Where No Man Has Gone Before, a Star Trek RPG with light rules, basically is a parody of Star Trek (though it can also be played seriously). Every silly trope of the classic series is in the rules: you can play a redshirt who dies each episode and is replaced in the next viable scene; NPCs will fall in love with a random PC at first sight; you can rip your uniform for an advantage in battle. The optional TV rules mean random stuff can happen based on ratings, like a chimp joins the crew.
http://www.abillionmonkeys.com/trek/