Want to stop info of yours from going out over Facebook's API? Then you'll need disable "Platform". (Go to privacy settings, and press "edit" for "apps, websites and plugins"). Go ahead and do it. I mean, who uses FB apps anyway? This ain't 2009. 
If for some reason you don't want to do that, at least edit "Apps Others Use" and uncheck all the categories of data there. (Note that data Facebook considers "public"--like name, gender, and friends list--will still be shared over API if you don't disable Platform.)
I will note with some pride that when Facebook tried in 2009 to take away the ability to opt out of Platform API sharing, we at @EFF called them out hard (along with the Europeans, natch), and FB ultimately restored it. So please: use it! eff.org/deeplinks/2009…
That said, though, it should not be the users' responsibility to prevent the kind of data misuse that is now being reported. That was Facebook's responsibility. And they blew it, whether you want to call it a "breach" or just the API working the way it was designed.
The hard part of this issue is that from a competition POV, we really do want and need Facebook to allow us to use our data with other services via APIs. Finding the right balance of security & usefulness is a hard one. But the options right now are needlessly broad and blunt.
Right now if I want to share Facebook data with even one non-FB app or service, I have to give permission for all of this so-called "public" data to be shared with any app that any of my friends use, including my social graph. We deserve more control. facebook.com/help/203805466…
