I race (well I ride, and pretend I'm competitive) in the Coaster Brake Challenge each January and July. I've got to tell you that it's about the most fun I've had on a bike since I was a kid building BMX "tracks" with my friends. Completing each race is really the goal - while riding, I'm just trying to catch up to the rider in front of me - winning isn't the point as much as challenging yourself on a cool old bike. Anybody can throw a klunker/bomber bike together that's up to the task, and we've had entries that rode unmodified department store cruisers, Chinese Flying Pigeons, and aluminum-framed 29'ers with coaster-hubs laced in with extra-long axles.
Everybody has their own idea of what the "right" bike to ride is, and everybody is welcome. It doesn't take much to start an event of your own... if you need advice, I'm sure Rev106 will help you out.