It seems to me that one of the most difficult things about preparing training material is finding applications that students can explore; a set of public applications that can help us to teach software testing. These may be applications based on traditional testing exercises, applications written specifically to challenge or puzzle testers, games that highlight a particular aspect of software testing or an application with unintended and interesting behaviours.
Here are some of the things I have found or been pointed towards:
A simple parking calculator hosted by Adam Goucher for testing based on the original from Gerald R Ford Airport. The challenge I was given was to find the maximum dollar figure I could be charged for parking.
The horse lunge game, which is a nice application for state transition modeling.
The Triangle Tester exercise from Elisabeth Hendrickson, with background information that can point you to specific bugs for investigation.
James Bach recommends the White Box exercise and Lye Calculator.
I'm very interested to learn what else is out there, please leave a comment.