Written as a response to an article about a boy's shyness on Free Range Kids:
If a child's fear is becoming unhealthy, irrational, overbearing, or excessively inconvenient, then it should be addressed.
Courage is a form of self discipline that most shy people can learn. It hurts, but not as much as a lifetime being paralyzed with fear. Know your child and what he is capable of, and set reasonable expectations. Don't be afraid to say, "No. I won't do for you what you can do for yourself". If he is healthy, then expect some tears and frustration, then watch for him to either do what he wants without you, or find something else to do. If it takes more than 48 hours for him to overcome his fear or find other things to do, or he gives an extreme and prolonged emotional reaction, you may need to see a specialist.
Recently my three yer old daughter overcame her fear of water. She had very good reason to be afraid. Last year a wave knocked her over and she went under and couldn't stand back up (she was 15-20 feet away from me, and thank God I saw her go under and got to her quickly). However, her fear was becoming a nuisance to the entire family. She would refuse to play in (or frequently near) the water while everyone else wanted to go swimming and wading. Even washing her hair at bath time was traumatic at times. Fortunately she has a daddy she trusts who her took her by the hand and walked her in ankle deep in the water along the shore of a still lake. She cried, and fussed, and after a while found some daisies growing at the water's edge. Then talked with him as they went out shin deep. Then she noticed the water was at her knees and squeaked a little, but realized she was safe. Now she plays happily with the family when we are out swimming. She doesn't have any problems now.
Obviously, fear of water is not the same as shyness. The reason I mention my daughter is to illustrate that fear can be overcome in the right conditions. It depends very much on the child, but sooner or later, their fears must be met.