Clusterbot was my first Arduino project, and I think he makes a great project for a beginner. While building Clusterbot you will learn how to use motor controllers, ultrasonic rangefinders and how to program an elementary robotic platform. The most important thing I learned from building Clusterbot was the importance in planning the location of things like your Arduino board, battery packs, wiring, etc.
Why is it called Clusterbot? The more I worked on Clusterbot, the more I found my form following function than design. I ended up with wires everywhere, the battery pack extended off the back to maintain balance and a mess of erector set odds and ends. The end result was a cluster%#&@ of parts really, so I named him Clusterbot. No matter what the rest of him looks like, the ultrasonic sensors gave him a good looking face, and at least you could tell where the front was.
You don't have to follow every step of the physical build, but I do recommend you pay close attention to the motor controller hookup and ultrasonic programming sections.
Let's get started!
Here's a video of a finished Clusterbot: