I compete in a competition called Mech Warfare (
www.mech-warfare.com/). It is a form of robot fighting in a way, but the robots do not destroy each other, they track airsoft bb hits via sensor panels to track scores. I personaly see the competition as a engineering challenge, as the robots are required to be walking robots, and have to carry a fairly large payload (airsoft guns, wireless camera, battery, target panels). Also, the community helps each other and shares designs, code, ect, it is not what you would expect with robot fighters. Although i will warn you that a LOT of people say they will build a robot, but never do - so some people may not take you too seriously until you share your progress.
Here is a video of my robot from last year:
http://www.youtube.com/watch?v=FrhlYsF2uTU
The competition is held at Robogames, i'd recommend taking a look at that event as there are about 60 different competitions you could enter.