This Bluetooth module ties directly into the Tx and Rx lines of the Arduino so a wireless serial connection between an Android device can be established.

Instructables user ASCAS shows off how to add voice control to your Arduino projects using your Android phone and Bluetooth. The Arduino gets a Bluetooth attachment and a set of code.

The Arduino half of the software relies heavily on [Oleg Maruzov’s] PTP/USB libraries to get things done, but the free Android control app is all [Manishi’s] creation.

This project incorporates communication between an Android Phone and the Arduino using Bluetooth. The basic functionality includes taking messages from an android phone, displaying them on an LCD ...

Thanks to the LightBlue Bean+, however, one of those roadblocks has been torn down. The Bean+ is basically an Arduino board that can be programmed via Bluetooth LE.

For now, it's only possible to connect to an Arduino board through USB via an OTG cable, but joaomcgd says he plans on adding support for Bluetooth or Wi-Fi receivers in the future.