I watched an exercise program on TV at home. One of the exercises was to reach the hand behind the back and move the fingers up as close to the neck as possible. I noticed my right arm couldn't go nearly as far as my left. Is this normal?

No one has ever measured adults to see what is the normal hand-behind-back range of motion. Therapists working with patients of all sizes, shapes, and ages report this motion varies quite a bit from person to person and even from right to left in the same person. This is what you've noticed in yourself.

Some of the factors that could make a difference might be age, previous shoulder or arm injury, and strength. It's possible that the muscles and soft tissues of your dominant arm are tighter. This can occur from using it more. Less flexibility means the hand can't reach up quite as far on one side.

A difference from one side to the other may not be a problem if you're not having shoulder pain and if you can reach behind while dressing or bathing. This may be a good exercise to include three or four times each week to regain lost motion and keep your flexibility. It's easy to injure the shoulder in this position, so move slowly and gently. Don't force the arm up the back by pushing on it.