Just read or hear them and a whole story leaps to mind.
“Oh, the humanity!”
“He is moving like a tremendous machine!”
“I am not a crook.”
“The die is cast.”
I recognize only 2 of those. Perhaps they’re not as iconic as you think they are.
“A date which will live in infamy”
“That’s one small step for (a) man”
“That’s no moon!” (in fictional history)
Which two do you not recognize?
Your #2 & 4. Numbers 1 and 3 are easy / obvious (to me).
“The die is cast” – should have used the Latin original, “alea iacta est,” attributed by Suetonius to Julius Caesar as he crossed the Rubicon.
“tremendous machine” – uttered by Chick Anderson, the track announcer, during Secretariat’s record-shattering winning of the Belmont by 31 lengths. Most racehorses are slowing as the race goes on and they tire; Secretariat was accelerating, running each quarter faster than the last. Half a century later, his record time for that race has never been beaten.
Are you referring to the legendary original usage, or did somebody quote at some more recent iconic moment?
A few more:
“Now we are all sons of bitches.”
“中国人民站起來了”
British ones:
“England expects that every man will do his duty.”
“Never in the field of human conflict was so much owed by so many to so few.”
“I counted them all out and I counted them all back.”
“They think it’s all over. It is now!”
Hmmmmm… I’m also not recognizing some replies. Maybe we should include a link to the source on these? Although so far Google has given me the answers.
ETA: Clearly we all have different histories!
“Carthago delenda est!”
Talk about obsessive compulsive, eh? Old Cato never gave up, did he?
Do you have a translation for this? It’s customary to always provide a translation for a non-English phrase, even if the poster thinks it’s well-known or idiomatic, simply because that assumption tends to be overblown.
Googling that is useless, since Google thinks that since I’m googling a Chinese phrase, I want only search results in Chinese. I can infer that this is a Mao quote, but I’m not inclined to do any guessing beyond this, as he said many widely-quoted things.
Same two I didn’t know.
Sure, but since this thread is kind of about figuring out the ones you don’t know, I thought letting people do a bit of detective work here was in order.
You can easily ask google to translate it, or you can search using the Chinese phrase and google will translate the search hits.
“I shall return.”
“I will go to Korea.”
“Happy birthday, Mr. President!” 
“Ask not what your country can do for you… .”
“The Eagle has landed.”
ETA: Ref @Riemann’s oriental example.
As a 100% total guess with zero research and zero knowledge of Japanese (at least I think that’s Japanese kanji, not Chinese whatever-they-call-them)
I fear we have awakened a sleeping/slumbering giant.
Allegedly said by Admiral Yamamoto after receiving reports of the successful attack on Pearl Harbor in 1941.
Ich bin ein Berliner
I have a dream
“… the brown acid that is circulating around us isn’t too good.”
“Can’t we all just get along?”
For:
中国人民站起來了
Google translate gives me:
“Chinese people stand up”
Perhaps it is refering to this speach by Chairman Mao:
“I did not have sexual relations with that woman, Miss Lewinsky.”
“Nuts!” (a WWII reference)