If you are using "Facebook Connect" to add a Facebook comments box on your web site, Facebook gives you no way to be notified when someone has posted a new comment -- I guess you are expected to just go and hit reload on each of your pages that accepts comments to see when a new one has arrived? Seriously?
So, this script uses the Facebook API to create an RSS feed of recent comments posted on your site via your Facebook Application. Run it from cron.
Likewise, it can generate a feed of comments posted to a "page" on Facebook itself, another thing for which they provide no RSS-based notifications.
Also, if you authorize your application to have full read-access to your personal Facebook account (which might not be a good idea, depending) then this script can generate a feed of any photos that your friends have posted -- which I wanted since, for no sane reason, photos are omitted from the RSS feeds that Facebook does provide.
See also: Mirroring Twitter onto Facebook, plus bells, whistles.
Update, Jul 2012: I no longer use Facebook Connect, so I don't need this for its original purpose; but in the intervening years, I had been using it to convert my Facebook stream to an RSS feed. Then of course Facebook went and deprecated the API that I was using so I rewrote that part as facebook-rss.pl.
Twitter/Facebook integration into LJ... +1 to the deathwatch counter. I'm waiting for the "Export my LJ as a WordPress XML dump" option ;-)
Are you running a sweepstake as to how long it will keep working before Facebook break it? [insert sarcastic emoticon here]
Interacting with Facebook has given me new appreciation for LJ in many ways.