An arcade shooter. Something in the line of Space Patrol with only left and right movements, or Space Invaders with no shields and alien ships coming vertically one by one or in small flocks.
Walker & shooter much like old good Danger Dave and Duke Nukem 2d.
Pick up a peg and move it over another peg to an empty space to remove a peg from the board. Only one peg should remain on the board.
Shoot passer-bys with snowballs.
A lander clone with lots of planetary missions.