Instant Mystery, Just Delete Scene

Alice gets home after a long day. Just as she makes herself comfortable, the doorbell rings. Suddenly the scene jumps to Bob and Claire, who are talking about how they haven't seen Alice this morning. Suddenly the audience realizes that it's the next morning, and we never found out who was at the door. Will Bob and Claire now have to investigate Alice's murder? Or is it all a Red Herring?

Often part of a Cold Opening or used as a way of setting up a case of Not Quite Dead.

This has become almost a staple of murder mysteries, especially in Live Action TV shows like Diagnosis Murder and Monk.

Film

 * James Bond.
 * An unintentional example of this inspired the Grindhouse cut of Quentin Tarantino's Death Proof, which has a 'missing reel' (restored on the complete cut). He had once seen an Italian crime movie with a missing reel which he felt made the film more interesting, because it obscured whether or not the detective had slept with the girl (he said he did, but the girl said he didn't).
 * The other half of the feature, Planet Terror, played it gloriously straight with a reel that was never shot. The film cuts from El Wray and Cherry starting to have sex, says "MISSING REEL", and when it cuts back, everything is on fire and we'll never know why. We'll also never know just who El Wray really is and why the police chief suddenly has the utmost respect for him.

Live Action TV

 * Diagnosis Murder.
 * Law and Order.
 * Monk.
 * Star Trek.
 * Without a Trace does this to set up every episode.
 * The X Files.
 * Averted notably in Columbo.
 * Some episodes of Doctor Who.
 * Leverage uses this trick to hide some of the crew's cleverer preparations: the audience usually isn't let in on the entire scheme until it actually goes down, when the missing steps are revealed in flashbacks.
 * Veteran viewers will have little trouble identifying the moments when someone in the crew is doing SOMETHING that is part of the unrevealed plan (ex: Sophie borrowing someone's coat, Hardison working on some random little device, etc) but it's not always possible to tell how the pieces all fit together until the end.
 * Home and Away has used this, with the audience never being quite sure about certain things such as Hugo's role in the 2009 mystery, or what the hell actually happened at the Sands on the night Penn died (assuming British viewers have caught up, here's one for those just starting to watch the week of this writing: Will killed him in self-defence after he threatened Shandi/Daria). They usually accomplish this by showing another storyline that ties into the characters involved in the scene.

Music

 * Possibly unintentional, but Hinder's "Lips of an Angel" starts off with the the singer getting a call from his old flame. He asks why she's calling so late and why she's crying, but we never find out the answers, as the rest of the song is immediately hijacked by him singing about how he still has feelings for her.

Western Animation

 * Scooby Doo.
 * Avatar: The Last Airbender does this when  We don't find out what happens to them until over halfway through the next season.
 * Lampshaded in The Simpsons episode "Wild Barts Can't Be Broken". Homer is asked about what he did the previous night. We see his memory of the event as a sepia-toned silent movie, with the parts he forgot due to being drunk replaced with a title card labeled "SCENE MISSING".

Anime

 * The Big O.
 * Neon Genesis Evangelion: Who killed Kaji?

Video Games

 * The World Ends With You has several instances where it jumps to the next day and only later flashes back to what happened in the previous day.
 * The PC version of Clue: Master Detective started with a still cutscene of Mr. Boddy alive in his chair. There is a blackout signifying an unknown amount of time passing and then we see Mr. Boddy dead in his chair. Makes one wonder as to how the "where the murder occurred" part of the mystery fits in....
 * A few Ace Attorney cases start this way, featuring stills of two characters talking and the insinuation that action occurs, but no identification of the speakers or display of the murder itself. Others involve a relatively coherent scene, but the criminal is shrouded in shadows and unidentifiable--and due to the text-based nature of the game, identification by voice is also impossible.

Webcomics

 * Drow Tales does it here.
 * Fleep plays with the reader by cutting from the initial shot of the protagonist entering a phone booth and him waking up in another phone booth surrounded by concrete. As it turns out, that interval is a lot longer than you might expect...
 * El Goonish Shive does it here.
 * Homestuck likes to show scenes in whatever order seems most dramatically convenient. It often leads to the narrator lampshading how we're DEFINITELY going to see what's coming next.