Star Trek (the original series), The Trouble With Tribbles, first aired Dec. 29, 1967.
An episode viewed with suspicion and some derision in the fan community, Tribbles was a quirky holiday installment of the show. Tribbles were the forerunners of Gremlins — adorable little furry things that could wreak havoc. (They don't quite destroy the ship, but they get close.) With this episode, Roddenberry no doubt wanted to lighten Trek's dusky mood and indulge his (thoroughly pre-irony) sense of humor. But as 1986's popular Star Trek IV: The Voyage Home would later show, Trek always connected best to a mass audience when the franchise didn't take itself too seriously. What sometimes goes unnoticed about Tribbles are its important canonical moments: it takes place on a "Deep Space" station, a concept that Trek would later spin off into the estimable Deep Space Nine (which later did a kind of Tribble remix episode). The original Tribbles also contains the most direct admission that Klingons are a stand-in for the Russians (in one of Chekov's best scenes, not that that's saying much). Finally, this show contains some of Leonard Nimoy's driest, best geek moments — as when Spock calculates the breeding rate of Tribbles: "one Tribble multiplying with an average litter of 10, producing a new generation every 12 hours over a period of three days." (Extra points to anyone who can redo Spock's math and arrive at the answer.)