Hope the title is clear enough…
Some examples to get us started…
Inspired by listening to the song Anything Goes, and realizing ever since Indiana Jones and the Temple of Doom all I can think of is the song starting off in Chinese.
And of course, if you’ve ever seen Reservoir Dogs, “Stuck in the Middle With You” just isn’t quite the same anymore.
The Darlene Love version of Christmas is in the opening credits of Gremlins, so now that’s all I think of when I hear it.
Yours?
“If You Could Read My Mind” (Gordon Lightfoot - 1970) was ruined for me by the movie Wonderland (about porn star John Holmes and his connection to the Wonderland murders). Ick. And it’s in the rotation on the Muzak at work so I hear it all the time.
Let’s make this thread last all night!
Not so much a movie, but I can’t hear “Don’t Fear the Reaper” without picturing Will Ferrell playing the cowbell in a too small shirt.
I 2nd the “Stuck in the Middle with You” mention too.
Stuck in the Middle with You leaps to mind as well, and also American Girl as seen in Silence of the Lambs.
Hell, I love “Stuck in the Middle Wid Youse” in Reservoir Dogs.
For me, I’ll never see Gene Kelly dancing to Singing in the Rain without thinking of Alex in A Clockwork Orange
After seeing Girl, Interrupted, “The End Of The World” by Skeeter Davis gained some…interesting connotations in my mind. In the movie, the song is playing as the protagonist walks into her friend’s room to see that she has cut her wrists and hung herself.
“Time is on my Side” by the Rolling Stones was used to great effect in Fallen, but won’t ever be quite the same for me.
And, “We’ve Only Just Begun” as used in 1408.
Did “Dueling Banjos” come out before Deliverance?
Stuck in the Middle With You is now associated with something Stealers Wheel never intended.
I Got You, Babe is forever associated for me now with Groundhog Day (but that’s an improvement over when I associated it with Sonny and Cher).
My brain associates the Sundays cover of Wild Horses with Resse Witherspoon getting finger-fucked on a rollercoaster. Granted, as far as mental imagery goes, it beats the hell out of some guy getting his ear hacked off but I was happy enjoying the song on its own merits before Fear came out.
Bohemian Rhapsody by Queen will always remind me of Waybe and Garth’s headbanging scene in the Mirthmobile in the movie Wayne’s World
The Power of Love by Huey Lewis will remind me of Back to the Future
Immediately thought of Stuck In The Middle, seems to be the winner so far.
Seconding “Singing In The Rain” from A Clockwork Orange.
BTW: One of my fave films. 
I always think of DIVA whenever I hear the aria “Ebben?..Ne Andrò Lontana” from La Wally.
“Born to be Wild” by Steppenwolf involuntarily invokes images of Dennis Hopper and Peter Fonda cruising around on their bikes.
Not a song but … what music do you think about when you hear “I love the smell of napalm in the morning”? So do I.
And, unfortunately, I can rarely listen to “Air” by J.S. Bach without remembering glimpses of Se7en.
Not on topic but “Maybe” by the The Ink Spots and Louis Armstrong’s “A Kiss to build a Dream on” have an eerie quality since I heard them in the intros and outros of Fallout I and II.
Don’t Stop Believing by Journey will NEVER be the same after The Sopranos.
And I don’t know the name of that classical violin concerto piece from There Will Be Blood, that plays when they’re building the first oil derrick in the town, and then later at the very end of the movie during the credits - but if I ever hear it again in another context, I won’t be able to dissociate it from the film.
Argent Towers, it might not be classical in the “composed decades ago”-sense. Greenwood just “borrowed” heavily from classical composers like Brahms, Bartok and contemporary ones, including Arvo Pärt.
Here you can listen to pieces of the soundtrack - it might help you identify the one you have in mind.
added:
he also used music from his earlier “Popcorn Superhet Receiver” – which might be to your liking.
I associate that song with the scary beginning of the miniseries The Stand.
The Bodyguard killed a very good Dolly Parton song.
And IIIIIIIIIIIIIIIIIIIIIII will always love YYYYYYYYOOOOOOOOOOUUUUUUU
I found that Ludwig van was spoiled for me due to all that aversion therapy.