Форуми / Cotonti / Extensions / Facebook Plugin?

It logs you in automatically if it finds an existing facebook connection linked to your Cotonti account.

Added 8 hours 23 minutes later:

Well, guys, current version is ready for testing. You can grab it here.

What this plugin enables your visitors to do:

• Login to your site using their FaceBook account
• Register new account on your site with some fields prefilled by FaceBook
• Link existing account with FaceBook account
• Logout from both your site and FaceBook (separate logout is not technically possible if accounts are linked and logged in)

Notice that you have to register your site as FaceBook application in order to use it. FB developer docs are located here. Apart from installing the plugin and filling the configuration (AppId, Secret), don't forget to put tags into your header.tpl.