Allowing users to log in to your application using Facebook is quite common. It can be easier for users. It can give you access to demographic data with less work. But the API can die, change, or act generally unpredictable. And you have zero control over it.
This particular issue is impacting 9gag, Pinterest and others. Whilst many of these sites support user logins without Facebook, just as many of them don't. Imagine if tomorrow Facebook charge to connect to their API or there's some extreme exploit. How much damage would your application face?
[1]: http://techcrunch.com/2011/08/11/facebook-wins-worst-api-in-...