Among other interesting things, Android 4.3 introduced a proper way of accessing notifications from an app. I used this API to make an external notification light for my phone:
It uses Adafruit's Trinket, a Bluetooth serial board from dx.com to talk to the phone and it's powered via USB. Here's a diagram of the connections:
The Arduino sketch that's running on the Trinket is very simple, it listens on the serial line that's connected to the Bluetooth board and turns the LED on and off depending on what character is received. You can see the sketch here. On Android side, the code is also pretty simple, there's an intent filter in the manifest to register a listener that gets called whenever a notification is posted or dismissed. In the listener we check what notifications are active and if they requested the notification light to be turned on (your phone might not even have a notification light, but the information is still there). Then we connect to the Trinket via Bluetooth and tell it to turn the LED on or off. You can see the code here. There is no UI and the Bluetooth address is hardwired.
There is no special permission in the manifest to let the app access notifications, instead you grant access via a checkbox in the security section of your phone's settings:
As usual, there's room for improvement. For example if the phone fails to connect to the device via Bluetooth (because it's out of range or powered off), it should probably try again in some time. Also, we could have an RGB LED and send color and timing information, instead of just on/off state, to better replicate the behavior of the notification light.