I think it depends on the child. I have one child that started at four (with flag football) and one who is eight and still not ready. Football is a big commitment for a child so it is important to keep it fun!
I agree with James but would add, too, it depends on the childs committment level, sport, physical endurance, and build. Also the age they start into puberty. Absolutely no heavy weight training until after they are well into or almost through with puberty. As a sports medic I have seen 9 year old veteran players who can out train 12 year old first year players. The better conditioned they are the less chance there is of injury. Getting them in shape to play at an early age and early in the season can help to prevent injury. Playing multiple sports is good for conditioning different muscle groups and can help them to develop into a better athlete.