Kindle Fire tablets in the next month. If you recently acquired an Android tablet or your students have, check out the Amazon Appstore for Android. Everyday the Amazon Appstore for Android gives away one paid app for free. From what I've seen over the last few weeks, the bulk of the apps they give away are games, but they do sneak in a non-game app occasionally.
You do have to have an Amazon account to get the free apps and the initial set-up with your device has more steps than the standard Android Market. If you can deal with those two inconveniences, a daily visit to the Amazon Appstore for Android could be a good way to score a good app or two for free.