Frankly, my dear, I don’t give a damn.
“Fill yore hand, you sonuvabitch!”–Rooster Cogburn
*Casablanca *had so many. My favorite is:
Renault: I’m shocked, shocked to find that gambling is going on in here!
Employee: Your winnings, sir.
Renault: Thank you very much.
I could add another dozen or so, but the OP restricts me to one.
I realize that I’ve quoted more than one line. That’s for context, I guess, and the line, the great line itself, is “Thank you very much.”
Harry Callahan: I know what you’re thinking. “Did he fire six shots or only five?” Well, to tell you the truth, in all this excitement I kind of lost track myself. But being as this is a .44 Magnum, the most powerful handgun in the world, and would blow your head clean off, you’ve got to ask yourself one question: Do I feel lucky? Well, do ya, punk? – IMDb Quotes: Dirty Harry (1971)
Seinfeld, The Contest.
Kramer: “I’m out!”
“Non!”
– Marcel Marceau, Silent Movie
“Kirk to Enterprise. It’s been two hours, are you ready?”
– Admiral Kirk, Star Trek II: The Wrath of Khan
“Name it.”
– John Rambo, First Blood, on being asked “What do you hunt with a knife?”
“Hey you! That’s right, you stupid Kraut bastards! That’s right! Say hello to Ford, and General fuckin’ Motors. You stupid fascist pigs. Look at you! You have horses! What were you thinking? Dragging our asses half way around the world, interrupting our lives. For what? You ignorant, servile scum!”
Pfc David Webster shouting at a passing column of German prisoners, Band of Brothers ep. 9, Why We Fight
My current favorite line from ‘The Big Lebowski’, which would put it in the running for my current favorite of all lines… but I digress.
Two police officers, one 20-something and white, the other older and black, have come to take the dude’s report about his stolen car. The younger cop,who does all the talking, is polite to this disheveled pothead. But the older cop makes no attempt to hide his disgust as he wordlessly takes in the squalid surroundings.
The dude describes the contents of the car, including a tape deck, “and some Credence”. When he asks, “Do you find them much, these stolen cars?”, the younger cop replies, “Sometimes. But I wouldn’t hold out much hope for the tape deck”.
"Or the Credence", adds the older cop.
Never have so few words, so neutral in literal meaning, conveyed so much contempt.
“Where the fuck is Wallace?” - D’Angelo Barksdale, The Wire
I hate picking just one. Of anything. You suck. 
Y Tu Mama Tambien: Julio Zapata (translated): “Truth is cool but unattainable… the truth is totally amazing, but you can’t ever reach it.”
Another from Casablanca:
Well if we are doing Casablanca
I love the last line about NY.
I’m not sure it’s the greatest, but it’s a favorite of mine, from Broadcast News:
Paul Moore: "It must be nice to always believe you know better, to always think you’re the smartest person in the room. "
Jane Craig: “No. It’s awful.”
“Take your stinking paws off me you damn dirty ape!”
(Sorry if already posted – so, I’m lazy.)
Number Two: You destroyed me.
Number Six: No.. you destroyed yourself. You destroyed yourself. A character flaw. You were afraid of your masters. A weak link in the chain of command waiting to be broken.
Number Two: Don't tell them... don't report me.
Number Six: ***I don't intend to. You are going to report .....yourself.***
Number Two: [*taking the phone*] I have to report a breakdown.. in control. Number Two needs to be replaced. Yes, this is Number Two reporting. [*breaks down in tears*]
- The Prisoner (TV, 1967) “Hammer into Anvil”
“It’s Chinatown, Jake.”
All very fine choices indeed.
First one that popped into my mind was “We’re gonna need a bigger boat.”
Followed by “Frankly, Scarlett, I don’t give a damn.”
You have that last one wrong. Someone else back thread has it correct. It’s “Frankly, my dear, I don’t give a damn.”