[Ryoku]

Well, your privacy is simply limited to whatever permissions you give to the web app you're logging in to (And all your public information as well), on one side. And on the other side, facebook records all the websites you visit who have a connection with them, when you do and for how long, etc. If you're comfortable with that, then... Well, you've got half the problem down.

I think what would really be worrying is the amount of power you are giving to a single authentication method. You are putting "All your eggs in one basket" As soon as someone is able to compromise your facebook account, either by facebook's or your own fault, all your other facebook connected accounts will be compromised; and the attacker can simply check your security app settings to know who have you logged in to.

And then again... What will happen when Facebook is not around anymore? Will all the websites you logged in to have a nice easy fallback option? Or will some/all of your related accounts be lost?