There are many different types of mountain biking, and slightly different kinds of bikes are required for each:
XC / Cross Country:
Cross country mountain bikes are generally very light weight, and don't have very much front or rear suspension. Some XC bikes don't have any suspension at all whilst using a rigid fixed front fork, which means a rider must have much skill and experience to ride over rough terrain. They are made light by using lightweight materials and partly through their construction - meaning they are not as rugged and durable as some other types of mountain bike.
AM / Enduro/All-Mountain:
All-Mountain bikes are usually heftier than Cross Country bikes, normally weighing approximately 30 pounds. They also have greater suspension, which is sometimes adjustable. These bikes are designed to easily cope with the ascent and descent of mountains.
FR / Freeride:
Freeride mountain bikes have more emphasis on suspension than weight. The components of these bikes are built from sturdier, and as a result more weighty, materials than AM or XC bikes.
It is possible to ride them up hill, but their design makes them nearly impossible to maneuver at this angle or when travelling a slower speeds. With their steep frame angles, they are efficient on down hill trails which are more technical.
DH / Downhill mountain bikes:
These DH mountain bikes are built to be as sturdy as is possible. Due to the fast speeds involved with downhill riding most bikes of this type have just one chain ring at the front, a chain guide and a bash guard.
Single-speed mountain bikes:
These bikes only have one set gear. The gear chosen depends on the type of terrain being ridden, the size of the bike and the skill and physical strength of the rider.