There are a variety of ways to use the multi-purpose exercise ball to work your various back muscles, and this will give you better muscle symmetry and true strength, as you will be working your tendons and ligaments as well, and will not have the stability of a machine to compensate fro any weaknesses.
Some back muscle exercises you can try with an exercise ball include the following:
Upper Back
It is best to use hand weights in conjunction with an exercise ball to effectively work the upper the upper back muscles. Any number of exercises can be done with your hand, arm, chest or upper half stabilized on the ball and your feet on the floor.
For instance, try lateral raises and rowing movements with your chest stabilized on the ball and your feet on the floor. For individual sides (to improve symmetry and/or to work a weak side for a few more reps), stand with your non-working arm or hand on the ball for stability and tighten your abs, then perform one-armed raises or rows.
Lower Back Extension
The lower back often gets missed in workout routines, which is unfortunate as it is an important component in your overall health and strength. This simple (not easy, as balancing on the ball is a great stability exercise on its own!) exercise will help strengthen the muscles in your lower back.
Lie with your stomach draped over the exercise ball, feet on the floor and hands behind your head. Using your feet for stability (put them against a wall if need be until you are stronger), lift your head and torso so that you are flexing and tightening your lower back muscles. Do not lead with your neck or head, rather focus on the lower back muscles you are working to ensure they are being isolated. Your glutes will be involved in this as well, especially until your lower back muscles grow stronger.