A meditation game where every minute you meditate you gain a block, and with those blocks, you can build.
A spectating game where you set up a civilization and watch them play. You essentially setup the paramaters up front and then let this simulation play itself out.
An MMO game where you score and collect points for mundane tasks. Everything you do in the game gives points, however these points can never be exchanged and you cannot do anything with them.
A game where you if you win, you can give the winnings to a charity.
Hide and go seek style of game but with your eyes open. The hiders and seekers have a symbol inscribed on them and the goal is to remember the symbols and find each other.