Super Mario 3D World

Super Mario 3D World might be the best child-friendly game ever made.
The levels are open and friendly. The game can be played with simple controls but hides a fair amount of depth for experts. Most importantly, Super Mario 3D World is designed from the ground up for cooperative play. Some games have co-op tacked on, but everything about this game is designed to suit people playing together. 
If you’re looking for a game to play as a family, this is the one. If you have a Wii U, that is. The good news: Nintendo is planning to bring this game to the Switch.