TOS #28: The City on the Edge of Forever

Of all episodes of TOS, I believe this might be the one that affected me most, personally. In it, Bones OD and transports down to some weird anomalous ruins on an otherwise unremarkable planet. He jumps through this time gate into about 1930, altering the timeline significantly. The rest of the away party appears to be inside some kind of immuned area, as they are now trapped in an alternate timeline in which there is no Enterprise in orbit. The gate lights up when it talks, and it kind of insults Spock.

It agrees to replay Earth's history and Kirk and Spock try to jump back to just before where Bones went. They miss by what appears to be several weeks. Once they get back to 1930, Kirk meets Joan Collins and falls in love with her. Spock figures out that the timeline alteration is that Bones saves her. By saving her, he causes the US not to enter World War II in time, letting the Germans develop atomic weapons first and win the war.

Although Kirk is in love with her, he stops Bones from saving her at the critical moment and fixes the timeline. The gate thing then allows them to jump back to their own time and beam up to the Enterprise. The thing I like best about this episode is how Kirk and Spock work for pennies a day to buy parts which Spock uses to build a computer to interface with the tricorder to figure out what's happening to the timeline.