If I had to pick one of your limited categories, I would pick the Constitution ep, if only because it offends my super-refined sensibilities (tm) as a Canadian. As well, it laid the groundwork for decades of thinly veiled American flag-waving in the Trekkie-verse.
Well, the reason the choices are limited is because 1) they only allow so many options for polls on this forum, 2) you only REALLY need "Spock's Brain," 3) I'd be remiss if I didn't mention the Shari Lewis episode (yes, THAT Shari Lewis), and 4) If there was an "Other..." choice, everybody would pick that one and it would defeat the purpose of a poll to begin with, wouldn't it?
Hey come on, the Space Hippies episode was great!
Yeah, that's true. I loved that one, and even Spock with that funky autoharp of his joining a hippie jam session is more "wow, that's kinda kitschy and cool," sort of like episodes of the cartoon where the Harlem Globetrotters travel through time, or that episode of KNIGHT RIDER that guest-starred Gary Coleman.
I think that the show jumped the shark after season 2. Gene Roddenberry took a much more reduced role, less hands-on, in the 3rd season. As a result, his humanistic message was lost, and people were completely out of character - I even remember one 3rd season episode in which Spock (yes, Spock, not Kirk) was trying to pick-up some space babe!
There's a famous story about Gene leaving and Freddy Frieberger taking over.
When Frieberger was shown the series bible, he was leafing through it, and then suddenly looked up and said, "Oh, okay, so this is pretty much 'tits in space!' "
For me, Season III was the "shark jump" point too. Here's an amusing story about Gene Coon, writer of "Devil in the Dark" and that tribble episode:
According to Coon, he wrote "Spock's Brain" (the Season III opener) as a parody script to spoof Gene Roddenberry, who Coon felt never really understood science fiction. Coon never actually intended it to be filmed!