Vertigo Effect

The camera lens zooms in on the subject, while the camera itself is physically moved away from it, or vice versa. This effectively changes the focal length of the lens without altering the image composition. This causes the image's depth information to either compress or stretch, making the image look like it's getting deeper or flatter.

Goes by many names, including optical compression, tracking zoom, dolly zoom, Hitchcock zoom, contra-zoom, trombone shot, and push-pull zoom.

Often used to tell the viewers that the character in the focus of the camera has just had an emotional shock, although it may not actually be shown on his/her face. Sometimes goes hand in hand with Oh Crap.

First used by Alfred Hitchcock in the movie Vertigo as an Impairment Shot to show the audience what the protagonist is experiencing every time his fear of heights kick in. The opening scene can be seen here displaying the effect about 55 seconds in.

Compare Whooshing Credits.

Examples of Vertigo Effect include:

Anime and Manga

Ghost in the Shell used this technique digitally in 1995, when it was hailed as a major advance in 3D animation.

Film

Used by Peter Jackson in both The Lord of the Rings: The Fellowship of the Ring (when Frodo senses the arrival of the Black Rider in the Shire) and The Return of the King (Frodo's first look into Shelob's lair).
Jaws, when Chief Brody (Roy Scheider) reacts on the beach to the Kitner boy being attacked by the shark.
- This trope is often called "The Jaws Shot" by people who haven't seen Vertigo.
The opening shot of Jean-Pierre Melville's Le Samourai is a Vertigo Effect shot of a man lying down on his bed, smoking. Unlike most examples, however, the shot is jerky and uneven, representing the man's lonliness and mental instability.
Josie and The Pussycats (the movie), when Josie realises she's been brainwashed.
The Lion King, when Simba sees the wildebeest stampede charging right at him.
Used on a mailbox in How I Got Into College: it is the only memorable shot in one of the world's most forgettable films.
Brick, when Tug punches Brendan.
A Goofy Movie, when Max learns his father is taking him on vacation.
There are quite a few simulated trombone shots in the computer-generated Pixar movies, notably in The Incredibles.
In Goodfellas this happens during a scene in which Ray Liotta and Robert Deniro are speaking in a diner. The shot happens so slowly that you don't consciously notice it, to show how paranoid the characters are getting at this point in the movie.
There's a remarkable one in Road to Perdition, where Jude Law's character first appears walking toward the camera underneath an L track. It takes about thirty-plus seconds of screen time, whereas the typical Vertigo shot is much more fast-moving.
A notable version of this happens in the movie Poltergeist during the ghost's assault on the family at the end of the film. The mother gets thrown out of the house at one point and then battles her way back in to save her children. As she's running down the hallway to the children's bedroom, a Vertigo Effect begins which soon turns into a full-blown special effect in which the hallway itself starts becoming stretched and distorted. The more the mother runs, the longer the hallway becomes and the further away she gets from her children's bedroom door. She eventually catches up to it by running at full speed.
Done too often to count in the A Nightmare on Elm Street movies, during a Freddy chase or Freddy reveal.
A huge, hilarious version is used to comic effect in The Mask.
Ghostbusters uses this for its 'weird feeling' effect in a shot of a doorway to the collapsed roof of the 55 Central Park West tower. The commentary track between the director, main actor, and director of photography addresses that they considered themselves to be pioneering the technique—Harold Ramis jokingly suggesting "Scorsese ripped you off!"
In Psycho, the infamous stair scene may be as iconic as the shower scene.
There's one on Ralph Fiennes inside the "soundproof" booth in Quiz Show, at a particularly anxious moment.
Used in Return of the Living Dead, when Tina first sees the "tar man" zombie.
Used to the point of self-parody in The Quick and the Dead. A textbook-worthy example happens while Herod and The Kid (Father and Son) square off.
The French spy satire OSS 117: Lost in Rio steals not just the effect, but the entire staircase scene from Vertigo.
In Apollo 13, Jim Lovell announces "Houston, we are venting something out into space"; we cut to Gene Krantz back in Mission Control, and use this effect to show just how dreadful this news is.
In Back to The Future Part II when Marty watches footage of his mother marrying Biff in 1985-A.
Subtly used in How to Train Your Dragon, when Hiccup and Astrid see the Red Death for the first time.
Used in the film Merlin's Shop of Mystical Wonders when Michael sees the evil monkey has returned to his house.

Tom: My cabinets are flying away!

As well as Vertigo, Hitchcock used the effect very strikingly in Marnie to give the effect of a room shrinking and becoming claustrophobic.
Used in the Bollywood movie Rangeela ("Bollywood Dreams") -- possibly as a nod to Spielberg, whom the in-movie director character admires.

Music Videos

Michael Jackson's moment of transformation in the Thriller video.

Live Action TV

The Babylon 5 episode "Severed Dreams" features such a shot at a dramatic moment when a major character comes to a major realization: Sheridan discovers that the Earth Alliance is coming to seize control of the station.
FTL jumps in the new Battlestar Galactica.
Veronica Mars features one at the end of season 2, when Veronica figures out exactly what's going on.
Used in a Star Trek: The Next Generation episode. Aliens are affecting the crews' sleep, preventing them from getting real rest. At one point Captain Picard sees the turbolift ceiling experience the Vertigo Effect, showing how his perceptions are being affected.
Mr. Bean in Room 426 has one of these, when the title character realizes he's just consumed a bunch of rotten oysters.
In an episode of Malcolm in the Middle Lois inadvertently infects Malcolm with mononucleosis. As Malcolm is heading to the couch to lay down, Hal shoos him away saying he has to be quarantined from the healthy family members. Cue Malcolm looking down the hall towards Lois in her bed with the vertigo shot. It's definitely an Oh Crap moment for poor Malcolm.
Used in an episode of Casualty many years ago when Brenda Fricker's character realises that she has told a girl's parents that she has survived an explosion when, in fact, there has been a mixup and she is actually dead.
Psych in their Hitchcock homage.
To excellent effect in White Collar, to display Mozzie's extreme emotional distress on entering the federal building for the first time.
A scene in the Doctor Who episode "The Eleventh Hour" is shot from the Doctor's point of view, as he scans the Leadworth village green for inconsistencies. Eventually, he hones in on a disguised Prisoner Zero, whose background and shadow stretches out behind him in classic Vertigo style. Particularly odd example, as it's not shot on conventional film - rather, it's a series of snapshots slung together.
- Also happens at a vital moment in "The Unicorn and the Wasp".

Video Games

This effect is used to zoom in on Roman's horrified face when he and Niko get kidnapped in Grand Theft Auto IV.
Legacy of Kain: Soul Reaver 2 uses this effect to simulate a feeling of temporal displacement in scenes where time paradoxes can and will occur, going back and forth faster and faster as the paradox comes closer to happening, such as whenever the Soul Reaver's past and present versions of one another meet.
Instead of zooming in or out, The Legend of Zelda: Twilight Princess uses this for its camera controls.
Rock Band likes these. Really, really likes them.
Done in a cutscene in the original Tomb Raider. Tomb Raider: Anniversary also uses this effect whenever Lara looks down while hanging from a ledge.
- Used interestingly in a cutscene from a fan-made level: the camera enters a large room, then uses the Vertigo Effect before it begins to pan around, giving the impression that the room has doubled in size.
Used in the intro cinematic to Half-Life 2, when you first enter the train.
Used in one of the early hallways in Amnesia the Dark Descent.
Used in Mass Effect when sprinting.
- It also accompanies the Bullet Time effect (except when zoomed into a scope, for obvious reasons). In Mass Effect 2, this was mostly power-driven, but it occurs at several plot-mandated moments of Mass Effect 3, such as the final round of the Boss Battle on Rannoch, where the Reaper leeeeeans in and stares Shepard down, and it turns into a quickdraw contest between Shep's markerlight and the Reaper's Frickin Laser Beam.

Web Original

In Echo Chamber, this combines with Oh Crap and Say My Name after Tom runs into his Psycho Ex-Girlfriend. Or it would, if that weren't an outtake.
One entry for the Internet Raytracing Competition uses this effect to show off how MC Escher's famous "Waterfall" print works.
Red vs. Blue was able to do this after switching to Halo3, using the camera in theater mode. Previous games had a zoom feature, but it always switched to a scope of some kind. The camera in Halo3's Theater mode zooms seamlessly (although very quickly, making it a bit hard to control). One of the first times it was used was in Part II of Relocation, when Caboose sneaks up on Simmons.

Western Animation

The Vertigo shot (and quite a bit of the Hitchcock oeuvre) is parodied on Sylvester and Tweety Mysteries with Sylvester in the place of the main character.
Used frequently in Sam and Max: The Devil's Playhouse, as a bit of visual jargon representing the use of psychic powers.
In one of Batman: The Animated Series's many Hitchcock-inspired scenes, Batman gets hit with the Vertigo Effect while under the influence of Scarecrow's nerve toxin.
- There's a episode that's actually called "Vertigo" that focuses on a gadget of some kind that can temporarily induce this effect in people's vision.
In the segment, "Hungry are the Damned" from the first Treehouse of Horror, this kind of shot is used when Lisa first sees the flying saucer.