Write a program that allows the user to play a game of Rock Paper Scissors.
Improve the game so that a score is kept and it becomes a best of x rounds.
Give the computers some AI so it no longer relies on a random choice and uses a set of logic to decide what to play next. You might want to read up on strategy or check out the following video.
Extend the game so it uses arrays (hopefully it should already) and has the extended options as described by Sheldon.