Huh, did not expect that memes and captioned image responses would outnumber typed text... fascinating. I still think of my favorite lines as lines first and organic parts of visual scenes second.
I personally like short monologues by powerful characters that later turn out to be insincere hypocrisy, like this daniel day lewis speech from there will be blood (I haven't watched the movie, but know the plot)
There's a great snippet in Rome where Caesar denies involvement in the murder of an opposing partisan -- "I didn't know he existed until he didn't" -- delivered so well that I believed him until proof arose of the lie.
(And of course the Usual Suspects quote I already gave.)