(This is a Community Wiki question. Please edit the post directly.)
Please recommend applications that are broadly applicable in the classroom. Try to focus on eductional apps (e.g. iStudiez Pro) rather than just generally good apps that could be used in class (e.g Bento).
iStudiez Pro (and Lite)
Timetable and assignment tracking application. A really fantastic app. Although it's a fraction US- and University-centric, it can definitely be put to good use in senior stage schools too.
Mental Case
Flashcard app that can sync with the Mac to transfer card packs. Has a nice "classroom edition" that makes deployment easier to a class.