2008 Student UAS Competition - This is one of the Association for Unmanned Vehicle Systems International student competitions. This one is for Unmanned Aerial Systems. In this case the concept of the mission in the challenge is a flying unmanned system that supports the U.S. Marines. Its job is to fly on a predefined route, but with changes due to emerging enemy threats, and to quickly locate and identify targets. Prizes have been in the >$20,000 range in past years.
The other competitions are for Arial Robotics (in this case not remotely controlled by humans), Intelligent Ground Vehicles, Autonomous Underwater Vehicles, and Autonomous Surface Vehicles.
I did notice 1 theater of operations that isn't represented (yet) in that list. This is one that's fairly expensive to get to at the moment, but I'm sure a student competition based on a simulation of that environment, or the ground-based parts of it, would be possible.