I'm a big fan of Sidi shoes -- road and mtn. I've got Dominators for cyclocross (and mtn biking). Here are the things that I like for cross (and what you should look for if you're getting new shoes):
Mucho Adjustability -- you can keep them loose in the toe bed and tighter in the heel -- good for running. I typically tighten my shoes more for races than I do for riding. I have very small ankles, so it's important to find a shoe that tightens really small at the ankle. There's nothing worse than losing a shoe at the bottom of a mud pit.
Big Tread -- the tread for cyclocross is extremely important since you'll be running on a variety of surfaces. The big tread on Sidi's is great. Unfortunately, even good shoes probably won't shed mud very well.
Spikes -- holes for spikes are key if you've got any uphill or downhill running. Ideally you can remove the spikes depending on the course. Most soes don't come with spikes so you have to purchase them separately.
Weight -- lighter is better when you have to run with them.
Material & Construction -- I want a rock solid shoe that won't fall apart when it gets wet, muddy, etc. Finding material that's a bit water resistant is important too. Canvas, cloth, or felt shoes just won't cut it.
Sole -- you want something that's not too stiff to run, yet stiff enough to transfer optimal power to the pedals.