Bounces is a one-button game originally designed to be playable by toddlers.
Enter exhibit A: Proof of Toddler Playability!
The controls are simple:
It features a collection of singleplayer levels that vary from puzzles to dexterity challenges. If that's not enough, it also has a level editor within the game itself.
Finally, it's also an IO-style game with a massively multiplayer racing mode with procedurally generated levels and AI-bots for when too few players are online.
The latest build can be played right here, if I can work out how to update my Heroku settings to a more recent node.js version...