There are Gameboy and Gameboy Advance emulators that are pretty good time-killers. Just be sure that you already own the games for any ROMs you intend to download.
If your plan has limited data usage (be sure to read the fine print) there are apps that will not only let you monitor your data usage, but also restrict it so you don't go over any limits your carrier sets. A great way to avoid big fees.
Many banks will allow you to perform online banking through their apps which is quite useful when you are "on the go".
All of the major social networking sites offer apps that are easier to use than through the browser.
Speaking of browsers, the Opera browser has a special feature that makes it particularly useful on mobile devices; it will automatically send images on webpages through a special proxy that lowers their quality before sending it to your phone. This makes image-heavy sites loads faster and uses less data. You can alter the level of compression (or turn it off) in the programs settings.
Gmail seems to work the best on the Android platform, so consider forwarding your other email accounts to a Google account (they are free). You can still access your regular mail through other apps, but the level of service and features aren't always that great.
Just so you know, WiFi is a real battery hog so disable it when you aren't using it. Do the same for Bluetooth and GPS if you don't need them.
