Birdman of Alcatraz
An Autumn Afternoon
The Loneliness Of A Long-Distance Runner
Il Sorpasso
The Sign Of The Leo
David And Lisa
His Days Are Numbered
Knife In The Water
Mamma Roma
Pitfall
Lonely Are The Brave
Lolita
L’Eclisse
Hara-kiri
Sundays And Cybele
To Kill A Mockingbird
Ride The High Country
The Manchurian Candidate
All Fall Down
As “To Kill A Mockingbird” is one of the best movies ever, it takes 1st for me.
You missed two of my favorites from 1962:
The Longest Day and Lawrence of Arabia.
I’ll give a shout-out to Gypsy and Dr. No.
Most of your list wouldn’t be movies I would want to see.
Lawrence of Arabia
Day of the Triffids
Dr. No
The Music Man
The Man who Shot Liberty Valance
Mondo Cane
Carnival of Souls
That one really messed with 4 year old me when I saw it on TV.
The Three Stooges in Orbit.
Wait, I’ll go with To Kill a Mockingbird instead.
mmm
Advise & Consent is easily my favourite from the era.
The Brainiac a.k.a. El barón del terror
The Brain that Wouldn’t Die
Cape Fear
The Creation of the Humanoids
Dr. No
The Exterminating Angel
The Fabulous Baron Munchausen
The Graceful Brute
Journey to the Seventh Planet
The Magic Sword
The Manchurian Candidate
The Testament of Dr. Mabuse
Walk on the Wild Side
It’s a movie that I wish, for personal reasons, would disappear from all space and time, and the novel with it.
Lonely Are The Brave
Lawrence Of Arabia
What Ever Happened to Baby Jane?
I took my wife to see this at a revival theater and she still hasn’t forgiven me.
To Kill a Mockingbird
Cape Fear
Hell is for Heroes
The Manchurian Candidate
Dr. No
Mr. Hobbs Takes a Vacation
Days of Wine and Roses
The Music Man
The Manchurian Candidate
The Loneliness of the Long-DIstance Runner
David and Lisa would make the cut if there was a way to filter out the horrendous musical score. Baby Jane is half of a good movie: I would have preferred it to be more like Misery, with no outside world.
And apologies if I’ve told this one before. A few years ago, I listened to Blake Edwards’ commentary on Days of Wine and Roses. He was talking about how it was a tough year for Oscars: Lee Remick lost Best Actress to Anne Bancroft for The Miracle Worker, and Jack Lemmon lost Best Actor to Gregory Peck for To Kill A Mockingbird, when in another year, they might both have won. Skip ahead to a very powerful and scary scene in which Lemmon tears a greenhouse apart looking for a hidden bottle. Edwards was silent throughout, and when the next scene started, remarked “I think that killed three mockingbirds!”
Jack the Giant Killer was my favorite at the time.
Cape Fear
How the West Was Won
Lolita
The Man Who Shot Liberty Valence
To Kill a Mockingbird
What Ever Happened to Baby Jane?
Why??
She dreaded the fate of Whisky before the opening titles even ended.
Ah. Just like Mrs. Cretin. Give a dog, cat, horse, more than one second of screen time and she spends the rest of the movie dreading the critter’s fate. Sad to say her fears are justified more often than not.
And don’t even think about saying “It’s only a movie” - but I bet you already know that.
Oh, God, The Magic Sword! I saw this back in the '70s and have never forgotten it. What a romp! 
Lonely Are the Brave was Kirk Douglas’s favorite film, and my pick of the list.
Lolita is great for the performances of James Mason and Shelly Winters, but Sue Lyons was just too old to play the titular (so to speak) character. I also didn’t care much for the liberties Kubrick took with the story. I still think it lost the mood of the novel.
I liked The Manchurian Candidate, but I still don’t understand why a John Bircher would cooperate with the Red Chinese, or why the Red Chinese would want to see a right-wing dictatorship in the United States.
To Kill a Mockingbird is a very powerful film, but such a downer! 
Dr No deserves to be on the list simply for “Bond. James Bond.”
Journey to the Seventh Planet both freaked me out and turned me on when I was seven.
I spent the next five years playing Army after I saw Hell Is for Heroes with my dad.
I always thought The Longest Day came out in 1964, because that’s when I first saw it. (I spent hours listening to the soundtrack album afterwards.)
Not on the list is The Pink Panther, which I always thought was a sequel to A Shot in the Dark because I didn’t see it until 1967!
Plenty of movies I agree should be listed have already been listed, leaving me with just this to say about that:
I’d argue that Sweet Bird Of Youth, considered on its own, is a terrific enough film for you to see why it racked up award nominations for the lead actor and the lead actress and the supporting actor and the supporting actress — unless you start playing the Might Have Been game by comparing it to the Broadway version that so many of the castmembers were in beforehand.