In A Fistful of Dynamite the main protagonist has flashbacks from his better days back in Ireland, with his friend and an unnamed woman featuring in brief scenes featuring no dialogue. Later we see the reason he left Ireland in the same style.
Airplane!!: Ted and Elaine (meeting in the bar, in the Peace Corps, in the hospital, rolling on the beach), Ted's war memories. These can get ridiculous... The reactions to them can get a bit more ridiculous.
Batman Begins uses the non-congruous Nolan style jump. First, we go back and forth between Bruce in a Chinese prison and being trained by the League of Shadows to a young Bruce being rescued from a well by his father and watching his parents' death. When Ra's asks Bruce what inspired his travels, another lengthy flashback is used that documents Bruce witnessing Joe Chill's death and his encounter with Carmine Falcone.
Blazing Saddles. While Sheriff Bart and Jim are talking, Sheriff Bart tells Jim about how his parents came out West in a covered wagon and dealt with hostile Indians.
Bruce flashes back to Ra's talking about his family in Batman Begins.
In the finale, Gordon flashes back to putting Thomas Wayne's coat around young Bruce decades earlier.
Fearless uses flashbacks extensively, showing the lives of characters affected by a plane crash intercut with flashbacks to the crash itself.
John Carpenter's film Ghosts of Mars use extensive flashbacks that get more and more convoluted as the film goes on. The film is framed as one character telling the events to her superiors later; but every time she or another character meets up with someone new on the planet, that person explains whats been happening to them in their own flashback, and this repeats itself when they meet new people. This eventually devolves into the viewer watching a flashback within a flashback within a flashback within a flashback. Quite jarring if you let yourself become aware of it. Kudos to the character speaking to her superiors, though, who could remember everything she heard fourth-hand verbatim.
In Jaws: The Revenge Ellen has several flashbacks throughout the movie, although there is no way the majority of the scenes could be in her memories as she wasn't present for many of the events.
The 1956 melodrama The Locket bears the distinction of having a flashback within a flashback within a flashback within a flashback.
In the beginning of Lola Rennt, Manni's predicament is shown in flashback as he describes it. Then there are numerous flash-forwards as Lola encounters various characters, in rapid-fire montages showing their futures.
Passage to Marseille was a movie in which a reporter comes to an air base to interview a Free French officer who starts telling the story of one of his men (Humphrey Bogart). Flashback to the man being recovered at sea by a ship along with four others. It is revealed that they are escaped prisoners. Flashback to them planning to escape in order to join the fight against the Germans and saying why they absolutely...
Inverted in Memento, which flashes forward at intervals until the movie ends in the middle of the story.
Hoodwinked was based on Rashomon and uses the same thing. In fact, close to half of the film is flashbacks as the characters are interviewed by Nicky Flippers to explain how they ended up in Granny's house.
Saving Private Ryan plays around with its flashback a bit. It starts with an Age Cut into the flashback, except the old man in the graveyard is Private Ryan, not Captain Miller seen in the landing craft. Ryan isn't in the flashback at all until the final battle, and couldn't have remembered everything shown first-hand. (It is, however, possible that the story is relayed to Ryan through Upham).
Mission to Mars ends with Jim having rapid flashbacks of his late wife and all his friends, as he is preparing to leave for another galaxy to meet the progenitors of humans.
The Saw films do this extensively as a means of explaining the convoluted plots and building character development, even when many of the main characters are dead in the 'current' timeline.
Pope John Paul II begins with the assassination attempt in 1981, then flashes back to tell the story of the Pope as a young man, before eventually catching up and continuing on to his death in 2005.
Shaolin Soccer features a unique subversion: While Sing is trying to convince an old soccer coach of the value of Kung Fu, there are flashbacks to an ancient master performing techniques described, a master played by the same actor as the coach. The coach interrupts the last flashback by pulling off the old master's costume and stepping out of the character.
In Silent Night Deadly Night Part 2, the whole beginning is a flashback to the first movie even though there is no way that Ricky could've remembered any of the events depicted except for the last one because he was either a baby or wasn't present.
Jay in Sky Blue has a flashback to when Shua showed her the blue sky; Shua later has one to a few minutes later, showing why he was exiled. Later still, Cade has a flashback to the same event, where it turns out he framed Shua for his own action.