I have a game I have run a number of times with good success for kids on a pick-up basis. It is designed to teach kids about miniatures gaming with a quick, easy to play set of rules. It is fairly stripped down keeping rules and modifiers to a minimum. For example almost all die rolls are: roll 2D6, add your stat and score 12 or better for success.
The rules are written in such a way that they can be used for any period, any genre, and figure scale. So if a kid happens to own Vikings, or Elves or Paratroops, you can pull these rules out and play. All measurements are given in "bands" which you can set to fit your figure and table. Using 25mm figures on a 4x6 table a 6" band works great. You can reset to any value you like (but it should be easily divisible by 3 because a few measurements are 1/3 or 2/3 of a band).
They are primarily infantry rules though rules for maybe a vehicle per side are included.
The rules assume a GM is running things (since it will often be for pick-up games on the fly the GM will need to "tweak" the game occasionally to make sure everyone has fun).
The rules make no pretense at being "accurate" or a "simulation" etc. They simply give a balanced game for any setting. Of course the GM can introduce special rules where needed. For example, the WW2 lists give the MG42 a bonus if set up on a tripod and served by a 2 man crew. But this si a note in the army lists, not part of the rules.
If you would be interested in play testing a set of rules like this please let drop me a line and I'll send you a draft. The draft includes some work-in-progress armies for Lord of the Rings type fantasy, WW2 Normandy, and SciFi (think power armor and blasters).
Email: mark@scalecreep.com
Thanks!