I am a Facebook developer who runs a popular quiz application (myPersonality). Firstly, I don't understand why this article is picking on quizzes, since any application that you use will have access to your profile. Secondly, Facebook has a couple of good ways of preventing spam from any application. At the start, an application has to specifically ask for an "extended permission" to send you an e-mail. That means another box pops up and the user has to choose to receive e-mails from that application. Even after a user has given permission, applications never actually have access to your e-mail address - all they have is the ability to tell Facebook to send a specific user ID an e-mail on their behalf. This means that if you remove the application, it can no longer e-mail you as Facebook simply denies the request.
Finally, although an application is given access to your profile information (age, gender, etc. but not e-mail address or phone number), the Facebook developer terms state that it is not allowed to store it for longer than 24 hours from your last use. Although this doesn't stop applications from doing it, at least if you find out then you can report the application to Facebook and they will take action.