10. The Enemy Within
The Enemy Within is a lot of things. Hilarious? Absolutely. Completely and utterly entertaining? Even more so.
Famous for Shatner's impeccably hammy "I'm Captain Kirk" routine, The Enemy Within exemplifies all there is to love about classic Trek. When a faulty transporter splits the Enterprise's Captain into two halves - one good, one bad - its crew have to band together to make things right, with the added caveat that the evil half isn't as agreeable about the whole thing as his kinder, albeit less authoritative counterpart.
Written by Richard Matheson and directed by Leo Penn, the fourth episode of the show's first season served as a fine indicator of what was to come in the series' immediate future. Evil Kirk roams around the Enterprise in a drunken, violent stupor until the good version and Spock track him down in the engine room, all while Sulu and other members of the Enterprise's crew are trapped in the worsening climate of a nearby planet, unable to beam up after the resulting battle onboard the Enterprise.
It's remarkably tense stuff, not just for the plight of the crew on the planet below, but for the zany duality of Shatner's performance too.