Ball chairs are great as a second chair to rotate out if your primary chair is not doing it for you because you've been sitting in it for too long or you've got multiple chronic injuries that sometimes aren't alleviated by your primary chair. Just make sure you get the right size or it's not going to do your posture much good.
The plus side of the ball chairs is that they tend to enforce good posture because if you slouch, you tend to become unstable and drift off to one side. They're also comparatively cheap and you can always deflate it if you find yourself not needing it and want to put it away. No frills cheap chairs are usually really bad for your body and ball chairs are one of the few exceptions. Plus, they don't wear down like most chairs do.
The negative side of ball chairs is that they're not terribly practical as chairs that you can sit in for for extended days because your back and abdominals tend to get tired from having no passive support at all the entire day. I'd find it hard to put in a 12 hour day sitting on a ball.
While they tend to encourage good posture, they can also be even worse for your posture because unless you're a highly trained gymnast, you will start getting tired whether you realize it or not. The more tired your midsection gets, the more likely you'll be to find some way of slouching without falling off the ball and that can cause you to assume some really funky postures to achieve this feat or you might start leaning harder on your wrists for balance. You'll find some way to compensate.
If you're not a great shape, you might also find yourself really sore the day after you sit on a Theraball. On the positive side, it actually is a good way of getting some light trunk strengthening endurance exercise. You just have to get used to it, but just don't be surprised if you're sore the next day.
BTW, my comments are for just a ball and not a ball plus the chair frame. I'm not that familiar with using the frame with the seat. I've only briefly tried it out once and I'd make a guess that the frame takes away some of the benefit and some of the downsides of sitting on a ball. Good posture is still possible with it, but it won't enforce good posture, it won't work your muscles as hard, but it also won't encourage you to develop drastic ways to compensate as your postural muscles get fatigued.
Final disclaimer... this is all relevant for your "average person." If you need special chairs because of an injury that you have, sitting on a ball may not be good for you at all depending on the kind of injury that you have. In particular if you have an injury that makes hyper-lordosis (over-arching of your low back) dangerous, sitting on a Theraball may not be for you.
