Signed my now 4 year old up when he started traveling on paid tickets after turning 2. We fly AA, DL, and WN domestically so signed him up for AS Mileage Plan (to accrue on AA/DL) and for WN Rapid Rewards. He has a little over 20k AS miles and 7k WN points.

If they are flying, you should sign up for a program to get the miles - why let that go to waste? One thing to remember though is if they earn miles on a carrier you do not fly often, put their accounts into your rotation to check expirations. While we do not pay to fly United, UA was our main mileage redemption carrier for years (until the recent devaluation; miles earned via credit card). Since we had credit card activity our account expirations always extended. But in 2012 my son picked up a couple Star Alliance flights in Europe. I forgot about them and the miles expired. Only a few thousand miles, but still a rookie error to let them be taken.