Star Trek: 15 Greatest Ever Time Travel Episodes

This episode could probably have qualified based on the fact that it was the first time the show ever played with time travel as a story element, but it actually deserves mention on its own merit too.

Beginning with the image of a 20th century fighter pilot spotting the Enterprise and calling it a UFO, after the ship is accidentally whiplashed into the past (just before the Moon Landing, actually) by the gravitational pull of a black star. He ends up aboard the ship as the crew attempt to fix all damage and return him to his past. There's also a side kicker of the reprogrammed computer being in love with Kirk, which is always a nice touch.

Obviously, there are some issues with the time travel explanations (in that beaming the pilot back to his own time suddenly wipes out the future version of himself and all of his memories), but if james Cameron can make millions ignoring his own "scientific" rules of time travel, that much is forgivable.