Atomic Sock Monkey Press offers a free boardgame, Monkey, Ninja, Pirate, Robot, its not-free expansion Monkey, Ninja, Pirate, Robot Deluxe (which also includes Clowns, Cowboys, Mutants, Punks, and Zombies), and Monkey, Ninja, Pirate, Robot: the Roleplaying Game, which includes Aliens.
A popular variation on Rock Paper Scissors is Bear Ninja Cowboy. Another variant, Rock Paper Scissors Lizard Spock, introduces two new hand signs.
There's a boardgame called For The Win where each player controls two Monkeys, two Zombies, two Pirates, two Aliens, and two Ninjas. Each piece has a special ability and you win by forming one of each into a group.
In the popular board game Small World, player-controlled factions are combinations of unique powers, one 'adjective' special ability and one 'noun' race. Vampire Elves, Were-Orcs, Seafaring Ghouls, Magic Giants, Flying Dwarves...
The entire premise of the game Smash Up! is combining cool things: the base game comes with Aliens, Robots, Pirates, Ninjas, Dinosaurs, Fey, Zombies and Wizards, which are then combined into decks such as "Ninja Dinosaurs", "Wizard Pirates" or "Zombie Robots"; expansions add things such as Steampunk and Bear Cavalry (AKA Russians).