Robot Sumo is a fun contest where typically two robots drive around inside a ring, and each robot tries to push the other robot outside of the ring. Here is a design for a basic Sumo robot based on the Line Follower.
Build a Test Opponent
Want to test your robot's ability to push other robots before meeting up with other real robots? You could use a LEGO or other toy car, or, with the leftover parts in your MINDSTORMS kit, you could build the Fake Hub and then use it to build a dummy robot using a slightly modified simple design such as Practice Bot, 5-Minute Bot, Classic Bot, or anything you design. A dummy robot doesn't push back, but it at least resists with weight and tire friction, especially when pushed from the side.
Building a Sumo Ring
There are many ways to build a Sumo ring, and you can search the internet for ideas if you want. The ring can be circular, or shaped like an octagon (but square or rectangular doesn't usually work out well). You can use a light background with a dark ring, or a dark background and a light ring. The program above assumes a light background with a dark ring and good contrast, but this is easy to change. See the Line Follower project for a Light Meter program you can use to test your colors.
A simple way to make a ring is to buy a sheet of white coated flat board from a hardware store and a roll of black electrical tape. If you stretch the tape slowly as you lay it down, you can try to make a circle, or an octagon is much easier to make. A ring diameter of about 3 feet (1 meter) works pretty well.
It is much more fun if the ring is raised off of the floor a bit, so put some wood blocks or something under it. This will cause the losing robot to fall off the edge and roll over
You can make up your own rules, but a format that I think works well is to have a pair of robots compete for the best of three rounds. In the first round, start the robots side by side and facing opposite directions. In the second round, do this again but swap the robot positions. For the third round, start them back to back facing opposite directions. Starting with the robots directly facing each other is usually not very interesting