War ’44 is a set of free wargames rules designed for play with a seven year old. They would be good as an introductory game.
simple
Simplus Medieval Miniaturis Rules (SMR)
Simplus Medieval Miniaturis Rules (SMR) is set of free wargames rules for battles in the medieval era.
Beer and Pretzels Modern Micro Armor
GHQ has a free pdf of its Beer and Pretzels Modern Micro Armor game, formerly a commercial effort, now a set of free wargames rules.
Beer and Pretzels WWII Micro Armor
GHQ has a pdf of its Beer and Pretzels WWII Micro Armor, originally a commerial set, now a set of free wargames rules.
Age of Fantasy Regimental Rules
Age of Fantasy: Regiments is a set of free wargames rules for simple fantasy Regimental actions. The rules fit on one page, and there are “army books” for various races.