In case you forgot: The Enterprise is charting new space territory and encounters a rainbow cube they (correctly) presume to be a buoy. When it starts emitting deadly radiation they have no choice but to destroy it, only to incur the wrath of Barok, representative of a group called the First Federation. After some tensions and bluffing, Kirk, McCoy, and This Episode's Navigator Bailey (who reminds Kirk of himself) beam aboard to find out Barok looks like a child and is perfectly kind and well-intentioned. Bailey stays behind to keep the lonely Balok company.
TOS makes a big deal out of how Kirk is an exceptional starship captain, or at least that you have to be an exceptional person to be a starship captain, but a lot of episodes Kirk ends up being a brave guy with a strong moral center, which while good is hardly unique. (Never mind the episodes where he ends up just plain being an idiot.) Sure, much is made about how his true love is the Enterprise, but Scotty is just as enamored of the ship, if not more. Inappropriate transferred feelings do not a starship captain make. "The Corbomite Maneuver" is great because it's one of the times where we see Kirk actually being the captain of a starship. Not only that, but he does a bang-up job of it. After he bluffs and maneuvers the Enterprise out of danger, he has both the giant brass balls and the compassion to beam aboard to what appears to be a ship in distress to meet Balok and see if everything is okay. (Though why couldn't they have just beamed Balok aboard if they were concerned? Anyway...)
I'll admit the reveal at the end (surprise! Barok is Ron Howard's baby brother!) is a "your mileage may vary" situation, but I like it. The dubbing is pretty well done and, well, considering all the other silliness out there in the Star Trek galaxy, I'm willing to buy a race of super-intelligent child-looking beings. It also wraps up the incessant character development we have for what would normally be an unimportant no-name navigator. On a more personal note, I watched the series in its production order, not its air date, the first time I saw it. This means that "The Corbomite Maneuver" was the first proper episode I saw after the pilots. In retrospect, it may have given me unrealistically high expectations for what was to follow.
Why the gratuitous medical exam at the beginning? Were they hoping to tap Shatner's sex appeal by having him spend the first few minutes of the episode without a shirt on? Did he insist on that himself?