Rock-paper-scissors game is referenced in Simpsons and Big Bang Theory.
Goalkeepers use a mixed strategy and dive left or right with equal probability since it is really impossible to follow the ball being kicked. The kickers also use a similar strategy and shoot the ball either to the right or left with some probabiilty.
Battle of the Bismarck Sea
Here is a detailed Wikipedia article on this battle and the resulting zero-sum game.
Dilbert and Prisoner's Dilemma.
Giacomo Antonio Domenico Michele Secondo Maria Puccini's opera Tosca. Read this to see what this opera has to do with game theory, in particular, the prisoner's dilemma.
The Nobel prize winner Professor E. Maskin has a wonderful explanation for this mechanism design problem.
"Chicken" game starring James Dean.
1830s: Antoine Augustin Cournot (Quantity competition)
1880s: Joseph Louis François Bertrand (Price competition)
1910s: Ernst Friedrich Ferdinand Zermelo (Chess)
1920s: John von Neumann (Zero-sum games)
1930s: Heinrich Freiherr von Stackelberg (Leader-follower games)
1940s: John von Neumann and Oscar Morgenstern (Multi-player games, cooperative games)
1950s: John Forbes Nash, Jr. (Non-zero sum games)
1960s: John Charles Harsanyi (Incomplete information games) and Reinhard Selten (Subgame perfect equilibrium)
1980s: Roger Bruce Myerson, Leonid "Leo" Hurwicz, Eric Stark Maskin (Mechanism design)
Please download the Gambit software which can help solve strategic and extensive form games.
Several problems will be solved with the help of Maple computer algabra system. I would advise using this software, if possible. Student version is available from Maplesoft web site.