ArdBot ($19 + Arduino)
The ArdBot is a basic rolling robot that you can get up and running in no time, and the chassis is highly expandable, so you’ll have a platform from which you can build and learn a lot more. The original ArdBot was detailed in Servo magazine, but you can find everything you need in this article from Robotoid. It also includes all of the part numbers of the components that you’ll need to get your first robot moving.
This kit comes with an Arduino and a motor shield, so you can get started with this simple two-wheeled robot and then move on to more complicated and involved projects. The ultrasonic distance measuring module will keep the robot from running into anything, and the chassis allows for easy mounting of other sensors and actuators. oddWires designed this kit to involved a minimum amount of soldering and interconnection, so it’s a great kit for beginners. (And if you already have an Arduino, you can get the same kit with the motor shield, but no microcontroller, for $54.)