ITPConnect is an extension for Joomla! that allow users of the site to login with their Facebook accounts. With this extension, you will take advantage from 540+ million people of Facebook. It will provide an easy way for registration of Internet users, which will increase the number of your customers.
Once your users establish the connection between social network and your site, they will be able to use all services of Facebook.
After successful authentication, the component sign up a new user automatically. The new user registration is performed by native Joomla code, and pass through all the standard verifications. The username is taken from the email of the user who connects to Facebook. The password is generated by the system automatically.
For login module, I use official "Joomla! Login Module". I just added a "Connection Button".
In the configuration settings of the extension will find a field for "Facebook Permissions". You can set the levels of access to Facebook's user data. You are also able to choose a profile picture size.