All trail users affect the trail surface and surrounding environment, especially when trails are poorly constructed. Those impacts range from vegetation loss to erosion, water quality problems, and disruption of wildlife.
However, there is no evidence that mountain bikers cause greater environmental impact than other trail users. The current research suggests that mountain biking impacts are similar to hiking, and less damaging than equestrian and motorized users.
An emerging body of knowledge holds that when it comes to trails, the major issue is not the type of user, but the way the trail is designed and built. If a trail is properly located and constructed, it can handle a variety of users without damaging the environment.
IMBA's books offer our most comprehensive treatments for this and many other important topics. Consider picking up copies of Trail Solutions: IMBA's Guide to Building Sweet Singletrack and Managing Mountain Biking: IMBA's Guide to Providing Sweet Riding at IMBA's online store.