There are two primary reasons for getting into a bodybuilding program: Trying to increase muscle mass, or trying to increase functional strength. Key to both of these is building core strength, which lies in the abdominal muscles, and, just as importantly (and often neglected) the muscles of the upper, middle and lower back.
Your back (and spine) are the primary stabilizing muscles in your body, and the ones easiest to injure when lifting weights. From a biomechanical perspective, your back consists of the spine, the ribs, the scapula and the ligaments that string them all together, like parts of a mobile or kinetic motion structure.
Injuries to the back are almost always compression or rotation injuries – they're damage to the soft tissue that lets your back move. Good weight lifting exercises (and muscle group isolation) are key to avoiding back injuries, many of which will not show up for years after you've done them to yourself.
Muscle groups that you need to work on in the back are your traps, lats and deltoids, and you need to take them slowly. Yes, you can get a ripped looking back by overdoing it, but it's better to focus on practical strength increases over physical appearance and muscle building when dealing with your back.
The trapezius muscles (traps) are the ones that form the bulk of your back; the basic exercise for them is a shrug motion, where you take a pair of dumbbells, one in each hand, and shrag your shoulders as high as they will go (and do not roll them – go straight up) and hold them for a breath , then let them down slowly.
A related motion, which helps the traps a bit, but mostly works on your deltoids, is a straight-arm lift. Hold a dumbbell in your hand with your elbow at your side, and your forearm out level with the map. Extend your arm until it's at height, in one fluid motion, and look down your arm at the dumbbell, like you're sitting on a pistol range. Then bring it down slowly. (This is a common exercise in martial arts groups that emphasize punching). This will work on your deltoids and the yoke of muscle linking your shoulders.
To build up the lower trapezius muscle (the part of the trap that runs down your ribs), you're going to want a sitting down 'V-bar pull down', where you're pulling down against resistance; This is better than a straight pull up because it isolates the muscle thoroughly.
Building definition, and most importantly, strength, in the lower back requires shoulder arches. Hold a light dumb-bell over the back of your neck and lay down on your front. With your hands clasped, arch your back, lift, and hold for a count of three, then lower slowly. Do these sparingly; it's very easy to overdo them.
As with all muscle building exercises, it's important to do stretches and a bit of cardio before and after doing them to maintain flexibility.