Rock-paper-scissors is a surprisingly popular game that many people play seriously (see the Wikipedia article for details). Due to the fact that a tie happens around 1/3 of the time, several variants of Rock-Paper-Scissors exist that include more choices to make ties more unlikely.

Rock-paper-scissors-lizard-Spock (RPSLS) is a variant of Rock-paper-scissors that allows five choices. Each choice wins against two other choices, loses against two other choices and ties against itself. Much of RPSLS's popularity is that it has been featured in 3 episodes of the TV series "The Big Bang Theory". The Wikipdeia entry for RPSLS gives the complete description of the details of the game.