I am a firm believer in taking your kids when they first express an interest. I started taing my son when he was three. I killed a deer with him that year (rifle) from a double ladder. He has been hooked ever since. He killed his first deer with a gun when he was six. Since then he has killed a lot of game with a rifle and a few things with his bow as well.
Without getting too far out of whack with this thread, I think that minimum age restrictions on hunting, expecting kids to hunt with a bow right away, and imposing trophy standards on kids are the biggest threats we have to the future of hunting. If we don't get them out there early and often they will find other things to occupy their time. If we don't allow them to experience success the same will be true.
Here are some things that have worked for me when hunting with kids:
1. Use nap time to your advantage. Even older kids will nap in the stand if you wear their little tails out in advance or if they get up early enough. When my kids were young,I used to time things where they would sleep the first hour or hour and a half of a hunt and then I could keep them busy for another hour or two. Worked out well.
2. Make sure they are not cold, wet, or otherwise miserable. When it turns into an endurance contest, the fun is out. Sleeping bags, ponchos, etc. are essential when weather dictates their use. A sleeping bag pulled up to the waist or chest is great for keeping a kid warm.
3. Games with a plan. I always let my kids take nintendo, etc. in the stand, but would use it as a last resort. I never let them use it right away, and I always made them put it away at "prime time". Over the season, and after a number of successful sightings, "prime time" gets longer and longer.
4. Food. Kids get hungry and besides it is rude to talk with your mouth full!
5. Don't forget scouting and teaching. It is easy to forget that the experience is all new to kids.
6. Get them on a blood trail early. I am amused by people that want to hide the fact that a dead deer is the net result of a hunt. Blood will not gross them out and neither will gutting a deer.
7. Give them something to do. Tally the number of chipmunks or tree rats they see. Draw a picture of a deer. Color in a coloring book. Take pictures, use binoculars, etc. My daughter used to take sticker books to the stand. She put an elmo sticker on an old compound bow I used to hunt with. It is the only compound bow I still own. Dumb huh? But I keep it for the memories.
8. And that leads me to the most important part. When they act like kids instead of hunters, remember that you made a choice...a wise choice... to include them in something that you like to do. You are building memories. The memories you are making now will taste better in your old age than any backstrap you slap on the grill.