Here's what I've been planning for Howduino. The hardware side isn't that complicated (at least I don't think it is!) because I've only had the Arduino for a little over week and want to make sure I get something working.
I should be able to code this up beforehand (just interfacing with Processing) and then I can hook it up to some RC cars on the day. I've already bought one of these Mazda RX8s from Argos, and it looks hackable. They also have a Subaru on a different frequency. I've ordered an L293D motor controller as suggested by Thom, but I don't think I will need it if I just hook up the forward switch of the radio control, as in this example. I've noticed oomlout has already posted about a Remote Control Car Retrofit, so I hope to get some advice in that area. I'd also like to hook the circuit up to a sliding potentiometer, which will slow down or speed up the race, but that will only be possible if I upload all of the timeline data to the Arduino.
Another possibility would be a Twitter fight, in which the objects hit each other rather than race! But it might not be as dramatic.