BARE MINIMUM SUPPLIES REQUIRED FOR EPIC WEBCAM INTERNET ROBOT:
Let's see, you'd need a controller, not necessarily a Raspberry Pi or an Arduino, just something that can be controlled wirelessly from a computer program. Also a wireless webcam you can attach.
For the robot you'd need probably a minimum of 2 servos, a power source, and a basic chassis. The cost would depend largely on whether you already have some of this stuff, but the wireless communication is most likely the hardest and/or most expensive part. When we made ours for class the cameras just used wifi, but the controller hooked up to a little radio board that I doubt any of the kids got set up without some help from one of the teachers.
Then we drove them around the school and spied on people. Good times.
Optional but probably a good idea: proper wheels, parts to make a circuit board for controlling the direction of servos, tools to fabricate parts, bolts, velcro and glue.
If I had more money to burn I might build it myself...
