One game I used to play with friends and neighbours as a kid and have just started teaching my own children to play is very simple, heaps of fun and teaches lessons in structural reinforcement.
Rules are simple...
-Build a car each
-Must have a driver/minifig in the car
-Driver must be able to 'see' out the front of the car. Minifig's 'vision' can't be blocked
-Sit about 3 metres apart
-Count '1,2,3, GO' and push your car as fast as you can towards your opponent
-Repeat the last step until one driver comes out of the car
-Only repairs allowed to vehicles between smashes is to wheels to facilitate rolling
It is fun and does teach you how to add strength to your creations and, with Lego being the hardy plastic that it is, means you have little worry about pieces breaking. Extended battering rams are a definite advantage.
