I was asked for a Touch-Me lamp, which gave me the idea for a Shake-Me lamp.
The idea is to use a shake-sensor, feed it into the the Arduino, have the Arduino randomly switch on and off 2 LEDs.
The 2 LEDs are connected seperately, so they can be controlled independently. Other algorithms like blinking, fading, ... could be implemented.
For the casing, I reused the case of a larger lamp, which had just the right size and 2 holes where I could stick the LEDs through.
You should be able to see how to build it from the Fritzing schematics and the photos.
The only problem with this project is that the lamp draws a lot of current from the 9V battery, and drains it quite fast, so you might want to add an on/off switch to the battery and turn it completely off when you don´t need it.