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This is basically how both Izaya and Shizuo of Durarara!! learned Parkour. Izaya learned it so he could escape and reach places where Shizuo would have to be insane to follow him to. Shizuo was simply insane enough to follow him. Shizuo eventually ends up doing this himself. Instead of letting himself be captured by the Yakuza for a murder he didn't commit, or undermining any chance of proving his innocence by attacking them, he instead opts to escape — and starts with a superhuman climb up a nearby building.
Played with in Ranma ½. Ranma and Jerk Jock Kunō are staring down in a school corridor, and Ranma declares that "this is no place for a fight" and proceeds out the nearest (third floor) window and Kunō, idiot that he is, jumps right after. While everyone in school gasps in shock (and Kunō himself is horrified when he realizes it,) this is not a problem for Ranma, who's used to this kind of leap. The problem is that Ranma didn't know about the swimming pool right below, and even though he can withstand the impact, it will also trigger his Gender Bender curse in full view of everyone.
Bone has a famous and catchphrase-launching subversion in an early sequence where little Fone Bone is being pursued by giant rat creatures. "Those rat creatures would have to be pretty stupid to follow me on this frail, little branch!"
Fone Bone: STUPID, STUPID RAT CREATURES!
In Sin City, a common technique in avoiding pursuing cop cars is to head to Old Town where they aren't allowed. A civilian car is fine since it's a possible customer for the prostitutes but since the girls have their own rules, a squad car is likely to get blown apart.
Films — Animation
Simba's escape from the Hyenas through a thorn bush field after Mufasa's death in The Lion King. Simba didn't mean to do this, but it had the same effect.
Oliver of Oliver & Company proves his mettle to the Dodger by successfully following him all over New York, through chaos, traffic, and construction zones, in pursuit of his share of a string of stolen sausages.
Films — Live-Action
In the second Crocodile Dundee movie, Mick is interrogating a criminal who's tied upside down hundreds of feet in the air when the police arrive. He uses the end of the rope to leap off the building and swing into a window. One police officer suggests they follow him, which suggestion is met with utter disbelief.
The famous dam jump. They made this into a perfect moment between hunted and hunter, and showed what extreme Richard Kimble was willing to go to prove his innocence.
In the sequel U.S. Marshals, the fugitive jumps off the roof of a building, uses a rope to swing over to a train station on the other side of the street, then jumps onto the roof of the departing train in order to evade Gerard.
In First Blood, Rambo was being chased through the woods and actually jumped from a small cliff into trees to escape.
Leia: What are you doing? You're not actually going into an asteroid field!? Han: They'd be crazy to follow us, wouldn't they?
See also the following line from Ben Kenobi...
Obi-Wan: Who's the more foolish — the fool, or the fool who follows him?
The Expanded Universe shows that such ploys are such a standard part of Han's repertoire that this trope could be named the "Han Solo Gambit".
Butch Cassidy and the Sundance Kid jumped off the cliff into the river below to avoid being caught. But that wasn't enough and they learned later that their pursuers would keep after them until they were captured or dead.
When Wesley and Buttercup escape into The Fire Swamp to evade their pursuers.
Buttercup: We'll never survive! Wesley: Nonsense! You're only saying that because no-one ever has.
And earlier, when Vizzini's gang climb the Cliffs of Insanity.
The most hilarious moment in the film True Lies involves Arnold Schwarzenegger on a horse (borrowed from a mounted city cop) chasing a bad guy on a motorcycle through an improbable array of settings, including crashing through an elegant soiree in a grand hotel. Eventually the villain uses a ramp to do a suicidal leap from the hotel roof... into a rooftop swimming pool a hundred feet away and twenty feet down. Arnold attempts to follow — only to have his horse come to a dead stop and give him an "Are you insane?" look.
Subverted in Fantastic Four: Rise of the Silver Surfer. When Johnny tries this move, apparently hoping his superior knowledge of the area will pay off, the Surfer phases stoically through the obstacles.
Probably one of the most popular sequences from Casino Royale is when Bond is chasing after a bomber who is employing Le Parkour moves to navigate a construction site and trying to lose Bond in the process. Instead of replicating his nimble target's movements, Bond would go for far more direct approaches to navigate the same obstacles, like slamming through a sheet of drywall after his target squeezed through a small, hard-to-reach hole.
In Mel Gibson's Apocalypto, Jaguar Paw's jump from a waterfall is a turning point for the character and story. When his pursuers actually do follow and survive, he realizes that he can't just outrun them. After all, he is Jaguar Paw. He is a hunter. And this is his forest.
Batman Returns: Batman heads directly toward a narrow alley far too small to accommodate the Batmobile, then transforms his vehicle until it will fit. The police following him obliviously maintain acceleration right until they crash into the alley
Part of the reason Agent J was recruited into the Men In Black was because he was able to keep up with an alien criminal who did this.
Axel Foley pulls off a less spectacular, but nonetheless clever, version in in Beverly Hills Cop. While driving, he spots two plainclothes cops tailing him. He stops at a traffic light and waits through the green and yellow cycles, confusing the cops. Just as the light turns red, he speeds through the intersection. By the time the cops recover from their surprise and try to give chase they're cut off by the cross traffic.
A rock cliff in New York's Shawangunk Mountains bears the name Sam's Point. According to legend, it was named back in the 1700s for Sam Gonzales, who escaped a party of pursuing Indians by jumping off the cliff into the bushes below. There is no record as to whether the Indian chief further guaranteed Sam's escape by looking down from atop the cliff and confidently stating "No One Could Survive That".
In Rudyard Kipling's The Second Jungle Book story "Red Dog", Mowgli is fleeing the rampaging dogs and jumps off a cliff into a raging river. This is a deliberate subversion, though — he knows they'll follow him, but is setting a trap for them.
In Men at Arms, Sergeant Angua (a w-erewolf) is running from a dog pack on the rooftops. She jumps over a wide street, and the dogs following stop. The leader tells them to keep chasing, and jumps over to demonstrate. It doesn't work.
In Lucky Starr and the Rings of Saturn, Starr evades pursuit by flying directly at Saturn's moon Mimas in an apparent crash dive. His drive exhaust vaporizes the icy substance of the moon ahead of him, giving him sufficient room to come to a stop beneath the moon's surface.
In the Descent novels, St. John, during a dogfight around Shiva Station, decides to lose his tail by flying mere meters above the station's hull, dodging and weaving among the towers, antennae, and other assorted space station stuff. This absolutely horrifies his co-pilot, who is convinced that they are going to die. Fortunately, they do not. Unfortunately, the pilot chasing them is good enough to follow them.
Explained in the top quote. The show has a "Spy Work for Dummies" narration and in trying to escape some pursuers, Michael jumped down two stories and ran home on a twisted ankle. From a later episode, "You bend your knees, tuck and roll... and just accept that it's going to hurt."
In another episode, he said that this is also an effective way to tell if you are being trailed, you take unnecessary risks. If in a car, you signal one way and go the other, speed through red lights, etc. In at least one episode, he notes that doing this is a tip-off to your pursuers that you suspect you're being followed, and gives the variant of driving extemely prudently... signaling well before turns or lane changes, braking and accelerating slowly and smoothly, stopping on yellow lights... until suddenly you do something like pull a right turn from the left lane to leave your tail, who had been lulled into thinking you'd never do anything crazy like that, behind.
On Top Gear, Jeremy Clarkson (being pursued through a shopping mall by "baddies" in a Corvette as part of an "extreme road test"), attempted dodging in and out of several tight spaces in his Ford Fiesta. The 'Vette still gave chase, but it got significantly delayed, and Clarkson eventually made his escape.
Clarkson: The Corvette is stuck in British Home Stores!
On Leverage, Parker specializes in this. She has rappelled down the side of a building, base jumped off a building, and flipped off a bridge and held on by her fingertips to avoid pursuit.
In an episode of Firefly, Wash attempts to lose the Feds on their tail by saying "Let's see them follow us through here!" and ducking and weaving through a narrow canyon. The camera pulls back to show the Feds are simply flying above the canyon and watching them from there. "Oh...I didn't think of that." Then they start with the bombing.
Path of Neo allows you to pursue the first option described in the second The Matrix example above, and see what could have happened. They might catch you anyway, but if you're good enough to escape them, Trinity is waiting outside on her motorcycle and will instantly take you to Morpheus.
In Heavy Rain, Ethan can escape from the police by jumping off a building and hijacking a taxi. It's not clear why this works though, since the police have a helicopter.
It's possible to invoke this trope in the X-Universe games. If your ship is small enough, you can do things like fly through gaps in space stations and make tight passes through asteroid thickets. Meanwhile, your A.I. pursuer's collision avoidance programming is likely to force it into going through a wide loop around the object while you continue to open the gap.
When playing games such as Snake or Light Cycles (TRON), getting into tight alleys that your opponent can't follow is a key tactic in advanced play. Of course, one has to be sure they can actually make it through the often tight maze to the other end before someone seals it off.
In Call of Juarez: Gunslinger Silas Greaves is after the Indian Chief Grey Wolf. After their first encounter, Grey Wolf flees and you have to follow him through a series of caves and on narrow paths leading down a cliff face. You have to do a number of 'Leap of Faith' jumps to get from one rock shelf to another and when you finally catch up to Grey Wolf, you end up walking straight into a major ambush. After all this, Grey Wolf still manages to escape and you never see him again.
In Girl Genius Tarvek, has a bright idea to run into the Castle Heterodyne. At the time, it's one big insane deathtrap used as a prison not seriously guarded once the prisoners are shepherded into the gate — usually the equivalent of a death sentence. Yes, the guards didn't follow him inside...
Violetta: Now do you understand what I have to work with?!
Parodied when Peter and Lois escape from wheelchair-bound cop Joe by jumping over a fence.
Another episode has a robber do the same thing. After he got away, Joe went through a Heroic BSOD and quit the force, but at the end crossed paths with the robber again, who tried the same thing, only for Joe to find a way to fling himself over the fence and land on the guy which ended up breaking his spine... killing him.
In Invader Zim, when Dib and Zim are driving the planets Mercury and Mars, Zim attempts this with Dib by challenging him to follow him through the asteroid belt. Dib is smart enough not to take on the challenge.
Parodied in an episode of King of the Hill: Hank is caught in a car chase with a pimp, and so he waits at an intersection for a yellow light and then guns it. When the pimp runs through the subsequent red light, Hank is shocked.
Criminals in car chases will sometimes take really crazy risks (swerving, going in the wrong lane) to get the police to stop following them—an officer's first duty is to protect the innocent, after all. Watch any episode of "World's Wildest Police Chases" or similar shows for confirmation. Of course, with police helicopters, the police can keep the criminals under surveillance until they can get the situation back under control.
There is one instance of a guy in a stolen tank leading the police on a merry chase that they couldn't follow directly (mainly because he was in a tank and crushed things rather than going around them) when he tried to lose them by swerving into oncoming traffic Reality Ensued and the tank got stuck on the concrete lane dividers. Linkage
Find yourself a victim of an Incredibly Obvious Tail? Experts suggest the best way to shake your stalker is to jump into traffic. The confusion ensures everyone is paying attention to you, and your stalker won't act with witnesses abound. Plus, if you really cause enough trouble, police might take you into (protective) custody. Of course, you might just get mowed over by a car.
Standard tactics for small tree-dwelling animals (squirrels, monkeys) when chased by arboreal predators: either climb out to the tip of a branch too flimsy for the pursuer to risk adding its own weight to, or take a wild leap into the next tree and hope the hunter doesn't take the risk.