Kerimil shows us how to communicate between Arduino and a custom Android app. It uses Bluetooth, and the MIT App Inventor for the app code.
Here are a few projects people have made that could provide a base for other projects. They aren’t as common as full projects, but they do provide a solid foundation for your next idea.
Andruino lets you control your Arduino projects using your Android phone. The app is free to grab and use in your own projects.