Since there are 2 ST threads going, why not start a third?
My favorite STs were…
ST:tNG - “Brothers” - where Data’s homing signal kicks in and he hijacks the Enterprise (Data kicked *ss!)
ST:tNG - the 2-part Borg cliff hanger where Picard is assimilated.
And since I also weighed in on one of those other two threads, might as well keep the ball rolling…
ST:TOS: City on the Edge of Forever (w/ Joan Collins)
Deep Space Nine: The two-parter consisting of “Improbable Cause” and “The Die Is Cast”
DS9: Waltz
DS9: The Wire
Sorry that I don’t know the actual episode names.
ST:TOS the one where they first meet the Romulans. It was a take off of the movie “Enemy Below”.
ST:TNG the one where picard is taken over by a space probe. He passes out and in his mind he lives a complete life on a dying planet in a matter of hours. Great acting and concept. It put great doubt into my mind as to who was the better Captain (I still think Kirk could take Picard in a fight. I mean, how could Picard contend with the devastating judo chop to the back?). 
ST:TOS: City on the Edge of Forever
Patterns of Force
ST TOS The Doomsday Machine
The Balance of terror (enemy below)
The City on the Edge of Forever
Arena
The Galieo 7
The Trouble with Tribbles
ST TNG The Inner Light (Picard probe one)
ST DS9 The final two episodes
ST Voy Well…
Can you guess which series is my favorite?
Anyone know the name of the original Star Trek episode where the crew beams down to a planet and finds that they’re fighting a war via computer simulation- when a bomb drops in the simulation, hundreds of people have to go to die? IIRC, Kirk destroys the machine (violating the PD) and then gives an impassioned speech about how war is ugly but you still have to fight. Blew me away when I saw it as a kid.
In addition:
-The Menagerie, the Cage
-ST: TNG where there’s an eldery couple (really super powerful beings) that are covering up the fact that they were involved in genocide.
DS9: Duet (Kira interrogates a suspected Cardassian war criminal)
DS9: In the Pale Moonlight (Sisko playes underhanded tricks to get the Romulans involved in the war with the Dominion)
DS9: The Visitor (Sisko disappears from existance in a tech-accident, and Jake spends a lifetime trying to retrieve him)
And in fact most of the rest of the series, with just a few exceptions.
TNG: Best of Both Worlds (Borg 2-parter)
TNG: The Pegasus (Riker’s old commanding officer comes to retrieve an illegal experiment from the wreckage of the USS Pegasus)
and… um… many, many others.
VOY: The one where it’s revealed that the whole series was a bad holonovel written by Wesley Crusher. (Oh, wait, that hasn’t aired yet, silly me!)
TOS: Balance of Terror - great suspense
I, Mudd - Spock trying to “act”
Mirror, Mirror - Spock sportin’ a goatee!
TNG: Yesterday’s Enterprise - kick ass ending
Best of Both Worlds - The Borg at their scariest
DS9: Trials and Tribulations - worth it for
Worf’s “explanation” as to why old Klingons and new
Klingons look different
Crossover - a look at the universe created in “Mirror,
Mirror”
(can’t find the title) - Where the station is armed to
the teeth. One of the best space battles ever shown.
VOY: A Year in Hell - even though it didn’t “happen” and
the idea that Plainway could keep the ship going that
long is insane, it had great EFX AND the dad from “That
70’s Show”
The City On The Edge Of Forever.
My favorites always make people look at me funny. Anyway, I have two, both from TNG. And, no, I don’t know episode names. Forgive me.
The first has already been mentioned - where Picard lives the alternate life on the extinct planet.
The other was the one just after the two-parter where Picard was assimilated, where he goes back to Earth and stays with his brother.
Both of those moved me nearly to tears, back when I was a teenager, of course. It’s easy to see how Stewart is a respected Shakespearean actor from those.
The TNG episode where Picard lives out a different life as ‘Kamen’ was called “The Inner Light”, and I think it was the best episode of TNG.
For the Old Series, City on the Edge of Forever, although I have a fondness for the comedy episodes like “I,Mudd”, “The Trouble with Tribbles”, and “A Piece of the Action” (Spock: I’d advise ya’s ta keep dialin’, Oxmyx!). And who can forget ‘Fizzbin’?
A Taste of Armageddon
My favorites (TOS only–I’ve seen TNG but was not as into it):
Balance of Terror
Mirror, Mirror (LOVED THE MST3K takeoff!)
City On The Edge of Forever
The Ultimate Computer
Turnabout Intruder (Captain Kirk filing his nails! Also having a tantrum in the courtroom.)
Journey To Babel
The Trouble with Tribbles
Where No Man Has Gone Before
Amok Time
The Doomsday Machine
Space Seed
I truly hated:
Spock’s Brain
And The Children Shall Lead (starring the friendly lawyer, Melvin Belli)
The Way to Eden
And of course, the Execrable Beyond Words: Star Trek V
I’m probably the only person who will admit to this but one of my very favorite things about the show was watching some of the actors overact:
–Shatner (numerous, numerous occasions)
–William Marshall in The Ultimate Computer (“Colleagues…mocking me as the boy wonder…and becoming rich and famous…building on my work. MY WORK!!”)
–William Windom in The Doomsday Machine
(“They’re on the third planet.”
“There is no third planet.”
“DON’T YOU THINK I KNOW THAT? THERE WAS–BUT NOT ANY MORE! THEY CALLED ME, THEY BEGGED ME FOR HELP! FOUR HUNDRED OF THEM, BUT I COULDN’T! I SIMPLY COULDN’T!”)
Damned if I know why I enjoy it so much.
TOS:
Mirror Mirror
The Enterprise Incident: Kirk steals cloaking device.
Trouble with Tribbles
City on the edge of forever
Where no man has gone before: Simply because Kirk beats Spock in 3d chess.
The Menagerie: Good, for it’s day.
The Cage: Loved it.
TNG:
Best of Both Worlds: if only for Riker’s line at the end. “Fire”.
The Big Goodbye: the first Dixion Hill holodeck. I loved the ending where the holograms ‘know’ what’s up, and realise that when the deck is shut off, they die.
Relic: Scotty was priceless
DS9: Um. The last season,mainly.
Voyager: the one where the crew finally gets home. Oh, that hasn’t happened yet. 
DRY said:
“Brain and brain, what is brain?”
Still cracks me up everytime I hear that.
Lessee…Next Generation:
The one where Picard is captured and interrogated by the Cardassians (“THERE…ARE…FOUR…LIGHTS!!!”)
The one where Riker jumps back and forth between a play on the Enterprise and a first contact mission where he’s disguised as a native then captured and imprisoned, and it turns out he’s a prisoner of the Romulans who are trying to find out the location of a secret base
The one where the Enterprise explodes three times while it’s caught in a time loop (“All hands abandon ship! Repeat…ALL HANDS ABANDON… KABLAM”)
Definitely Inner Light is also one of my favorites.
As for the others, I like pretty much all I’ve seen of Deep Space 9 and none of what I’ve seen of Voyager.
Correction: I’ve seen one voyager episode I liked. They had found an intelligent bomb and it takes over the holograph doctor and the ship, they talk it out of carrying out its mission because the war is over, and it blows up its comrades.
Original show: Hard to say. Like DRY, I really like the overacting and cheesiness, and I always watch if it’s on, no matter which one it is.
That is the best line in that otherwise horrible episode. Mr. Grey and I saw it again the other day, and now we quote that line around the house.
My favorites, other than the obvious ones like City on the Edge of Forever, are the funny ones. I laughed so hard I cried, watching I, Mudd and A Piece of the Action.
I liked TNG, but don’t remember many episodes specifically. I hate DS9, and I like Voyager, though I don’t watch it unless I happen to catch it while flipping channels.
That would be “Balance of Terror,” which had as a guest star Mark Lenard as the Romulan commander. Lenard, of course, would go on to play Spock’s father Sarek. He also played the Klingon captain killed by V’Ger in Star Trek: The Motion Picture, making him the only person to play a Romulan, Klingon and Vulcan.
Incidentally, Sarek was the first major Star Trek character to die.
I’m going to go turn myself into the geek patrol, now…
Since my favorites have already been mentioned for the most part, some others I liked:
TOS:
The Paradise Syndrome- I always felt so bad for Kirk in this one, even worse than in The City on the Edge of Forever. He had a beautiful wife, child on the way, and a sense of peace, all lost.
Conscience of the King- Very well done weaving the elements of both Hamlet and Macbeth into the storyline. Since I saw this long before I read either play, I was delighted to be able to get more out of the episode once I knew the stories it was cobbled together from.
The Empath- Not too many folks care for this one. I realize the sparse sets were mostly because of budget constraints, but I think the very austere, black sets add to the essential strangeness of the plot. Plus, the empath, Gem, was truly effective at conveying her emotions without ever speaking. Her movements and facial expressions were excellently done I thought.
I’m not nearly as big a fan of the other shows, although one I remember that hasn’t been mentioned yet is When Q is exiled from the Continuum and becomes human. I love that one! Especially the ending where he shrinks the energy cloud beings down into the palm of his hand. “You think I tormented you before…”
Oh, and DRY, you missed Nimoy’s hamfest in *Devil in the Dark, when he mind-melded with the Horta: “PAIN! Sorrow! Murder! The end of eternity.” Oink! Oink!
TNG:
Cause and Effect: Where the Enterprise becomes trapped in a time warp and blows up over and over again.
The Inner Light: I think most people have this one on their list.
Conundrum: Everyone has amnesia, and they think that they are at war. Riker gets frisky with Troy and Ro.
Remember Me: The crew of the Enterprise gets smaller and smaller, and Beverly is the only one that notices.
Tapestry: Picard has troubles with his artificial heart, and Q gives him a chance to go back and relive some of his youth.
DS9
Hard Time: O’Brien spends what seems like 20 years in prison, and tries to adjust to life afterwards.
Several others, whose titles escape me.
The one where most of the DS9 crew land on a planet, and discover their descendants. If they leave, everyone dies.
The one where Jake, as an older man, tells the story of how his father got caught in some kind of energy field and can’t get out of it.
The one where Quark has to assemble a team of Ferengi to negotiate to get his mother back from Dominion forces.
Speaking of the geek patrol, they’re banging on my door. What the heck do they want now? I already handed over my pocket protector…