ArduDroid APP
PLEASE RATE: This is a free app and only through your ratings I can determine if it's worth supporting or discontinuing.
1) Control Arduino's digital and PWM pins.
2) Send text commands to Arduino Uno.
3) Receive/Send data from Arduino Uno over Bluetooth serial using the ever popular HC05 Bluetooth over serial module. It may or may not work with other Bluetooth modules.
This app used to be named Andruino but has been changed to ArduDroid to avoid a naming conflict with another app.
For complete documentation and related downloads:
http://www.techbitar.com/ardudroid-simple-bluetooth-control-for-arduino-and-android.html
You can also try my free SensoDuino app which harvests over a dozen Android phone sensors for your robotics,VR, or UAV projects:
http://play.google.com/store/apps/details?id=com.techbitar.android.sensoduino