NBC rejected the original pilot for Star Trek, and in something that Gene Roddenberry has said was highly unusual for a network, ordered a second pilot episode to be filmed. The first pilot, "The Cage" told the tale of a completely different Enterprise crew, with Spock being the only character to remain for "Where No Man Has Gone Before."
This episode introduces the viewer to Kirk, Spock, Scotty, and even Sulu. However, Dr. Piper is on board as the ship's doctor, not McCoy.
The Enterprise has reached the edge of the galaxy, and unexpectedly receives a distress signal from the Valiant, a ship that disappeared 200 years prior. It turns out that the signal is coming from a distress buoy left behind by the Valiant. The buoy's tapes are damaged, but gives some details of how the Valiant encountered an energy barrier at the edge of the galaxy, survived the barrier, but then was intentionally destroyed by the Valiant's captain.
Inspite of the unknown danger, Kirk takes the Enterprise into the barrier. They too are almost destroyed by the field, but manage to return back to our galaxy, with the ship severely damaged. Two crewmen, Gary Mitchell, who is the helmsman, and Dr. Elizabeth Dehner are "zapped" (can't think of a better way to describe it) while the Enterprise is in the energy barrier and are unconcious. Mitchell is revived, and when he opens his eyes, we see that they are silver and glowing. Dehner is stunned, but seems to be normal.
Mitchell is put in sick bay, and very quickly begins to show signs that his mental powers are increasing. As Science Officer Sulu (yes, he is in this post rather than Spock) states, Mitchell's powers are growing geometrically, like having a penny and doubling it every day. In a month, you would be a millionaire. The dangers of Mitchell's powers grow obvious to Kirk, but he is torn by his long friendship with the crewman. Spock suggests that they dock the ship at a lithium cracking station to repair the ship, and then leave Mitchell behind on the barren planet. We see the first conflict between the logic of Vulcans and the emotions of the human crew.
The ship does dock at the station, but just as they have completed repairs and are about to leave, Mitchell grows too powerful, incapacitates Kirk, Spock, and Piper, and escapes with Dehner, who has now mutated into the same being as Mitchell.
Kirk revives and pursues the two super beings with a phaser rifle (the only time we see this in the entire series.) During the fight between Kirk and Mitchell, Dehner realizes that powers have made them corrupt and inhuman, and this forces a final battle between the two mutated crewmen.
One bit of trivia is that during the final scene, Mitchell creates a grave and tombstone, which reads "James R. Kirk" rather than James T. Kirk.
My favorite line in this episode is spoken by Mitchell, just before he escapes from his prison on the station, Mitchell tells Kirk that "Command and compassion are a fools mixture."