What creatures should I be leary of in desert?

I recently moved to the desert of southern New Mexico. The desert is called the Chiuauan desert ( not sure of spelling) I have been enjoying myself by riding the hard trails on my mountain bike. My concern is that every now and then I fly of my bike, and I'm always worried that I'll come across a dangerous creature. Like a rattlesnake or something else. I've been doing alot of reading trying to figure out what creatures to be on the look out for. So my question is besides the rattlesnakes what other things should I be on the look out for?