The episode of Gilligan’s Island, entitled “The Producer,” where they put on a musical version of Hamlet, put new lyrics to two different pieces from Carmen that have stuck in my mind for over forty years:
I ask to be, or not to be!
Neither a borrower, nor a lender be!
Feh, I should have read the OP for comprehension, as terentii mentioned the Gilligan’s Island episode.
However, those of us who grew up on the early years of Sesame Street will also always associate Carmen with a singing orange. 
I first heard Wagner’s ***Tannhäuser ***overture watching this movie, in which a German infiltrator in the opening scenes doesn’t know who Betty Grable is:
Go to 1:22:17 and you'll see Charleton Heston and Leslie Nielsen sharing some dramatic moments just before the concert starts. I challenge you to watch this without laughing.The association between Wagner and ***Counterpoint ***is etched indelibly in my mind.
I have no specific examples in mind, but I’m convinced that Satie’s Gnossienne n°1 and Gymnopédie n°1 were the default background music for all the weird weekday afternoon documentaries in the '80s. You know, things like “Contemporary Bulgarian Abstract Expressionism” or “The Art of Puppet-Making”…
I used to call the latter “The Drowning Song”, because there was a PSA about water safety when I was young that used that music in the background.
That reminds me - in a similar vein, for those in Canada of sufficient age, Chopin’s famous C# minor waltz is The Arthritis Song. 
Smurfberry Crunch is fun to eat
A smurfy, fruity breakfast treat
Made by smurfs so happily
They taste like crunchy smurfberries
It’s berry-shaped and crispy, too
And very red and smurfy blue!
Whereas John Williams literally copied the last few bars of Mars in Star Wars - down to harmony, rhythm and exact instrumentation. Compare 6:38 of Mars with 1:46 of the Star Wars Theme.
The aria Der Holle Rache from The Magic Flute is, I think, now firmly ensconced in people’s minds as “that music from the Volvo commercial”.
Not Dudley Moore and Bo Derek?
For me, “Toreador” recalls The Bad News Bears.
Another Kubric cinematic masterpiece, Barry Lyndon has 2:
Handel’s Saraband
Schubert’s Piano Trio in E flat, op. 100 (2nd movement)
Platoon: Barber’s Adagio for Strings
And who can hear Liszt’s Hungarian Rhapsody #2 (cute rendition) without seeing Jerry running the keyboard?
Billy Joel cribbed a melody from Beethoven for the chorus of “This Night.”
Speaking of Beethoven and a couple of aforementioned shout-outs to Kubrick’s, A Clockwork Orange, Ludwig van’s 9th Symphony figures pretty prominently in that flick.