Every site you visit that includes a Facebook resource gives them the ability to collect data about you and your habits. These are often part of a site's template, included without regard to the page it might appear on. You'd be surprised what a Referer URL can reveal about you.

[ptaipale]

Oh, that's what you meant. It was too obvious to me :)

I mean, of course elements that are embedded in Web pages may be traced by the party who sends them (and pages very often include off-site content).

[TazeTSchnitzel]

It's not just an image, either. It's typically a widget that may even show you if your friends also liked the page.

[ptaipale]

And, in fact, one should not trust that even if a page says my friends liked the page, they actually did.