The most electrifying moment in Abel Ferrara’s (mostly rather pretentious and wilfully nasty) King of New York of 1989, rereleased recently on DVD by Arrow Films, comes when Christopher Walken, as scary drug baron Frank White, arrives back in his apartment from jail and finds himself confronted with a group of gangsters, headed by Laurence Fishburne.

There’s a threatening silence in which the unsmiling, death’s-head Walken face stares back at the smirking crew. It’s broken only by some terse macho dialogue. But then, suddenly, the skull-face cracks a smile, White says “Bup-bup-bup” and swivels his hips sexily, and the long lean form unbends as he breaks into a convulsive, rhythmic little gyration to a long, rising “Ohhhhhh!” that they all join in – climaxing with the black crew mobbing their old friend and boss.

The rest of the film is a stylish but uninformative swaggering parade of guns, cocaine, rap and hip-hop, naked girls and foul-mouthed street-talk: as if Ferrera, too, wanted to show he was cool and black. But in much better films, the extraordinary expressiveness of dance can be harnessed even more potently to dramatic situations, and in particular its terrific power of conveying a release of inhibitions – as the brilliant (tapdance-trained) Walken’s frenetic number hints here.

Luchino Visconti’s enchanting White Nights of 1957, a free adaptation of Dostoievsky, follows a couple as they wander through the night streets of Livorno for four nights, the shy clerk Mario being Marcello Mastroianni, and Natalia, the girl he falls in love with, Maria Schell. The fragile Natalia has spent a year pining for her absent lover.

Which after a while persuades the shy, tweed-suited, overcoated Mario to urge the shy but excited Natalia onto the dance floor, where they sweetly attempt a genteel bobbing. But the dangerous chief beatnik (Dirk Sanders), who resembles a young Terence Stamp and whose bacchanalian dancing throbs with sexual energy, steps in and leads the giggling Natalia away, leaving Mario standing embarrassed and helpless, even struggling to get out of his heavy overcoat.

Mario gets rid of the coat, and starts to dance with the male beatnik's partner - waving confusedly to Natalia, who's enjoying herself. When he gets her back, she's rather breathless. But then, as they resume their comic, childlike bobbing about, the chief beatnik pulls off his leather jacket and the floor clears for what becomes an ecstatic gymnastic display of coolness. It's clear this handsome young man, showing off his narcissistic moves, wants to be the 'Only One Man in Town'.

Natalia is delighted by this display, clapping her hands and laughing; at her side Mario looks on in blank horror and repugnance. The beatnik wants Natalia to join him - and she's thrilled and tempted; a close-up shows her clinging to Mario, but drawn to the dark stranger, whose frenzied, jerking movements seem a public invitation to sex. She hesitates, and he picks another girl, whom he bounces through the air in acrobatic lunges of symbolic intercourse. Mario is provoked, and inspired.

He pushes forward, this respectable-looking, unhip tweedster, and goes into a fantastic, parodic frenzy of twirls and jumps and jerky hand movements and star jumps, upstaging the beatnik gloriously. What matter that he falls over? He bounces back up, Natalia is enthralled, and they finish with a lovely, silly made-up dance together before falling into each other's arms. The potency and pleasure of this scene is astonishing: Mario has broken through a barrier, and Natalia has pushed him to it.

Mastroianni's genius - in Fellini's later Ginger e Fred he shows what a fine dancer he was - is to convey the liberating, improvisatory discovery of dance by a non-dancer, who both joins in and anarchically mocks the male narcissism of the cool world. He's no macho predator - but he mounts a comic defence of his girl in this battle of the dance-floor. It's terribly touching, rousing, funny - and always keeps within the melancholy register of this whole achingly romantic art-movie.

One other great example - in John Ford's superb Western My Darling Clementine (1946), his version of the story of the gunfight at the OK Corral, the very staid, reserved, dignified Wyatt Earp (Henry Fonda) goes to the barber and gets himself spruced up because he's fallen for Tombstone's schoolmarm, Clementine Carter (Cathy Downs).

The barber squirts the dubious Earp with cologne. The marshal ambles out into the street, self-consciously checking the tilt of his hat in a store window, and takes his accustomed chair on the stoop to watch the world go by, bracing himself with his boot against a pillar so he can rock as he waits. His brothers Virgil and Morgan join him - and remark that they can smell honeysuckle blossoms. After a droll pause, Wyatt admits laconically, “That's me.” They go, and he stays on, rocking.

Clementine Carter arrives. She too remarks on “the scent of the desert flowers”. “That's me,” he says. They watch crowds of people going past in their Sunday best - as if they were back home, not in the wild territory, and she asks him: “You are going to the services, aren't you?" (a new church is being erected). In a beautifully composed shot they walk towards the church with the sun shining down, a few fleecy clouds, and the wind blowing in Clementine's white dress.

It's an image of the law-abiding, loving America that is being brought into being - and that the Clantons hate. We don't see the service - but cut straight to the elder announcing that now the church is “officially dedicated" there's nothing ungodly about “a dad-blasted good dance" and snatching up his fiddle. The dancers come forward, and we see them lumbering into action. Dancing really isn't Wyatt's thing, so he and Clementine are standing back while others get on with a good knees-up.

He looks twitchy; she looks impatient. Ford wrings a delicate comedy from the predicament of this brave, proud man deeply reluctant to dance - but knowing it's inevitable, that he can't refuse Clementine: there are lovely shots of them standing there while a creeping tension builds between them as feet are tapping all round. Clapping her hands to the music, she turns to look him in the face; he cravenly refuses to meet her eye. Other couples throng onto the dance-floor.

Knowing he can't escape, Earp removes his hat, with a grimace, and throws it aside, and gives her his arm. But it gets worse - as they reach the platform, the bandmaster tells everybody to “Make room for our new marshal, and his lady fair”. Poor Earp has to bite the bullet: he and Clementine dance round the cleared space under the eyes of the community - and there's a great surprise: Earp's tremendous, distinctive dance move is a jerking sideways knees-up, in a stiff high-stepping waltz.

His brothers drive up in a buggy - and can't believe what they're seeing. It's characteristic of Ford's greatness to make room for such delicate comedy, and such poetry, in a film that is moving inexorably towards the slaughter of the OK Corral.

It's because these films aren't musicals that the comic possibilities of dance, and the pathos of the non-dancer dancing (like so many of us), so fully emerge here; what's being choreographed and dramatised is the dancing of the amateur, dance as a ritual of real life. It's characterisation, it speaks fully to a dramatic situation - in the Visconti and Ford scenes, to the ambivalences of love.

Wonderful as are Fred Astaire and Ginger Rogers, or Gene Kelly, in the Hollywood musical, or the performers in a tribute to it like Jacques Demy's delirious Les Demoiselles de Rochefort, the dancing in such confected films doesn't quite emerge from something like the life we know - doesn't have this air of a thrilling small miracle, expressing and transforming the moment - like a magical burst of poetry in a passage of prose.