I've dealt with this with two of my three kids. For my daughter, it was about inner thoughts and angst and wanting to turn off the deep thoughts. Getting her into a highly demanding physical sport was actually the one thing that helped. She climbed competitively for years, and the required mental focus turned her thoughts off while she was climbing a route and the physical exhaustion helped her sleep and turn off the worry after exercise. It also had the added benefit of endorphins and staving off depression.

For my son, it was about not wanted to stand out or be different from his friends. He underachieved all the way through midschool and high school and had a horrible time adapting to college. And his perfectionism got in the way. If he was "normal" no one would expect great things of him. He was surprised to find out that I really didn't care if he ended up solving some great mystery of life - I just wanted him to be productive, responsible, a good person and happy. Having the load of parental expectations removed has really helped.

Good luck - this is such a worry for us as parents, isn't it?