I'm guessing most book reader apps will let you read books offline (once you've downloaded them), but this one is so good I haven't tried any others. I love it because it has a lot of public domain books for free, like many of the older classics.
- CoPilot Live
(link to USA version 8 )
Did you know you can use your Android phone for GPS navigation even without a data connection? CoPilot Live is a full-featured GPS app that lets you download map data ahead of time so you can use your phone as a GPS offline. It's not perfect, and nowhere near as good as Google Navigation, but it's well worth the savings on an expensive monthly data plan.
I'd recommend version 8 over version 9, mostly because the developers are using some pretty crummy bait-and-switch techniques and have split version 9 into "Standard" and "Premium" versions. The catch is the Standard version doesn't actually come with any features one might consider standard in a GPS app/device today, like 3D navigation, text-to-speech, and alternate routing. Let them know (via your wallet) that you think that's lame.
- ESV Bible
Many of the Bible apps out there require a data connection, and even when they let you download specific translations for offline use, it may not be the ones you want. If you're looking for a good, accurate, literal translation, the ESV is an excellent choice, and this app will do the trick.
- Merriam-Webster Dictionary
This is a full-featured English dictionary that works just great offline (except for a minor feature or two, like word-a-day). By full-featured I mean that it even lists example usage, origins, synonyms and antonyms.
If you're watching what you eat, most calorie counting apps require a data connection to look anything up. While GoMeals is a little sluggish, it does contain the entire CalorieKing database, which is quite extensive.
This is a really cool app that will let you monitor your data usage by app, and even limit or block specific apps. There are some other great apps out there that let you monitor your data usage, like My Data Manager Free, but this is the only one I've seen so far that lets you go the next step and block data usage for particular apps (at least the only one that doesn't require your phone to be rooted). The developers have stated that it's only free for a limited time, but it just may be worth paying for (provided it's not a recurring fee, which would defeat the purpose).
This app lets you create customizable widgets that will let you toggle many settings, including your data connection, allowing you to turn off mobile data altogether when you don't need it.