I've had this idea about Battlefield style game where instead of certain number of fighters spawning at a time you'd have full armies from beginning. And when you die, you can choose any of the computer controlled fighters to take over.
I always imagined this more of historical hack'n'slash than FPS, but it could work either way. You could have a strategy element that in single player you choose formation/starting point and in multiplayer it'd be done by voting at start of the game.
Another idea of mine is a game with GTA style city, but it'd be just about racing from one point to another (or several checkpoints). The point is that there are alternate routes and ways to do it: grab a car, a boat, plane, hang glider, grappling hook... and the fastest route might be a combination, like taking a boat to start of to completely wrong direction to go to airport for convenient plane or helicopter. Sometimes you'd be forced to go on foot inside buildings (with possible exception of bikes).
This could be kid friendly without guns or casualties or, well, GTA style.
I'm thinking mainly 20-100 racers, but also one-on-one, small group multiplayer...