Be-Bound, a new app launched recently and available only on Android for now, promises to help when you have network coverage but no internet connection (or when you don't want to cough up for internet access, whether because of frugality or stubbornness). Even without an internet connection, it gives users access to a small suite of services, including search, email, weather, stocks, maps and Twitter, among others.
It works through text message, which, like an internet connection, is simply a way of moving information around. Request your email through the app and it will send a text message (much like how you can tweet via text message without an internet connection) to its servers, which process the request and deliver the data back the same way. Be-Bound charges a small fee to act as the go-between, but it still works out to be much cheaper than either paid wifi or data roaming.