Well! That took a bit of doing!
I have managed to get Android and Arduino talking to each other over bluetooth. Steep learning curve on the Android side of the fence, but got there eventually.
The goal is to dispense with having to wire up LCDs, potentiometers and miscellaneous hardware in order to control and get data back from an arduino project. To provide a user interface, in other words.
One approach is to set up a web server on the Arduino and generating HTML, but this type of thing is a whole slab of coding that you don't want to be doing on an Arduino.
Bluetooth seems IMO to be an appropriate tool for the job. Close range, not super fast, but cheap. Android devices are portable and can provide a UI that's as complicated as you like - graphs, knobs and dials, interfaces to email, dropbox, text files and so on.
There are several "Ardudroid" type apps available on the store, but I wasn't able to find an open source version. So I wrote one.
The current version is just the android app itself. The arduino project just echoes to serial and sends a heartbeat message every 5 seconds. No biggie.
the project release is here ArdDrive v0.1.
The APK has a self-signed certificate with no verification chain.