Flame has written some ideas about building Linux Powered Battle Droids and demonstrating them [1].
It seems to me that the biggest problem with having a battle of a similar nature to Robot Wars [2] is creating a safe arena. Getting an area the size of a basketball court fenced off with bullet-proof plastic is not going to be cheap.
The first solution to this problem that occurred to me was to have a battle held underwater. Water really slows down projectiles. The disadvantages of this are that it’s slightly more difficult to view. The viewing options are to using a web-cam, having a port-hole in the side of the pool (impossible if you don’t own the pool), and having a transparent viewing platform on the surface of the water (which would also be difficult and maybe expensive). Another disadvantage of submarine warfare is that having a droid spring a leak and quietly sink is not very dramatic.
It might be a better option to use aerial warfare via helicopters and balloons. The amount of weight that such craft can carry is not particularly great so there will be no real armor and fairly weak weapons. A motorbike helmet and a heavy coat should be all the protective equipment that is needed if the usual rules prohibiting projectile weapons from such contests are implemented.
A petrol powered model aeroplane could do some serious damage if it hit someone at full speed. But I don’t think that an indoor basketball court or any other enclosed arena that might be available would be large enough for fighter-planes. So it would be just balloons and helicopters.