To Serve Man. Short story by Damon Knight.
It’s A Good Life. Short Story by Jerome Bixby
All The Time in The World. Arthur C. Clarke??
I wouldn’t have put “All the Time in The World” in there. But “Time Enough at Last” doesn’t actually have a memorable last line.
You’re right, it was Time Enough At Last. Thinking of the lines Meredith says before, ‘it’s not fair!’ Nah, you’re right, the story doesn’t belong. Put that vote instead towards mbh’s contribution of Clarke’s novelization of 2001.
More sci-fi: the last line of Iain Banks’s Surface Detail is amazing. Not for its literary quality, but for how it changes your view of several characters in the Culture series.
Clarke did have a knack for giving the reader a gut-punch at the end of a story. See also “The Star”, though that one, one might at least have seen coming.
The two that come to mind for me are Asimov’s Second Foundation and Clarke’s Rendezvous With Rama.
Matheson’s Born of Man and Woman has a good stinger too.
And With Folded Hands, the author of which escapes me.
Check out my original post. GMTA. 
And no big thing if some posters are quoting the last lines, as long as the surprise endings aren’t completely spoiled. I’m looking forward to reading all the suggested stories, my summer reading list just got a lot more interesting, and a lot longer!
The Weapon Shops of Isher by A.E. van Vogt.
“He Walked Around the Horses” by H. Beam Piper
I second (of fifth or whatever) The Last Question
Jack Williamson. I read it in the Science Fiction Hall of Fame, Vol IIA, which also includes the classics “Who Goes There” and “The Marching Morons”.
I had all three volumes when I was a teenager and I read them at least a couple times each. I can’t recall whether The Cold Equations was in one of them, but that’s got a hell of a final line as well.
The Cold Equations is in Volume I. The Wikipedia entries I linked have a list of the contents.
A lot of Asimov votes here, but it looks like I’m the first to nominate “The Dead Past”.
There are a lot of Fredric Brown stories that fit – Brown was a master of the short-short, and had lots of stories with twists or puns at the end, in addition to a lot of more serious stuff.
His story “Knock” has the same line at the beginning and at the end, but the meaning are completely different.
Others:
“Great Lost Discoveries I: Invisibility”
“The Ring of Hans Carvel”
“Abominable”
…and several others I can’t recall the titles of.
I concede Stephen King horror stories aren’t hardcore SF, but the last line of, “Pet Semetary,” and the last line of, “Survivor Type,” (short story) both gave me the willies.
“Nightmare in Yellow”?
The short story “Summer’s Lease” by Joe Haldeman - the last sentence totally changes your understanding about what just happened
Tool of the Trade by Joe Haldeman - a perfect concluding sentence, and a great setup for the sequel that he unfortunately never wrote
Tuf Voyaging by George R.R. Martin - echoes a sentence earlier in the book, and is chillingly ambiguous, under the circumstances
The two I immediatly thought of have been mentioned above (A boy and his dog, The Nine Billion Names of God), but by chance I just watched “Predestination” (2014), which is based on “—All You Zombies—” by Robert A. Heinlein.
I could be wrong about the last line – a movie has to be less dialog driven – but I remember a last line, and that would be the third one.