“Sir, there is a multilegged creature crawling on your shoulder.”
(Spock, in order to give the Vulcan neck pinch.
And, of course:
“Don’t give me any of that Star Trek crap. It’s too early in the morning.” 
The OP took mine. Set the pattern for all the Trek captains, every seres, every movie. The entire experience, allowing someone loved to die, simply to save the universe as we know it, summed up in seven words. It truly is a powerful line. Considering it was in 1966 makes it darn near supernatural.
So, I’ll go for a second line. It’s not actually a line, tho. It’s a series of notes. Played on a handmade flute. By Captain Picard. Alone in his quarters. Oh. My. God.
“The line must be drawn here! This far, and no farther!” - Quark, The Dogs Of War
And pretty much anything by Garak, the best character in Star Trek history, IMHO.
“You broke your little ships.”–Whats-her-face, First Contact.
Dammit Jim, I’m a doctor, not a (insert occupation here).
Don’t forget O’Brien’s response to the Jem’Ha’Dar battle cry, said to the younger crew under his command:
“I am Chief Miles Edward O’Brien, and I am very much alive. I intend to stay that way. Likewise the rest of you. Got it?”
No, it’s First Contact; Picard is about to violate his terribly stupid orders to stay out of the battle for Earth, and he’s just invited the senior officers to log their protest so as to keep them out of the board of inquiry they’ll be in for if they survive.
God, I’m such a geek.
“You had me at qa’plah.”
“Oh, shit!” Data, Star Trek: Generations
“Your analysis, Spock?”
“It’s yellow, Jim.”
Sorry.
For a single quote:
“If you can’t take a little bloody nose, maybe you ought to go back home and crawl under your bed. It’s not safe out here. It’s wondrous, with treasures to satiate desires both subtle and gross…but it’s not for the timid.” - Q
Nope, twas “First Contact” when they (the Enterprise E) is sent to monitor the Neutral Zone instead of engaging the Borg… Picard says something to the affect of “What I am about to do is a direct violation of Starfleet orders…”
Something about the way Gearge Takei delivered that line made me wish they could have made a series around him and Excelsior. I swear for a moment there he was more of a captain than Kirk, Janeway, or Archer ever was.
My nomination is, “Die.” Said by Worf when Q asks what he has to do to prove that he’s been made mortal. I also like the amused look Riker throws at him when he says it.
Certainly more than Archer.
That’s a good idead for a series, especially if he has been an older fat guy who didn’t go on landing parties. I am however annoyed by the way he pitches his voice deep like Tushiro Mifuni.
“Having a thing is not always as pleasing as wanting it. It is not logical, but it is often true.” Spok, Amok Time
Scotty: “It’s a bottle of very, very, very old scotch…WHISKEY!!”
That and McCoy’s :“She’s got immediate post-prandial upper abdomenal distention.” from ST IV.
Keyboard!? How quaint!
“That’s the stupidest thing I’ve ever heard, of course he’s a Russkie!” - 20th-century Naval Intelligence Officer.
“You hit me!..Picard never hit me!” or something to that effect.
Q, to Sisko, DS9