Great list of the 25 Facebook Apps for Education and Learning over at CollegeDegree.com
Heard great things about Courses which "display your courses on your profile for college or high school, find classmates, manage your schedule and assignments, create discussions, post notes, and form exclusive study groups. Welcome to Courses on Facebook." I don't currently have any courses, so I can't give it a first-hand review.
Also love the JSTOR Search app which lets you search scholarly journals directly from Facebook. You do have to add your school or public library proxy first, which means independent scholars may be able to access it if their library doesn't participate. The developers actually work at JSTOR which is an added bonus and seem to be very open to suggestions and feedback.