These simple game ideas are freely available for anyone to use. If you make (or have made) a game using one or more of these ideas, let me know so I can promote it here!
A 3D multiplayer game where you try to move, rotate, or otherwise disturb objects to change parts of the scene/environment while that area isn't on the other player's screen. Balance changing the environment with watching what your opponent(s) might be try to change.
Pong, but with paddles on all four sides of the screen. Either four players each controlling one paddle, or two players each controlling two paddles.
A golfing game with random encounters. When walking to get the ball after hitting it, monsters may appear to fight. Fighting too much will lower your stamina, reducing the distance you can hit the ball.
A baseball game, but with weapons. Don't want the outfielder to catch the ball you just hit? Have a teammate shoot at them. Don't want the batter to hit your pitch? Throw one of your limited number of grenades instead of the ball. Is a player badly injured? They go to the bench.
A strategy game that takes place in two periods of time. "Past units" are weaker than "Future units", but winning battles in the past will make a difference in the future.
A work of interactive fiction where the main character is unaware that they are being controlled by someone else. Handle situations as the character would to prevent them from getting suspicious.