It all depends on how we are with them. When they are 2-4, I tried to leave them home unless we had my in-laws tickets(we have 2 and they have 2 season tickets) and my full family could go. When my oldest was first born and could go for free, he went to every game until he was a toddler. We drive 200 miles round trip, so getting a babysitter was tough, but he was awesome.
By 4-6, they can start enjoying it and all the fun festivities. I buy them a Cosmo of their choosing, get them a BYU hat, and fill them full on all the food they want. Then we cheer as loud as we can, together, sing the song, and am constantly on the Cosmo hunt. It is great. My 8 year old son has been wearing BYU gear to school, every single day success the first home game this year, and is seriously a diehard fan for the first year. My 4 year old daughter has had her cheerleader outfit set out and ready for tomorrow, since Sunday. Next week, we are getting a hotel in Midway, and making a family BYU weekend out of it. BYU games are perfect for families and kids.