When training for the sport of mountain biking you will especially want to focus on your upper body.
This may seem odd since much of the power is generated from your leg muscles however if you do not have the upper body strength to support yourself then you are not going to be able to ride for as long as you would like.
A proper upper body strength-training program for mountain biking should include such exercise as chest press, upright row, side lateral raises, and bent over rows. These will really work the muscles that will be particularly used in this sport while mimicking the actions you may perform.
You might also want to add additional exercises to round out the program like bicep curls, tricep kickbacks, military presses and pull-ups. This will give you a great program that targets every muscle in the upper body.
Aim to perform some sessions with the 3-8 rep range so you can focus on strength and power and then some sessions in the 9-15 range so you can target your endurance abilities a bit more. Do your best to complete 4-5 sets for the lower rep range and then 2-3 sets for the higher range.
Also be sure to include some lower body work in the gym as well since obviously these muscles will be important. You may not have to train them as often however since they will be getting a great workout when you are out on the trails. As long as you include some squats and deadlifts you should hit the major muscles without having to do a lot of extra isolation work.
So don't be fooled into thinking that the only training you need to do is sport-specific. Adding additional cross training in the form of weight workouts will drastically help to improve your performance.