Come on, we already have a perfectly good protocol for this, OpenID. It's unfortunate how big companies try to lock users in their own authentication services rather than educate them about OpenID (although I think the new JanRain widgets turn OpenID into a "Connect with X" service, which is great).
As others have pointed out, OpenID isn't even better than Facebook at what it specialises in: at best OpenID asks the user to remember whether they signed up with their Yahoo ID or their Gmail one and at worst to read a third-party FAQ just to figure out how to log in. Facebook Connect is a big blue button with a recognisable brand, and you're quite possibly already logged in.
If only their API wasn't such a piece of shit...