The Cure’s ‘Charlotte Sometimes’ is inspired by the book by Penelope Farmer.
“Godzilla” by Blue Oyster Cult
And I can’t believe I’m the first to say “Tom Sawyer” by Rush
Mark Knopfler - Sailing to Philadelphia, based on Mason & Dixon by Thomas Pynchon
Books
Jefferson Airplane has two songs based on books:
“Crown of Creation” - based on John Wyndham’s the Chrysalids
“ReJoyce” - based on James Joyce’s Ulysses
Movies
In the 1980s, there was a band called the Smithereens who frequently wrote songs based off cult film titles, (not to mention their band name) including:
Killing An Arab references The Stranger by Albert Camus
Radio Birdman - ‘Aloha Steve and Danno’ - homage to Hawaii 5-0 - http://www.youtube.com/watch?v=pWR5n-ZT4xI
Flight of the Conchords - ‘Frodo, Dont weat the ring’ - Lord of the Rings [film rather than book I think]
Thanks for all the great ideas! 
Now I just have to do some researching on all of them.
Poe’s album Haunted is a companion piece to her brother’s book, House of Leaves, and at least a few of the songs directly reference parts of the book.
Books:
“Tender Is The Night,” Jackson Browne: Inspired by the F Scott Fitzgerald novel
Movies:
“Pinhead,” The Ramones: The “gabba gabba/We accept you, one of us” lines come from the 1932 film “Freaks”
“Brownsville Girl,” Bob Dylan: Includes several references to a Western movie starring Gregory Peck. Doesn’t mention the title in the song, but based on Dylan’s description of the plot, it’s probably “The Gunfighter” (1950)
The Decemberists’ 2006 album, “The Crane Wife” was entirely based on the Japanese Folk tale of the same name. If you want a specific song, “O Valencia!” is a good one.
Big Audio Dynamite’s E=mc2 is about Nicholas Roeg’s first five movies
Big Audio Dynamite’s Medicine Show has a boatload of quotes from The Good, the Bad, and the Ugly
Ultravox’s Reap the Wild Wind seems to be about the movie of the same name (could be wrong on that one)
Fine Young Cannibals take their name from the movie All the Fine Young Cannibals
Rigor Mortis had an EP called ‘Freaks’ with a song of the same name; the cover was a scene from the movie I believe.
Alice Cooper did ‘The Man With The Golden Gun’, supposedly in hopes of it getting used in the Bond film when it was made, which didn’t happen.
The Mothers of Invention did a song called King Kong, though I’ve only heard it on live albums and I’m not sure if there is a studio version.
Bob Dylan mentions going to see a movie called Gunga Din in “You Aint’ Goin’ Nowhwere.”
Bruce Springsteen’s “Nebraska” was based on Terence Malick’s movie ***Badlands ***(a fictionalized account of the Charles Starkweather murder spree). Oddly enough, Springsteen’s song “Badlands” was NOT insired by that movie!
So did The Kinks, but it’s not really about the movie.
(Their song “Celluloid Heroes” is certainly about the movies in general, though not about any particular movie.)
The title of Weezer’s Pinkerton references the character in Madame Butterfly, and the song “Butterfly” is a retelling of the story from Pinkerton’s point of view.
The Old 97’s has a song called “What We Talk About” that’s named for the Raymond Carver story “What We Talk About When We Talk About Love”. Oddly enough, it appears the band dEUS has a song with the same title.
Same name: “While You Were Sleeping” - Ke$ha song; 1995 movie
I’m somewhat amazed no one has mentioned Al Stewart’s song “Sirens of Titan”, based on Kurt Vonnegut’s story.
Steve Goodman did a song called “Moby Book” that is sort of a condensation of Moby-Dick.
The Velvet Underground song “Venus in Furs” was inspired by the novella of the same name by Leopold von Sacher-Masoch. (Note also that the group’s name came from the title of a 1963 book about “deviant” sexual behavior.)
Dylan’s song “Motorpsycho Nitemare” is certainly referential of the Hitchcock film Psycho, although it’s not really about the film ("There stood Rita, looking just like Tony Perkins/She said “Would you like to take a shower?”…).
A good chunk of Rob Zombie’s output is referencing some film or another (even his old band name White Zombie was such a reference). His song Never Gonna Stop is full of Clockwork Orange stuff, for instance.