I do recommend using an exercise ball chair if you have a desk job. It forces you to think about and practice improved posture. It also can help to strengthen your core (abdominals and back) muscles.
Exercise balls are beneficial for improving core stability and strength. They can be used for a variety of exercises and can easily be incorporated into your workout routines. You can find many exercise DVDs with specific theraball programs. The benefit of adding a chair to your exercise ball is that you can keep it at your desk or work station and potentially use it instead of your usual desk chair. Some exercise ball chairs have a little back support, but likely you will not lean against it; it is comparable to sitting on a stool. The chairs also have wheels, like most desk chairs.
The main downfall of the chair is that it may not be high enough for your desk. If that is the case, it is better not to use it. Good posture should be maintained while you are sitting at work, which means you need an ergonomic work station. The largest theraballs I have seen are 80-85 cm, which are appropriate for taller individuals. Some ball chairs may have a higher base, which could bring you up to the appropriate sitting height for your desk/keyboard.
Another problem with using the chair is that you do not have any back support. Therefore, it may be hard for you to maintain good posture or your back may just get tired. With a normal chair, you have the option of sitting against the back of the chair and adding a lumbar roll or pillow behind your low back to improve the position of your spine. Realistically, most people tend to slump when sitting, and that is true with ball chairs as well.
A feasible option is to use a ball chair for 1-2 hours of your workday. Or you could simply sit on an exercise ball (without the chair) for short periods of time at work. The most important thing about your work station is to have upright posture, which matters more than the chair you use. If you really want to improve core strength, the best way is to do core exercises along with your workouts.