This is an especially enjoyable episode if you close your eyes and visualize Piglet speaking all of Hengist’s lines.
Star Trek IV: The Voyage Home seems to have most of the best lines I can remember from the ST movies. A few that haven’t been mentioned yet:
Chekov, to a cop in present-day San Francisco: “Excuse me, I’m looking for the nuclear wessels.”
Scotty sits in front of a 1980s PC and says, “Computer.” Nothing happens. Someone points to the mouse and says “No, you use that”. Scotty picks up the mouse and speaks into it.
Spock to Kirk, after they’ve been thrown off a bus: “What does it mean, ‘Exact change’?”
Do controlled substances help you do that? 
John Fiedler (Mr. Hengist) was the voice of Piglet in many of the Winnie-the-Pooh movies.
I hate having to explain my jokes.
Really? I thought Piglet was Stanley Holloway (hence, the whoosh). I’m off to the IMDB…
When I was a computer tech, picking up the mouse and saying “Hello Computer” in my best Scotty accent was deffinately my most used Star Trek quote.
Kirk’s all-time best line:
“No more bonk bonk!” (from Miri)
I must agree that Worf gets the absolute best comic moments. My favorite is in the Robin Hood episode when he reaches over, grabs Geordi’s lute, smashes it against a tree, hands the fragments back, and deadpans…
“Sorry.”
City on the Edge of Forever.
Kirk has just stopped McCoy from rescuing Edith Keeler, and she’s struck by a car and dies. Bones is furious, asking, “Do you know what you’ve done!”
Spock: “He knows, Doctor. He knows.”
Bones: “Shouldn’t you be working on your time warp calculations?”
Spock: (just standing there) “I am.”
I always think of Mr. Peterson from The Bob Newhart Show.
TUC has some of my absolute favorites:
Spock: “Logic, Logic, Logic. Logic is the beginning of wisdom, Valeris, not the end.”
Kirk: “How on earth can history get past people like me?”
Spock: Mr. Scott, I understand you are experiencing difficulties with the warp drive?
Scotty: There’s nothing wrong with the bloody…
Spock: Mr. Scott, if the Enterprise responds to hails and returns to Starbase, there is a good chance that we will never see Captain Kirk or Doctor McCoy alive again.
Scotty: Could take weeks, sir…
From “The Immunity Syndrome”
“Spock! You’re alive!”
“Obviously.”
(We omit here the too-often-quoted moment from “The Naked Now” in which Data is interrupted in his recitation of a limerick he does not understand.)
From “Generations”:
Geordi: “Data! That’s not funny” (patently lying, as the entire movie theatre is in stitches).
“Keyboard! How quaint!” (The rest of Scot’s “Hello computer!” at Plasticorp)
Another Scot-ism from ST III: “The more they overthink the plumbing, the easier it is to stop up the drain.” I use that one just about every time I encounter a nyetwork. (Computer says “Nyet! I can’t find the printer!”)
Data had a couple in Generations:
Scanning a planet for life: “Life forms! You tiny little life forms! You precious little life forms! Where are you?”
As the ship is hurtling out of control to the planet surface: “Oh shit” Just totally out of his normal behavior.
From a TNG episode, when tending bar, he’s asked about a particular beverage: “It is green”
Isn’t that from the episode where the TNG crew found Montgomery Scott’s pattern in the transporter, from within the Dyson Sphere or something? IIRC, the line was supposed to be homage to his identical line from one of the TOS episodes…
From Miri.
Punk kids chant “Bla, bla, bla. Bla, bla, bla.”
Kirk replies " No blah, blah!" in that special Shatner kind of way.
Data: How is your diplomatic assignment progressing ?
Worf: Fine.
Data: I have heard that in moments of diplomatic tension it is often helpful to find elements of commonality.
Worf: Mister Byleth is demanding, temperamental and rude.
Data: You share all of those qualities in abundance. Perhaps you should build on your similarities
Spock: “I’ve been dead before.”
Data, smiling, to an arguing bunch of dweebs (a line I’ve been able to use here from time to time): “Please continue the petty bickering.”
oooo ooo I though of some more:
From **The Changeling ** when Kirk has logiked Nomad into a self destruction
SPOCK: “Captain your logic was impeccable, we are in great danger!”
From The Deadly Years
Senile Kirk: “Go on ask me anything… ask me. We are in orbit around gamma hydra II” (Several times he has been reminded that they are orbiting Gamma Hydra IV, it is a subtle slip up that works)
Kirk upon being told he will be executed on Roman TV:
The Proconsul: Of course you are well beyond anything as primative as Television
Kirk:I’ve heard it was… similar
From the same episode McCoy’s berating of Spock:
McCoy: Do you know why you’re not afraid to die, Spock? You’re more afraid of living. Each day you stay alive is just one more day you might slip and let your human half peek out. That’s it, isn’t it? Insecurity. Why, you wouldn’t know what to do with a genuine, warm, decent feeling.
(long pause)
Spock: Really, Doctor.
Cold it was… Like a stinking draught from out of a slaughterhouse.
“In Theory” is the name of the episode.