You'd be surprised what kids can make with wood, even at an early age. Bird houses, toys, puzzles, picture frames, shelves. There are several good books devoted to teaching woodworking to children.
I don't have kids of my own, but two other people and I helped the youth group at our church learn how to correctly use hammers, electric drills, and handsaws...and we and the kids loved it. Kids need to work with their hands. Learning woodworking at an early age builds confidence, mathmatical skills, eye-hand coordination, resourcefulness, and problem-solving skills. 10 year olds can be taught to use a scroll saw and younger children can be taught to use hammers, hand drills, hand saws, and all sorts of measuring tools.
Creating things with your hands is becoming a lost art in our younger generations, who instead prefer to sit in front of a computer or text their friends (I know how curmudgeonly that sounds, and I'm only 43!). If you have a child, I encourage you to build something with him or her. You'll be spending time together, you'll be creating something, and I guarantee that you both will benefit from the experience.
Link added 10.20.07 for kids and woodworking programs.