Stayin’ Alive is forever linked to Airplane! for me.I
Shake, Rattle and Roll is linked to Clue.
Assuming we’re discounting songs written for the movie, like “Always Look On The Bright Side of Life”, there’s always the slow movement from Mozart’s Piano Concerto No 21, in Elvira Madigan
John Cusack’s boom box playing Peter Gabriel’s “In Your Eyes” in Say Anything.
Royal Wood - Don’t Fall Apart
Only because it’s where I first heard the song, at the end of an episode of Flashpoint. It’s a Canadian show about a “SWAT” like team. Except for the action parts it’s almost wall-to-wall contrived melodrama, but I did like that the “bad guys” were very rarely just black and white cartoon bad guys, there was almost always an element of moral ambiguity involved in the conflict.
Queen’s “Don’t Stop Me Now” in Shaun of the Dead.
In Jackie Brown there is a scene where Max Cherry (Robert Forster) is in a car with Jackie Brown (Pam Grier) and the song Didn’t I Blow Your Mind This Time by The Delfonics is playing. Jackie likes the song and begins to appreciate Max.
“Thus Spake Zarathustra” in 2001: A Space Odyssey.
“Singing in the Rain” in A Clockwork Orange.
“The William Tell Overture” in A Clockwork Orange.
“The Mickey Mouse Club” theme song in Full Metal Jacket.
Stanley Kubrick messed with my head.
I never liked that song until I heard it in that movie.
Also adding Journey’s “Don’t Stop Believin’” from the Sopranos finale.
Thanks to Pulp Fiction, “Miserliu” is more evocative of the mid-Nineties than the early-Sixties.
There’s that one, and also “Oh Yeah” by Yello that makes me think of the end credits scene with Vice Principal Rooney on the school bus.
The Kubrick ones for me are:
“Surfin’ Bird” for Full Metal Jacket (although Family Guy has kind of ruined that one).
“Waltz 2”, Eyes Wide Shut.
And of course “Beethoven’s 9th Symphony”, A Clockwork Orange.
And Kubrick messed with me by choreographing the brutal fight scene between Alex’s droogs and Billy Boy’s to the overture to Rossini’s “The Thieving Magpie.”
Not to mention the first time I ever heard Vera Lynn sing “We’ll Meet Again” was in “Dr. Strangelove.” 
Iggy Pop’s Lust for Life and the opening of Trainspotting.
Goodbye Horses - Silence of the Lambs
I once heard of a bar fight starting over someone picking that song on a jukebox
Tom Petty - American Girl - Silence of the Lambs
Flight of the Valkyries - Apocalypse Now
Day-o from Beetlejuice
Another good one is Dirty Dancing and The Time of My Life.
Some obvious ones seem to have been omitted.
Flashdance
That song from Titanic
Of all the classical music that Kubrick appropriated, "Thus Spake Zarathustra” in 2001: A Space Odyssey stays most in my mind.
Does the question exclude theme music?
I know Gary Glitter’s Rock and Roll Part 2 is more recently associated with Joker (great scene, by the way) but it will always make me think of the lads’ rehearsing their strip routine in The Full Monty.
I Saved the World Today by the Eurythmics from the end of S2 from The Sopranos.
Let’s exclude any song that was written specifically for the movie or show.
So regarding theme songs, it depends. “Won’t be Fooled Again” and CSI: Miami would count, since The Who released that song decades before the show. “Car Wash” would not, since as far as I know it was written specifically to be the theme song for the movie of the same name. Unless, of course, you associate “Car Wash” with a completely different movie.
OK, no theme music.
One thought:in general: if the song has been out for a while, it is harder to associate it with a movie later. Lots of movies have older music playing.
I haven’t seen “Three billboards…” but i would instantly associate the song with Joan Baez and the summer of '68. And nothing else? Maybe it’s an age thing?