When I was 12 I had a cool game called Weapons and Warriors. It was really fun. You get to sit around on the floor, roll a die, then take these cool plastic marbles and shoot at each others men with these neat little plastic cannons, catapults, etc. There were many different ones, castles, pirates, etc. Excellent games, I would still play them today if I did not break all the little guys. I would recommend this game, I got a 5, 7, and 8 year old to play it ... they enjoyed it. (However, I am not sure if it is still sold)
Stratego may be a little advanced as of yet for a 6 year old... but it is good for 8-10 year old.
When they get to ages 11+, Axis and Allies and of course, RISK!