Here are some of the many different things I've found on the net. For a complete list of cool Arduino projects I've found just follow this link. Some of the projects listed below don't use the Arduino, but they all could.
Originally written in Spanish and translated by Google. This one uses the Arduino as the brains for a robot. It looks very doable.
Use the Arduino and electromagnets to create a pendulum that never stops.
If you don't know the correct way to knok, you can't get in.
Persistence of vision machine.(Here's his refined code)
Cool synthesizer type project.
This one doesn't use Arduino, but it could.
Make music in a very different way.
Stuff you might use as a piece of a project
Use the accelerometer and such with your Arduino
This will take some tweaking, depending on the remote you have
Pretty easy, but will take some tweaking.
Not just a motor, it can function as a sensor.
Collection of sound/music projects
Cool little robot that drives around and drums on stuff.
Use sensors on the Arduino to interface with programs running on the computer
A much better way to measure temperature.
This one triggers a camera to take a picture, but the same sort of thing could work for other devices as well. Here's a similar one used for high speed photography.
I'm not talking about Mickey. Here's a way to use an optical mouse with your Arduino.