I work in the industry, so I see it all the time. If its something you guys can do together, I think its a great activity for a family to participate in. In my humble opinion, its a great idea to start them off young. Not only is it fun, its a great tool to teach a child responsibility and a sense of accomplishment. As his or her skill level increases, the training wheels come off, and the obstacles in a dirt enviroment are always changing, so its a good challenge. Dirtbikes and ATV's are also a great way to learn some mechanical skills- they always need maintence, so its a good way to teach a kid how to work on things and follow a service schedule. Typically a kid that grows up riding and working on their own stuff will develop some pretty good wrenching skills, which is becoming more and more rare these days.
Speaking from personal experience, it kept me out of trouble in my younger years- I was never concerned with partying, drugs, or alcohol, because all I was looking forward to was getting out of school to go get my bike ready for the weekend. I will never forget the days of Dad and I loading up the bikes and going riding together.