Leonard Cohen, who died last week at 82, was a poet, a pop star, a womanizer, a monk, a poor man, a rich man, a joker, a sage. But for those of us who are movie fanatics, he also occupied a role as extraordinary as it was utterly accidental: He was one of the most natural-born composers of movie soundtracks who ever lived. I say “accidental” because if you look at the films that made indelible use of Cohen’s music, there isn’t one among them in which the songs in question were written or recorded for the movie. In each case, the songs were composed several years beforehand and appeared on one of Cohen’s 14 studio albums.

The mystique of a great Cohen soundtrack was tied to the fact that he was almost never a Top 40 artist. If, like me, you followed his career from a distance, when you encountered a song of his in a movie, that was usually the first time you’d ever heard it. The effect was startling: Leonard Cohen may not have known that he was writing soundtracks, but it’s as if he knew. It’s as if he’d written that song, and then sat back and waited for destiny to create the movie it would be perfect for.

I can remember, as if it was yesterday (though, in fact, it was 1977), the first time I ever saw Robert Altman’s incandescent mist-and-dust Western “McCabe & Mrs. Miller.” At the time, I’d never heard of Leonard Cohen (my tastes ran to ELO, the Sex Pistols, ABBA, and Steely Dan), so I didn’t recognize his voice. I just knew, as the movie started, that I was seeing images — a woodland wilderness that somehow glowed, a shaggy silent man in a dark suit and bowler hat lumbering by on horseback — that possessed an aura I couldn’t account for. The acoustic guitar on the soundtrack spun out a series of slow-paced-yet-rapid notes that were sad and wistful but that truly seemed to be spinning, and the voice on top of them — craggy and oddly becalmed, mournful yet lordly — was already telling the story of the movie.

There are moments when a pop song will declare what’s inside the hidden heart of a movie’s main character. Think of “Everbody’s Talkin'” in “Midnight Cowboy,” and how it catches the sunny alienated dreams of Joe Buck (the thing the world’s about to crush out of him), or the falsetto aggression of the Bee Gees singing “Staying Alive” at the start of “Saturday Night Fever,” and how it expresses John Travolta/Tony Manero’s secret vulnerability. That’s what Leonard Cohen singing “The Stranger Song” (“Like any dealer he was watching for the card that is so high and wild,/He’ll never need to deal another”) does for Warren Beatty’s McCabe. The character never has much to say — he’s about as introspective as a pine cone — but the song is murmuring something about his nature. It’s telling the audience that he’s sweet, and idealistic, and doomed.

Altman had been a fan of Cohen’s first album, “Songs of Leonard Cohen,” when it came out in 1967, but three years later it was an associate of Altman’s who suggested layering on a few songs from it as a temp soundtrack for “McCabe.” The temp track stuck, and you can see (and hear) why: Without those songs, “McCabe & Mrs. Miller” would be a completely different film. Altman shot a rough-hewn, dark-toned revisionist Western filigreed with despair. The hero has little idea of the forces he’s up against, and Julie Christie’s tough-cookie madam drowns her loneliness in smoky wisps of opium. Yet Cohen’s songs, especially the great “Suzanne,” transform the film into a frontier daydream. The music says: The world you’re watching is harsh, but if you look close enough (which no one could do like Altman), you’ll see that it’s also the Garden of Eden.

In the years since “McCabe,” Cohen’s music has been used in more than 50 films (and countless TV shows), a handful of which stand out as drop-dead sublime. His greatest songs have a shimmer of majesty, and part of what makes them uniquely cinematic is Cohen’s voice: that low, talky, mellifluous man-in-black rasp — the sound of a holy man who smokes four packs a day. One of his greatest songs is “Everybody Knows,” and while fans of “Pump Up the Volume” will point to its celebrated use there, I confess that I’ve never been able to get past my dislike of Christian Slater’s late-night-cornball-rebel cult fable.

To me, the greatest use of “Everybody Knows” is in Atom Egoyan’s “Exotica,” where it’s the recurring theme to Mia Kirshner’s ominous strip-club dance. It makes sense that at least one Canadian filmmaker would tap the magic of the folk-pop bard who was Canada’s answer to Dylan, and in “Exotica,” “Everybody Knows,” with the back-and-forth insinuation that makes it sound like “Eleanor Rigby” on downers, is used as a warning. The film asks a question to any man who has ever sat in the darkness of an “exotic” club staring up at a stripper: What, in truth, are you staring at? In “Exotica,” it’s “Everybody Knows” that knows the answer.

Then there’s the Cohen-soundtrack movie that’s as memorable as “McCabe & Mrs. Miller” — though the world is still catching up to it. Fans of Oliver Stone’s “Natural Born Killers” don’t necessarily think of it as a “soulful” movie. The words that come to mind are more along the lines of: delirious, ultra-violent, over-the-top, meta-satirical, crazy. Yet it is soulful, and it’s also a gonzo jukebox musical. The unruly collage of pop that Trent Reznor assembled for the movie adds up, in context, to one of the greatest soundtracks in history, and the beating raw heart of it is three songs from Cohen’s 1992 album “The Future.” It’s those songs that lace the madness with a tragic humanity.

The opening sets the stakes. The sound of Cohen singing “Waiting for the Miracle,” a gorgeous dirge (“Baby, I’ve been waiting,/I’ve been waiting night and day”), tells you that the film you’re about to see will touch something that is — for lack of a better word — religious. So what could be religious about a gory postmodern “Bonnie and Clyde” that hitches itself to two wild-ass serial killers on a joyride to hell? The answer is: The kaleidoscope of images that they worship and live inside. Because it’s the one that we live inside too. The message of “Natural Born Killers,” embodied in the film’s every channel-surfing frame, is that we’re all now helpless addicts of the media dreamworld. Trapped in that hall of mirrors, we’re waiting for the miracle to come, the one that — until we free ourselves — will never come.

Speaking of religion, Cohen’s most famous song — and his most famous movie song — is a prayer, but it didn’t start off as the song you think you know. Just go back and listen to his original version of “Hallelujah,” which appears on the 1984 album “Various Positions.” It’s got the lyrics, and the basic melody, but they add up to the nuts and bolts without the glory. Jeff Buckley, who had the voice of an ethereal angel, did a celebrated cover of “Hallelujah,” but the artist who was responsible for transforming Cohen’s version of “Hallelujah” into the lilting epiphany that launched a thousand tears is John Cale (it appears on his 1991 Cohen tribute album “I’m Your Fan”). Cale took the slight bombast of Cohen’s version of and elevated it with his salvation-in-the-heather Welsh melancholy.

Rufus Wainwright duplicates the Cale version almost exactly — which is why Cale’s could be used in “Shrek,” and Wainwright’s could appear on the film’s soundtrack album. (Is there anything less religious than music-licensing issues?) Through all the musical chairs, there’s something fitting about the notion that “Hallelujah” is a Leonard Cohen song that is no longer Leonard Cohen’s; it belongs to everybody. In “Shrek,” it expresses the joy that’s swelling in Shrek’s heart, making this ogre more receptive to the one thing — love — that will save him from ogredom. It’s the most overt example of something that’s been there almost every time a Leonard Cohen song shows up in a movie: He’s not just making us feel good — he’s letting you hear the rapture.