I have heard a lot of different answers for this, from six to eighteen. I would like for someone who actually knows what age is appropriate to answer this. Also, how much weight training is safe for children?
Taking Eric and Dave's answers into consideration, we must understand that children's bodies are still developing. They won't have what we consider complete neuromuscular control over their bodies quite yet.
I believe a structured lifting program for children can be a fantastic introduction to controlled multiplanar movement. I believe we tend to throw our kids into sport too early, not taking their developing physiology into account.
One point I would like to drive home is that because your child/ren are still developing, recognize that most of the adaptations will be focused on the central nervous system and its ability to use the body's musculature; that hypertrophy, strength, or power should not be the end goal here. Rather, you should focus purely on movement patterns. Learning how to do an exercise safely and with great form vs. trying to get stronger.
Once they hit puberty, then would be a great time to pursue muscular adaptation alone.
Pierce, Byrd, and Stone (1999) concluded a structured weightlifting program (including Olympic-style weightlifts such as the clean & jerk, and snatch) can be safely performed by girls and boys, ages 7-16. Interestingly, Faigenbaum et al. (1998) showed that 8 to 12 year-olds that were supervised during maximal lifting resulted in no injuries, demonstrating that even maximum intensity training can be a safe for children when properly supervised.
The medical community and the public in general seems to regard strength training as a general voodoo practice that will "hurt you". Fortunately, this has been getting debunked soundly for over a decade now.
Despite earlier concerns regarding the safety and efficacy of youth strength training, current public health objectives now aim to increase the number of boys and girls age 6 and older who regularly participate in physical activities that enhance and maintain muscular fitness.
The American Academy of Pediatrics recommends strength training for children 8 and up. As a father myself, not all children grow up the same and some kids are quite frankly much more physically gifted than others.
I don't think anyone's recommending throwing a child into a competitive power lifting program on their 8th birthday, and honestly some kids at 8 (or 10, or 12, or 18) simply don't have the attention or care-factor to learn serious strength training and execute it safely.
What I've personally found is that kids tend to play sports much earlier than they can strength train. Those sports and basic calisthenics teach motor control, discipline, and physical prowess. As sports continue to evolve in the 4-10 year old range, you can slowly start introducing targeted body weight activities that aid in their sport development.
From there, you have kids who are:
- Used to spending focused time on physical training.
- Used to moving their bodies.
- Used to drills/skills: activities that are not sports themselves, but necessary for helping sports.
That's a pretty good platform to start strength training, and you're using the actual skill development and prowess of the child to gauge further development. When they can safely do 20 body weight squats, they can do a few less with a ten pound barbell on their back or holding a dumbbell at their chest.