I've had a wisdom tooth out in the chair (and the rest out under general anaesthetic) and it was fine. It's the only thing I've ever had done to my teeth and had always been nervous of a needle in my gum but the pain of the infection was so bad I didn't care and it was fine.
A friend of mine is really nervous of dentists. She got an emergency appointment at a private dentist when in a lot of pain and I went with her to help her get there (I know the area better) and for moral support. The dentist was great and she said the sedation was brilliant - she said it seemed a lot more than she would get on NHS. I was holding her hand (literally, she is really nervous!) while it was done so could see it being done and was very quick and simple. Just pulling, no crunching or anything like that.