It's awesome to pedal out into the dry New Mexico air and see not only incredible terrain but also ancient history. Just about the entire state is conducive to the sport, making it one of the most popular places in the United States for avid mountain bikers.
Albuquerque has some excellent and very challenging trails in the Sandia Mountains, as well as less strenuous routes west of town, through Petroglyph National Monument. In Santa Fe, you'll find some very rugged and steep mountain trails, most accessed off the road to Ski Santa Fe. Taos is a rider's paradise, with lots of extreme mountain trails, as well as some that are purely scenic, such as the west rim of the Rio Grande Gorge.
In northwestern New Mexico, you can ride around El Malpais National Monument in the Grants area. You can also take your bike with you to Chaco Culture National Historical Park and ride from Anasazi ruin to ruin. The Farmington area has its renowned Road Apple Trail within Lions Wilderness Park, which you can ride even through the winter.
In the southwestern region, bikes are not allowed in the Gila Wilderness, but they are permitted in other parts of Gila National Forest; you'll find terrific trails that originate in Silver City, particularly the Continental Divide Trail. In the southeastern region, the Cloudcroft area has some excellent trails; there are a few that explore history as well as natural terrain, most notably the 17-mile Rim Trail.
Some books to check out are my book Frommer's Great Outdoor Guide to Arizona & New Mexico (Wiley Publishing, Inc.) and Sarah Bennett's Mountain Biker's Guide to New Mexico (Falcon Press).
Known World Guides, in Velarde (tel. 800/983-7756 or 505/983-7756; www.knownworldguides.com), offers single-day and multiday trips all over New Mexico, with options such as 3 days in the Jemez Mountains west of Santa Fe or 5 days in the Gila National Forest in Silver City. Mellow Velo, 102 E. Water St., Santa Fe (tel. 505/982-8986; www.mellowbike.com) runs bike tours to some of the most spectacular spots in northern New Mexico. Trips range from the easy Train Tour south of Santa Fe, in which you ride beside the Santa Fe Southern Railroad tracks from Lamy, to a challenging Borrego Bust ride in the Santa Fe National Forest.