I think you can race just about anything, depending on the organization putting on the race. You probably don't want to race a Giant Faith, but if you have a hardtail, it'll work. If you have a road bike, you'll want to figure our if you have clearance for some beefier tires as they are the most important difference IMHO.
cross crash = no big deal. get up, keep going.
road crash = maybe a big deal, maybe not, but your race is over most likely
you can't get dropped in a cross race, you just finish DFL. On the road, if you get dropped your race is basically over. Therefore cross = easier for a beginner.
Originally Posted by mr_tom
Cycling isn't a sport. It's more like a really, really expensive eating disorder.
Locally for me (Portland, OR area) the major cyclcross series is open to any bike, and especially in the beginner level you see pretty much anything. Plenty of hardtail mtn bikes, some FS stuff, road and touring bikes with as much knobby tire as will fit, "real" cyclocross bikes, there was even one guy in beginner class last year on a BMX bike.
Unicycles run in their own class though
And, like kudude said, crashing in cross is no big deal (on most of the course anyway), just try to scramble out of the way.