You must remember this. Philip Marlowe (Humphrey Bogart) is looking tattered and torn, but pleased with himself all the same. He has solved the mystery, sent the bad guys packing and told the cops all they need to know in order to look like they've been on the case. "You've forgotten one thing," says Vivian Sternwood (played by Lauren Bacall) - "me." "What's wrong with you?" asks Marlowe. Vivian moves toward him: "Nothing you can't fix." And the credits roll - over a close-up of two cigarettes in an ashtray, their coils of smoke entwining.
What kind of picture is The Big Sleep (1946)? The Raymond Chandler novel on which it is based is a winding and weighty detective thriller. But Howard Hawks's film, which follows Chandler's story pretty closely, is an altogether sunnier number, a lighter-than-air romantic comedy ballasted by the odd thud of a sap, the occasional crackle of gunfire. So it's rather like To Have and Have Not (1944), which took what Hawks called a "piece of junk" by Hemingway and twisted its sententious disquisition on the nature of masculinity into a war-torn bedroom farce: Noël Coward meets the Nazis.
The meeting that really counted in that picture, however, was the one between its two leads, Bogart and Bacall making their debut together. It was fascinating enough that these two really did fall for one another while making the film. Better still that, in doing so, they created a new kind of cinema couple - one that refused to grant Hollywood's conception of romance its customary restrictions. When Bogart's Harry Morgan makes Bacall's "Slim" walk right round him to prove he has no strings attached, he does so to woo her with a vision of love that acknowledges no ties.
The French film theorist Raymond Bellour once characterised Hollywood as a machine that produced couples, and the old post-structuralist was clearly on to something. Rare is the film that does not bring together a man and a woman. But what Bellour left out of his equation was history. Hollywood might produce couples, but couples also produce Hollywood. On-screen love affairs either reflect the changes in off-screen love affairs or they perish at the box office. If the punters don't feel that what they see on the screen is related, however remotely, to what they see off it, they won't go back for more. Romance, no matter how high-flown, must always be earthed in the humdrum.
When Rock Hudson and Doris Day got together for some Pillow Talk (1959), they did so only after several reels of the internecine joshing all the best relationships are founded on. Leave such byplay out, and you leave everything out. Nora Ephron said of Sleepless in Seattle (1993) that she "dreamed of making a movie about how movies screw up your brain about love". Alas, Ephron was so in love with the idea of engineering a get-together between Meg Ryan and Tom Hanks that she succeeded only in screwing up her own film. Meg and Tom are so squashy and accommodating that they could never convince us they need one another.
Spencer Tracy and Katharine Hepburn were quite the opposite. Their nine pictures together centre on relationships as much remonstrative as romantic, but you could no more think either of them self-sufficient than swim in treacle. Films such as George Cukor's Adam's Rib (1949) and Frank Capra's punningly titled State of the Union (1948) speak to us still because of Tracy and Hepburn's instinctive understanding that marriage is, by definition, political - a clash between what ought to be two equals. Though there is a lot of talk in their films about the need for "south-end spankings", the talk is distributed evenly, Hepburn threatening Tracy as often as he threatens her.
Hepburn's on-screen dealings with Cary Grant were spikier still. With the exception of the opening scene of The Philadelphia Story (1940), in which Grant puts his hand over Hepburn's mush and pushes her to the floor, it was she who called the shots in their four films together. Cukor's Holiday (1938) might seem to be about Johnny Case (Grant) and his desire to live a less materialistic life, but the picture's heart really beats inside the Hepburn character, Linda Seton, a society girl so full of beans, that society wants nothing to do with her. In Bringing Up Baby (1938), meanwhile, Hepburn's Susan Vance sexualises Grant's bottle-eyed boffin David Huxley, a chaste and charmless dinosaur buff who has - get this - mislaid his bone.
In this way, Hepburn's films with Tracy and Grant, like those of Bogart and Bacall, offer us a vision of male/female relations as democracies of dependence. The sad thing is that there would be nothing else like them for the best part of 20 years - and even when something similar did return, towards the back end of the Sixties, the two-way street had become a one-way cul-de-sac. Eisenhower's childish vision of American innocence put paid to the idea of marriage as an arena of reciprocal liberation, and the America of Johnson and Nixon killed the idea of the mutually sustaining heterosexual couple.
No convincingly redemptive romance has come out of Hollywood since the dog days of the Vietnam war. Instead, we have been offered over and over again a vision of an atavistic America, a Melville-esque America, Hemingway's America of men without women. Yes, there have been pictures about marriage, but none of them has seen it, without irony, as a forum for beneficence. Brad Pitt and Angelina Jolie's Mr and Mrs Smith (2005) was bad for any number of reasons, but chief among them was its inability to paint that (real-life) couple as anything like any couple you could have come across in what we ought perhaps to call real real life. The movie was named after an uncharacteristically cosy Alfred Hitchcock comedy, but it had far more in common with the post-'Nam buddy movies of the late Sixties and early Seventies.
The progenitor of this genre was George Roy Hill's Butch Cassidy and the Sundance Kid (1969), starring Robert Redford and Paul Newman, who remain Hollywood's definitive buddies. Nearly four decades on, there is no denying the enduring lustre of this defiantly non-sexual couple. (The film tosses in a handful of scenes featuring Katharine Ross, a bed and a Burt Bacharach number - a ragbag that can't be dignified with the epithet "sub-plot" - to vouchsafe our heroes' straight credentials.) Nor the lustre between Clint Eastwood and Jeff Bridges in Thunderbolt and Lightfoot (1974), Robert de Niro and Charles Grodin in Midnight Run (1989), or Geena Davis and Susan Sarandon in Thelma and Louise (1991). But, for all their pleasures, these pictures short-change us with a vision of a world where half the inhabitants barely exist. The only thing more dreamy than a movie about love is a movie that pretends to have done away with love.
Howard Hawks said that the Lauren Bacall Humphrey Bogart fell for was a dream: Bogart was in love not with the real Bacall, but the character she played in To Have and Have Not. Hawks had rather wanted Bacall for himself, so there is envy in that insight. Yet insight it remains. Half a century after his death, Bacall is still singing Bogart's praises, but there is enough other evidence to suggest that his early demise may have been all that prevented their marriage ending the way most Hollywood marriages end. On screen, however, they are united for ever, the most inspirational lovers in the world of movies, devoutly non-possessive, resolutely self-possessed. To have and have not, that is the answer to cinema's - to life's - eternal question.
Humphrey Bogart & Lauren Bacall, a month-long season, is at the National Film Theatre, London SE1, until 31 January. www.bfi.org.uk