Quite funny, we just have this discussion this morning: we ask ourself if one should propose a Facebook or Twitter login while designing a new login page. MailShimp in Social Login Buttons Aren’t Worth It gives some really good reasons (and analytics) not to use social login buttons:
Sometimes you log in with Twitter, sometimes with Facebook, sometimes with a username and password specific to that app. It’s hard enough to remember your username and password, let alone which service you should bloody use to log in. As you add login buttons to a page, you also add decision points for users, while creating visual complexity in your design. The marginal gains in login rate are chipped away by the additional cognitive load you’re adding for your users.
Is it worth it? Nope, it’s not to us.