I build joomla sites for a living and every site owner wants this now. A couple years ago there were a handful of small integration plugins (mainly sso, or single-sign-on), now there are dozens. The problem for all of them is Facebook is dynamic - constantly improving (or at least making changes!).
So your facebook-joomla integration needs to be a little more robust than just SSO, and if you want to do it right (and not have to keep going back to fix sites) you should use jfbconnect (http://tiny url.com/29a7qer
) and do so on a subscription basis... they keep up with the latest FB is doing, retool, and give you the latest upgrades. For $50 it's more than worth it, esp. if your site uses jomsocial, community-builder, etc... or any type of commenting system.
For example, you know those little notices you get in FB that your friend wants you to try some new app or it's your turn to play a game? That's in the latest jfbconnect pkg (see image) ... free for me because I have a subscription. This let's you send messages to page followers as those types of requests. Very cool and with all the anti-spam (anti-business?) algo changes within FB it's probably the best way to engage customers these days via FB... and I think JFB is the only tool that has really kept up with this.
I'm not big on "only 1 way" to do things, but in this case, the jfb developers (sourcecoast) have earned it. Heck, even joomla.org uses jfbconnect for their facebook integration.