Tic Tac Toe game comes to mind as one of the most classic games. The most simple way to play it described as creating a game schema in seconds with paper and pencil. Here is the HTML5 version of Tic Tac Toe Paper Note. It is both available in mobile devices and PC. You can play the game against a friend or against the CPU.
Instructions:
You can control the game by Mouse or by Touch controls.