According to the IMDB, the original cut of James Bridges' MIKE'S MURDER (filmed 1982, released 1984) was told in reverse, beginning with the final scene, then working its way back to the beginning. This way of structuring a film subsequently became fairly commonplace: see Jane Campion's 2 FRIENDS (1986), Lee Chang-dong's PEPPERMINT CANDY (1999), Christopher Nolan's MEMENTO (2000) and Francois Ozon's 5x2 (2004). But if the IMDB are correct, then MIKE'S MURDER may have been the first film structured in this way. Does anyone know of earlier examples?

BETRAYAL starring Jeremy Irons was a 1983 movie using the same structure but based on a 1978 play by Harold Pinter.

And wonderfully referenced in the Seinfeld episode "The Betrayal," which is also told in reverse.

Wikipedia mentions a Czech comedy, HAPPY END, from 1968.

The festival crowd pleaser IRREVERSIBLE is also told that way. Can't think of anything earlier though.

THE LOCKET (1946), a film noir done at RKO and directed by John Brahm, has a flashback within a flashback within a flashback, and maybe even one more, so for part of the film it's practically being told in reverse. It's pretty amazing. It stars Laraine Day, Brian Aherne and Robert Mitchum like you've never seen him.

As Brian hints, the flashback as convention flirted in the direction of backwards story telling nearly from the beginning (of the end) of filmmaking. Preston Sturges was much taken by the possibilities of mixing up or reversing time sequence for dramatic effect, ironic and otherwise. THE POWER AND THE GLORY (a movie he wrote but didn't direct and one which I haven't seen) intercuts past, present, and future fancily and portentously. THE GREAT MOMENT allows a tragic story to end triumphantly by semi-reversing the flow of time and beginning sadly in the present, concluding happily at a climactic moment in the past. Yes, the film is essentially an extended flashback, but our foreknowledge of what lies ahead is used to similar effect as in later 'reverso' films.