The earliest narrative to disrupt its story-line was Virgil's Aeneid, which begins "in medias res" -- in the middle of things -- and fills in narrative gaps through the recollections of different survivors of the Trojan War. Its innovation is that it mimics psychological symptoms of wartime sufferers; it may be the earliest written recreation of post-traumatic stress disorder. Although Virgil's reverse narrative was not respected as story-telling by the ancient Greeks, it pointed the way for future writers, including authors as diverse as Edgar Allan Poe and Harold Pinter.
Poe, in "The Purloined Letter," began the tradition of starting a mystery with its climax completed; a crime has already been committed. Poe takes half the story's text to retrace the action and solve the puzzle, thus setting the reverse narrative pattern for the works of Agatha Christie, Georges Simenon and dozens of others. Pinter went them all one better with "Betrayal," a play whose mysteries are unfolded in its exposition: it begins with the enigmatic end of a long affair and proceeds backwards to the first seduction.
Numerous filmmakers have used the reverse narrative technique; Quentin Tarentino is particularly fond of it. His movie "Pulp Fiction" makes unnerving use of flashbacks and memory tricks as it presents assassinations first and then explains the motivations behind the killings later. The best film thus far to demonstrate complete reversal is Christopher Nolan's "Memento," which replays every plot point in reverse, saving its surprises for the ending exposition. Since Nolan's tale is that of a detective with no ability to retain memories, his technique and narrative join seamlessly.
The author of a reverse narrative has a difficult task: to create an exposition that will be his ending, and which is as riveting as his resolution, which is his beginning. Meanwhile, he has to render each falling action plot point in the tale's first half, and detail rising action in the second. Although the writing is a daunting challenge, it's a delight for readers to find an author who successfully creates a story that plays with narrative time.