Except from the White House's point of view, because they get to harvest your email address.

Did you notice there's a Facebook Like button?

So Facebook knows when you go to a government site.

I imagine Facebook also knows which petitions you sign, or at least which ones you click on. I say imagine, because although I'm signed in, it still asks me to sign in before I can sign the petition, and signing in while I'm signed in leads to a 404.

Can they use them for anything? Wouldn't it be illegal to use them for any political purpose at all?

I never understand the gambit about trying to hide your email address and I understand it even less here. Who cares if the White House has my email address?