For me, the biggest benefit is the speed with which you can get a new user into your app or site. With a couple of clicks, they are in and you know quite a bit about them. No email verification or lengthy forms requesting personal information neccessary, since Facebook already did that for you.
It's a huge help that you can get a lot of profile information with little effort or conversion rate impact. Try asking a potential user of your new and unknown site for their birthday, hometown, full name, email, phone number, list of friends, profile picture, work history, etc, etc, and see how that changes your signup form conversion rate. Facebook Connect allows you to get this data by leveraging a user's trust in Facebook as a company.
Another benefit is that you can assume with some certainty, that the person signing up is real and not a random drive-by user creating a throw-away account. Of course, the Facebook account could be a sock puppet, but this requires more work and foresight than simply allowing someone to select a username and enter a junk email address.