Because making lists is FUN!
This Side of Paradise
The marijuana sex pollen ep, where Spock finds Romance, McCoy finds a Mint Julep, and I'm not sure what everyone else was doing.
The City on the Edge of Forever
This won a Hugo. McCoy goes back in time and changes history, wiping out this timeline. Kirk and Spock have to fix it. This is very dramatic and tragic and also Kirk and Spock wear plaid and share a room.
Amok Time
The slashiest episode in the history of the world. Pon farr!!!!!! Spock has an emotional outburst!!!
Mirror, Mirror
Everyone knows this one - the original alternative universe!!! where there's an Evil Empire and Spock has a Beard!
The Trouble With Tribbles
Possibly the most famous episode ever, and for good reason. Importantly, Scotty starts a barfight.
Journey to Babel
Where Sarek and Amanda are adorable and Spock and Kirk are both stubborn. Or, you know, plot.
A Piece of the Action
This is not a great plot but I don't care - Kirk and Spock get to dress up in snappy suits and play at being gangsters!! Fizbin is invented.
By Any Other Name
This was always my favourite episode, even though it doesn't make it on to any official lists nowadays. Powerful aliens assume human form and take over the Enterprise. Our heroes distract them by provoking strong emotions. Kirk, of course, kisses the beautiful woman and Spock taunts the leader by telling him how hot Kirk is, attractive the woman finds Kirk. There is amusing fight scene! And then everyone lives happily ever after. What? I'm a sucker for romance!
Patterns of Force
Kirk and Spock in Nazi uniforms really shouldn't look that hot, is all I'm saying. And then they lose their shirts, get whipped a bit and get thrown in jail together!
The Enterprise Incident
This is AWESOME. Kirk goes mad! Spock kills him with THE VULCAN DEATH GRIP *dun dun* Spock seduces the Romulan Commander! Kirk has plastic surgery to look Romulan! WHAT'S NOT TO LOVE.
The Tholian Web
Spock and McCoy have to put aside their differences to save the Captain.
Wink of an Eye
There's some plot and then Kirk has sex! *gasp* We know this because he is sitting on his bed putting on his boot, while the girl fusses in front of a mirror. This was VERY RISQUE at the time.
NOT favourites of mine but deserving of special mentions are -
The Menagerie
Also won a Hugo. Only two-parter. Spock displays intense loyalty to his previous captain, Pike, and nicks off with the Enterprise to help him out. Kirk is miffed.
Turnabout Intruder
The sexism in this episode is almost hard to believe - Kirk's old girlfriend is crazy jealous and just plain crazy because she wasn't allowed to be a Captain, because, you know, women can't be captains and look what happens to them when they delude themselves into believing they should be allowed to!!! I actually find these scenes nearly too uncomfortable to watch. Anyways, so she finds a way to swap bodies so she can be Captain Kirk, and Kirk is forced live as a pathetic inferior woman. Where this episode keeps its awesome is the scenes where Spock realises Kirk is in the woman's body by mind melding with him and supports him against "Captain Kirk", and of course Shatner's portrayal of a crazy woman.
What do you think?