Evan Prodromou introduced me to FU RPG (Freeform/Universal) which seems like a great game to play completely impromptu and, aside from the acronymn, seems like it would be great to play with kids. http://perilplanet.com/fu-rpg/
It's also free culture (CC BY) and Pay What You Want. I tossed $10 at it. Looking forward to giving it a try!