Top 10 personal greatest Trek moments

[Balok's Decoy]

Not confident about putting these in any particular order other than when they came to mind:

1. In TMP when Kirk gets on the turbolift of the refit, and he reaches out to turn the handle, which isn't there anymore, and looks wistful as he glides his hand along the wall.
2. Spock's death, obviously.
3. Kirk's speech at the end of TUC. Just a beautiful send-off.
4. The battle with the Orion ship in Journey to Babel. "You speculate."
5. Basically every scene with Kira in Duet.
6. Kirk's death in Generations. "It was....fun." (Oh God I'm gonna cry!)
7. "Risk is our business."
8. Spock shouting, "Jim!" when he sees Kirk is alive at the end of Amok Time.
9. Jarok's conversation with Picard, when he talks about his daughter in The Defector.
10. Picard's defense of Data in The Measure of a Man.

I could probably name a hundred other moments that affected me, moved me, or made me think. That's why I love this franchise.

Great question!

EDIT: Honorable mention: "Ode to Spot."

 

[The Old Mixer]

In TMP when Kirk gets on the turbolift of the refit, and he reaches out to turn the handle, which isn't there anymore, and looks wistful as he glides his hand along the wall.

I've never noticed that...I'll have to remember whenever I watch it again.

 

[UnknownSample]

My favorite Trek moment/scene (though it's broken up into 2 or more segments) is in City on the Edge, from when McCoy arrives in the 1930s in that creepy slow motion, through his horror at 20th century medicine, up through the hobo accidentally phasering himself in the dark in the alley. I tend not to go so much for sentiment, but for odd, unsettled, conflicting emotions.
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"Time is the fire in which we burn." -- Generations.
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Q Who... when it appears hopeless, and the final few seconds with amazing music that expresses wonder at the universe, but a bit of horror at what's coming, at the same time. A sort of appreciation of the dark beauty of what may be a hopeless situation for civilization.
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BoBW... the conversation between Picard and Guinan, in which her "hopeful" remark is that humanity will survive the Borg, even if just in small scattered numbers across the galaxy. That made it all very real.
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Faceless corridor woman from Charlie X.
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Decker's story about beaming his crew to now destroyed planets.
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[flandry84]

I won't list ten but here are two
When the Prometheus assumes multi-vector assault mode...it just made me smile.

"...and Mr.Worf,prepare quarters for minister Yale..she will be joining us"Probably my favourite scene from a great episode.

Edit;how could I have forgotten the Picard/Jarok scene from "The defector"?

 

[ClayinCA]

There are so many wonderful, brilliant ones. But the one I can't believe no one here has mentioned yet is:

"Jim. Your name...is Jim."

 

[Tracy Trek]

It's not really part of the plot of Star Trek 6 The Undiscovered Country. But at the end when all the cast signatures came on the screen. It was a good send-off for the last time the crew was together.

 

[f14peter]

Not 10, only 8, but not even my top 8 ...

McCoy: "That's a mighty big ship"
Scotty: "Not so big as her captain I think"
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Sulu: "C'mon ... C'mon!"
Helmsman: "She'll fly apart!"
Sulu: "FLY HER APART THEN!"
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the final scene of TOS: BALANCE OF TERROR when Kirk consoles the grieving almost-bride Martine, then strides down the crowded corridor, isolated and alone with his own grief in his captaincy
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Scotty: "I didn't get that exactly, Captain. 100 what?
Kirk: "100 ... serpents. Serpents for the Garden of Eden. We're very tired, Mr. Spock. Beam us up home."
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The very opening sequence of ST: TMP with the attack by the three Klingon Battlecruisers. The "Klingon Imperial Theme" is still my favorite piece of music in the franchise
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in TNG: LOWER DECKS after Ensign Sito is handcuffed by Joret Dal, she girds herself to meet the Cardassian border guards
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In TNG: LOWER DECKS the reaction of her friends as Picard announced Sito's death
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Jem H'Dar Ikat'ika: "I yield! I cannot defeat this Klingon. All I can do is kill him. And that no longer holds my interest."

 

[Balok's Decoy]

The very opening sequence of ST: TMP with the attack by the three Klingon Battlecruisers. The "Klingon Imperial Theme" is still my favorite piece of music in the franchise

Agree, that theme is iconic. I also love the overture before the movie officially begins. I think it's called Ilia's Theme. Gorgeous.