follower, the creator of the Handbag “Android Arduino Accessorizer”, wrote in with this excellent use of Android’s Open Accessory API, Arduino, and an LCD screen:

The Android App is invisible and starts automatically when you connect the accessory. (You probably need to approve the running of the application within a few seconds or the accessory may time out.) A background service is started which displays a notification of the accessory found, listens for new text messages and starts sending the current time to the accessory for display. You can use your phone as normal while the service is running in the background.

When the accessory is disconnected the notification is removed and the background service cleans up after itself before stopping.

Dual-screen Nexus One by follower