Exit Music wasn’t about that movie, it was written for the soundtrack. I guess that might put it in a ‘sorta’ category. Radiohead’s Motion Picture Soundtrack certainly seems connected to the Romeo and Juliet story, though not any movie version in particular.
Does Martin Scorcese (sp?) by King Missile count?
Frank Zappa also gave us Conehead, which wasn’t a movie at the time he wrote it. Then SNL had to go and make a movie out of it.
See also Silence! The Musical, an entire musical about The Silence of the Lambs. It’s available on mp3lizard.com , artists Jon and Al Kaplan. It’s worth a listen. Put The Fucking Lotion In The Basket is particularly touching.
This must be a coincidence but 4 Bob Seger songs from the same album are movie titles “Night Moves” “Fire Down Below” “Ship Of Fools” and “Main Street”. I don’t think any of these have anything to do with these movies.
"The Man Who Shot Liberty Valence" by Gene Pitney is definitely about the movie but is never heard in the movie.
A number of Gary Numan’s songs are about Blade Runner. He seems obsessed, and rightly so. Time to Die is based on Roy Batty’s final speech, there’s a remix of Rip that features whatever Japanese drama or poem that’s announced over the blimp’s P.A. system (or was it the billboard? I can’t remember just now), and there’s a third that has Deckard’s “Move! Get outta the way!” spliced into it. The name of that song escapes me at the moment. Gary Numan’s quite prolific, so I imagine he’s based more music on Blade Runner, but those are the songs I’ve heard.
See also The Kinks’ “Celluloid Heroes” (though it mentions more movie stars than specific movies) and “Oklahoma, USA.”
"Planet Claire" by The B-52s mentions the old sci-fi flick Destination Moon.
Correction, the B-52s song in question is “There’s a Moon in the Sky”.
Bruce Springsteen’s “The Big Muddy” was based on the Pete Dexter novel Paris Trout, which became a movie with Dennis Hopper. (So that kina counts, ey?)
23skidoo, I dig your tune! What’s with the Heart homage at the end there? It’s a nice touch. 
Springsteen’s <b>“Nebraska”</b> was based on the movie <b>Badlands</b>.
The Statler Brothers sang a song called Movies that specifically references all the following films:
The Wolfman
Bridge on the River Kwai
The Best Years of Our Lives
Citizen Kane
The Caine Mutiny
Mutiny on the Bounty
The Bounty Hunter
The Sting
Thunder Road
Road to Rio
Rio Grande
Grand Hotel
Tell Them Willie Boy Was Here
Bride of Frankenstein
Shane
Peyton Place
The Wizard of Oz
Captain Blood
Ben
Ben-Hur
The Way We Were
True Grit
The Music Man
Thunderball
Walking Tall
Jaws
Dr. No
Vertigo
Singin’ in the Rain
Blood and Sand
Santa Fe
The Getaway
Mexicali Rose
Rose Marie
Blackboard Jungle
Jungle Jim
Jim Thorpe, All-American
An American in Paris
Paris Blues
Blue Hawaii
Teacher’s Pet
Ship of Fools
The Graduate
Twelve O’Clock High
One Flew Over the Cuckoo’s Nest
Then there’s “Werewolves of London” by Warren Zevon, a reference to the movie The Werewolf of London.
A New Hope Blink 182
they also did a song called I miss you where they mention Jack and Sally from Nightmare Before Christmas.
Red Angel Dragnet by The Clash includes pieces of Travis Bickle’s monologues from Taxi Driver.
ETA: Zombie thread! Run away!
Roky Erickson’s “Creature with the Atom Brain” is about the 50’s B-movie horror flick.
“Bringing Up Baby” by Talulah Gosh is about the film Bringing Up Baby
“Western Movies” - The Olympics
Lord, I’m old.
“Die Hard” and “Requiem” by Guyz Nite
All of these these.
Hey Leonardo (She Likes Me For Me) by Blessid Union Of Souls contains a reference to “That guy who played in Fargo”, if that counts for the OP.
Lloyd Cole & the Commotions have Rattlesnakes “She looks like Eve Marie Saint, in On the Waterfront”
Fields of the Nephilim have Dawnrazor (which samples and references Oz horror movie Razorback) and Reanimator(a shoutout to the eponymous film more than the Lovecraft original)