Shore Leave

Bogmeister and others have pretty much nailed this. Shore Leave is really TOS' first attempt at lightweight sci-fi (which they would later perfect with the classic Trouble with Tribbles). It gave both the crew of the Enterprise and its TV viewers a needed respite from the universe threatening consequences of, for example, The Corbomite Manouever.

Looking for a place to chill out for a while, the Enterprise happens across a seemingly idyllic M Class planet, and sends an exploratory team down to take a closer look. Soon enough all kinds of absurdities begin to take place - some seemingly perilous - but it all seems a morass of human emotional extremities played out in a weird blend of fantastic mystery (McCoy has gone through the looking glass), psychological thriller (Kirk is stalked by an indefatigable bully from his past), and romantic comedy (no comment).

TOS was the least serialized of all of the series in the Trek franchise, so it is easy to forget how many episodes in the first season focused on heavy-handed, potentially calamitous drama. Unlike later series franchise writers, TOS' production team was not afraid to literally go where no TV series had gone before. And Shore Leave, despite its occasional problems, is an example. My only criticism of this episode is that the cast (particularly Shatner - ironic given his legendary sense of humor) didn't seem to know how to handle this new wrinkle on ST's themes. The last scene is possibly one of the worst scenes I can remember from the entire TOS run - both compositionally and in terms of acting.

'nuff said. My recommendation - see it while watching the entire first season as it was meant to be seen - it order.