Yeah, but how many of them suck?
So maybe we leave out most SF, War, Children’s movies and start from there. What great movies without a romantic plot or subplot are left?
Walt Disney’s Pinocchio
Intruder in the Dust
The Battle of Algiers
The Spirit of the Beehive
Monty Python and the Holy Grail (Castle Anthrax notwithstanding)
Dead Man
“Saving Private Ryan” used Captain Miller (Tom Hanks) talking about his wife quite a bit to flesh out his character. Very effective use of a character we never see or hear.
I’d say the winner is “Lawrence of Arabia.” Any movie I can think of that competes with it has some male/female dynamic to it.
Bridge on the River Kwai
Did they even have any women with speaking roles in that movie? Interesting, I never gave the matter much thought.
No female speaking role made the final edit. The DVD shows a deleted scene with a female detective.
Didn’t the waitress in the restaurant, in the first minutes of the film, speak?
You’re forgetting Ann Sears as the nurse dating William Holden’s character.
Doesn’t qualify due because it depicts Kane’s relationships with his first and second wives (who he tried to turn into an opera singer).
How about The Great Escape?
On the other hand Saving Ryan’s Privates would be a terrible example for these criteria.
The City of Lost Children (no romance, plenty of familial love)
The Shawshank Redemption (mostly, he speaks about how he did his wife wrong)
I don’t think so.
I don’t remember Alien Having anything akin to romance in it.
Well, sometimes you have a Token Love interest, just to (apparently) draw women.
You’re forgetting about the scene with the five of them in the poppy field.
Or maybe I just imagined it. I’m a sick sick sick human.
I don’t think that it does. Frank Poole receives a birthday greeting from his parents, who, as I recall. are even touching in the recorded greeting! You can’t watch that scene without being reminded of their animalistic coupling! 
The Killing
Glengarry Glen Ross.
What about E. T.?
Or perhaps Willy Wonka and the Chocolate Factory?
I don’t think that WIZARD OF OZ qualifies, because the Tin Man dreams of having a heart so that he can fall in love:
TIN MAN:
Picture me: a balcony . . . above a voice sings low:
SOPRANO VOICE-OVER:
Wherefore art thou, Romeo?
TIN MAN
I’d hear a beat! (Lub-dub!) How sweet!