Endings are, arguably, the most important aspect of a movie's narrative apparatus. The final minutes, or seconds, form the most immediate basis on which an audience, emerging from the dark, will judge the success or failure of the story they've been involved in. We have a natural human desire for resolution – "closure", in modern parlance – and we will be more inclined to forgive a movie its other shortcomings if it manages to astound us, or move us, or choke us, with a great ending.

David Mamet, who has written plenty of endings in his time, both for plays and films, puts it like this: "Turn the thing around in the last two minutes, and you can live quite nicely. Turn it around again in the last 10 seconds and you can buy a house in Bel Air."

The great ending is an extraordinarily difficult thing to pull off. Film-makers by and large want to fulfil their audience's expectation, and the safest way to achieve that is with a happy ending. These tend to be unmemorable: the boy gets the girl, the soldier makes it home, the cop catches the killer, the sporting legend proves he's the best after all. As Pauline Kael once wrote: "The motive power behind much of our commercial entertainment is: Give the public a happy ending so they won't have to think about it afterwards." The real challenge is to give an audience something that confounds rather than reassures, something that turns expectation on its head yet makes perfect sense.

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It's a challenge some of the most accomplished film-makers have flubbed: think only of the third and final instalment of the Lord of the Rings trilogy, The Return of the King. Peter Jackson naturally wanted a grand conclusion to his epic, and had several opportunities to bring the curtain down with appropriate gravitas. Sadly, like a chronic gambler who doesn't know when to quit, he just kept on raising – and finished up with a full house of duff endings: a textbook lesson in how not to do it.

The list below is a highly partial and non-definitive selection of endings that are remarkable either for an element of surprise or else for the way the final moments elegantly dovetail with the moods and themes the movie has been exploring. It might only be a few words, or fleeting images, or even a freeze-frame, but each of them impresses for its absolute and immutable rightness. It will also remind us that the great endings are not, usually, happy endings.

10. The Taking of Pelham One Two Three

(US 1974, dir. Joseph Sargent)

This so-so group-in-jeopardy thriller stars Walter Matthau as a New York Transit Authority chief forced to deal with a crisis: a subway train has been hijacked and its passengers held to ransom. The gang, led by a somewhat mechanical Robert Shaw, have already executed two hostages, and Matthau has the job of negotiating with them.

In the course of their fraught exchanges via radio, Matthau can hear that one hijacker (Martin Balsam) has a heavy cold, and occasionally interrupts his boss with a loud sneeze. "Gesundheit!" says Matthau distractedly. Cut to the movie's endgame: all the hijackers are dead, apart from Balsam, who has somehow escaped with the loot and hastily hidden it in his kitchen. Matthau and his partner arrive to interview him – a standard suspect because he's actually a subway train driver – and seem to have drawn a blank: Balsam claims to have been home with a cold all day, so he couldn't have been hijacking a train. Matthau is out the door and mentally striking the suspect off his list when, suddenly, Balsam sneezes. Gesundheit! Matthau's head pokes round the door again – he's busted. A superb final twist: it deserves that house in Bel Air.

9. North by Northwest

(US 1959, dir. Alfred Hitchcock)

William Goldman has said that he doesn't know of a "more adroit" ending to a film than this. Cary Grant is hanging on to the edge of Mount Rushmore, while his lady, Eva Marie Saint, is hanging on to him. Martin Landau, the subvillain, stands a few feet away, holding a statuette containing microfilm that would endanger America if it fell into enemy hands. He walks over to the dangling man and, instead of helping him up, grinds his shoe down on Grant's hand. It looks all over for our hero. The scriptwriter, Ernest Lehman, has an escape of his own to make here, and yet, as Goldman expresses it, the following occurs:

"a) Landau is made to cease and desist.

b) Grant saves himself.

c) Grant also saves Eva Marie Saint.

d) The two of them get married.

e) The microfilm is saved for America.

f) James Mason, the chief villain, is captured and handed over to the authorities.

g) Grant and Saint take a train ride back east."

Can you guess how long it takes Hitchcock and Lehman to tie up all these narrative ends? Goldman has timed it for us: 43 seconds. No, I couldn't believe it either, until I watched the film again. Not a great ending, perhaps, but a marvel of efficiency.

8. Don't Look Now

(GB 1973, dir. Nicolas Roeg)

This is the ending as unrepeatable shocker. Donald Sutherland and Julie Christie, grieving the death of their young daughter, repair to off-season Venice and try to forget. They are approached by a blind woman who has clairvoyant messages of danger, apparently delivered by the ghost of their dead child. But what is the danger? Nicolas Roeg creates an ominous, disorientating pattern of flashbacks, echoes and colours around the couple's troubled sojourn while Venice, almost incidentally, becomes the scene of several unexplained murders.

The closing minutes of the movie find Sutherland caught between hope and dread, pursuing a red-coated apparition through the dank alleys and courts of the eerily empty city. Finally, breathless, he catches up with his quarry, and offers up some gentle words of reassurance: "I'm not going to hurt you." Too right: the hooded figure in red turns round to reveal a dwarfish face of unutterable malignity, and a knife is suddenly slashing at Sutherland's jugular. He collapses, dark gouts of blood pouring from his neck. Death in Venice, indeed, only this time with horror instead of seedy pathos.

7. The Long Good Friday

(GB 1980, dir. John MacKenzie)

Bob Hoskins, as East End gangster Harold Shand, has come to the Savoy Hotel to finalise details of a business partnership with an American mobster. But the Americans are getting out, spooked by an Easter weekend of carnage, all traceable to Harold's vendetta with Irish Republicans. Disgusted, Harold storms out, though not before delivering a great (if ungrammatical) putdown: "The Mafia? I've shit 'em!" He then emerges on to the hotel's circular concourse and climbs into his limo – which suddenly accelerates away. His own driver is gone, replaced by a man whose hooded eyes are reflected in the rear-view mirror, while another (a fresh-faced Pierce Brosnan) trains a gun on him from the passenger side.

It's the IRA, whose tenacious reach Harold has hubristically underestimated. John MacKenzie's camera fixes on him in the back seat, and as Francis Monkman's busy, brassy score kicks in, we watch a grim rictus settle on Harold's face that seems to pass from anger, to resignation, to a sort of rueful admiration. For another iconic gangster face that closes a movie, there's De Niro staring up from his opium dream in Once Upon a Time in America. But I think Hoskins shades it.

6. The Private Life of Sherlock Holmes

(GB 1970, dir. Billy Wilder)

I owe my love of this movie to the novelist Jonathan Coe, who wrote an excellent essay on it for the French film magazine Cahiers du Cinéma. Billy Wilder and IAL Diamond wrote more famous endings (to Some Like It Hot, to The Apartment) but none more moving, I think, than the epilogue to their Holmes pastiche, a film whose charm must be weighed against its unevenness – great tranches of it were inexplicably lost.

The second half concerns a shaggy-dog story in which Holmes (Robert Stephens), on a mission in Scotland, pretends to be married to a woman (Genevieve Page) who is later unmasked as a German spy. The final scene has Watson (Colin Blakely) reading a letter which reports that she has been executed by firing-squad, though a postscript adds that the woman had lived her last months as "Mrs Ashdown", the name Holmes assumed when they pretended to be man and wife.

Holmes, broken by this belated revelation, bids Watson prepare his needle – only cocaine can salve him – while Miklos Rozsa's beautiful and melan choly violin concerto plays mournfully in the background. There is a level of pathos here that one would not usually associate with the great detective – or, indeed, with this great director.

5. The Conversation

(US 1974, dir. Francis Ford Coppola)

This could be a companion piece to Chinatown, resonating as it does with contemporary American crises: the curdling of idealism, the fear of conspiracy and an intuition that the bad guys are getting away with it. Gene Hackman has never been better than as Harry Caul, a professional wire-tapper who steals privacy for a living and whose latest assignment seems to have endangered the lives of an innocent couple.

Coppola's masterstroke was to hinge the plot on the misinterpretation of a single line ("He'd kill us if he got the chance"), but it is Hackman's presence that reverberates in the film's devastating coda: double-crossed by his paymasters, he now knows that he is under surveillance and has torn up the walls and floors of his apartment in search of the bug. Our last sight of him, blowing on a saxophone amid the ruins of his home, is a picture of pure loneliness, and a chilling physical metaphor: a man who has stripped down his life to the core and found absolutely nothing.

4. The Third Man

(GB 1949, dir. Carol Reed)

Screenwriter Graham Greene torments Holly Martins, the naive American protagonist played by Joseph Cotten, from the moment he arrives in rubble-strewn post-war Vienna to attend the funeral of his friend Harry Lime. Martins, a hack writer of pulp westerns, finds himself blanked by the locals, patronised by the urbane British major (Trevor Howard) and duped by the very man (Orson Welles) he believed to be cold in his grave. But Greene saves his most poignant humiliation until the very last scene.

Having attended Harry's funeral (his real one) Martins waits for Harry's actress girlfriend (Alida Valli) in the hope of a reconciliation, perhaps even a romance. Valli walks towards camera down an avenue lined with cypress trees – and passes right by him, without a glance, while Anton Karas's famous zither score keeps up a mocking jauntiness. Holly's last illusion – that this woman might have cared for him – lies shattered. Robert Altman liked this ending so much he paid homage to it at the conclusion of The Long Goodbye.

3. Casablanca

(US 1942, dir. Michael Curtiz)

It would be churlish not to include this. Curtiz's wartime melodrama has lines in it so terrible even the cast would break up with laughter, yet it remains as fond and familiar to us as a comfortable old sofa. The trick of this ending is to give the audience what it wants, but not in the way it expects. Bogart, as the defiant lone-wolf Rick, has already proven himself a romantic by helping a young woman escape Casablanca and the corrupting grasp of Captain Renault; but who could have anticipated the last-gasp nobility of his handing Ilsa, the woman he loves, back to her freedom-fighting husband Laszlo?

Having tied up the romantic narrative, Rick then opens up a new political front by shooting dead Major Strasser and converting the cynical Renault to patriotism. "Round up the usual suspects..." What nerve! As Rick and Renault slope off into the fog we seem to be witnessing not just the start of a beautiful friendship but a stirring alliance that will, hell, alter the whole course of the Second World War.

2. Chinatown

(US 1974, dir. Roman Polanski, scr. Robert Towne)

"Forget it, Jake, it's Chinatown." One of the most quoted lines in cinema snaps the lock shut on one of its most perfect plots. Yet the key line is the one Jake Gittes first uses to head off Evelyn Mulwray's question about what he used to do as a policeman in Chinatown: "As little as possible," he deadpans, later repeating the words (though they're not in the published screenplay) as he looks horror-stricken on Evelyn's corpse and realises his own implication in her doom. The lieutenant on duty, Escobar overhears and says: "What's that?" Incandescent with rage – "As little as possible" evidently encapsulates police procedure in Chinatown – Escobar orders Gittes to clear off. "Go home, Jake – I'm doing you a favour."

Slowly, Jake and his associates turn away, the camera rises and the sad trumpet theme fades in. Towne argued bitterly with Polanski over this ending, after the latter insisted that Evelyn should die and the satanic Noah Cross escape justice. Polanski got his way, and Towne got the best screenplay Oscar .

1. The Wild Bunch

(US 1969, dir. Sam Peckinpah)

A whole movie about endings: Peckinpah's ageing outlaws, on the run through Mexico in 1913, have reached the end of the line and gone down in a savage, apocalyptic gun-battle (itself a shocking new departure in screen violence). Robert Ryan has unholstered his friend William Holden's gun for the last time, and now sits in front of the shattered fortress. Edmond O'Brien, the other survivor, tells him there's only one more fight left – the Mexican Revolution. "It ain't like it used to be," he grins, "but it'll do."

As the two men ride off, laughing together, Peckinpah does one more startling thing: he elides their laughter into a montage of dead members of the Bunch – Holden, Ernest Borgnine, Warren Oates, Ben Johnson, Jaime Sanchez – whose own laughing faces fade in and out to the tearful chorus of "La Golondrina". Paul Schrader called it "one of the strongest emotional kickbacks of any film". It's a transition only Peckinpah, one feels, could have finessed, and a great ending to a great movie.

Anthony Quinn, 2007. This is an edited extract from 'Ten Bad Dates with De Niro: A Book of Alternative Movie Lists' edited by Richard Kelly (Faber and Faber); www.tenbaddates.com