As part of their series on Arduino and Android device interaction, Manuel Di Cerbo has written a short and useful tutorial on communicating between an Android app and an Arduino without using the Android SDK. Basically this involves using the Arduino board as the USB device, which is possible with the Arduino Uno, Freetronics Eleven, EtherTen, etc. Demonstration source code is available for the Arduino and Android app.
If you're looking to go deeper into Android and Arduino interaction - you will need an Arduino-compatible board with inbuilt USB host shield suitable for Android ADK work. So look no further as we have the Freetronics USBDroid board:
Apart from being a fully Arduino Uno-compatible, it has onboard microSD socket and the full USB socket and host-mode controller. As well as the Bluetooth application described above, this is the ideal platform for developing peripherals or projects based around Android devices with ADK (Android Developer Kit) functionality, but without requiring a USB host controller shield stacked onto an Arduino. For more information and to order, visit the product page here.