Flashed Badge Hijack

The bad guy is fleeing the scene of the crime in a vehicle, and our hero officer is without his or her car at the moment. No problem, he just hops in front of the next car that comes down the street, flags it to a stop, flashes his badge and commandeers the vehicle.

The occupants will either gladly surrender their car, or only offer token resistance, maybe a confused "Hey! What's going on?" as they are unceremoniously dumped in the street.

If the Hero can't convince them to give up the vehicle, or can't drive a stick, expect the person to become an all too enthusiastic participant in the chase anyway, as being able to ignore all road rules is a wistful fantasy to just about everyone.

This is in fact legal, though uncommon, in most of the United States, and if your car is damaged you're not likely to see any compensation for it. The Straight Dope has details. How quickly an officer can persuade a person to give up a vehicle is another matter.

See also Hero Stole My Bike, Follow That Car!. If the hijacker doesn't actually have the authority to hijack the car, it's a Bavarian Fire Drill.

Examples of Flashed Badge Hijack include:

Film

Martin Lawrence pulls it off in grand style in National Security. His partner later attempts the same thing, only to be shut down by the Sassy Black Woman who owns the car.
Subverted in a running gag of the original Taxi movie series, where the black comic relief cop can never get a car to stop for him.
Subverted in the movie So I Married an Axe Murderer, when a cop stops a passing motorist, but can't get him to give up his vehicle. He has to settle for getting a ride from the driver to the crime-in-progress.
Played for laughs in the movie Turner and Hooch.
Parodied Trope in Bad Boys 2 when Martin Lawrence's character tries to commandeer a run down car and gets yelled at by Will Smith to get a better car than that. A second later they take a Cadillac that was being test driven by Dan Marino.
- This also leads to the memorable line, "Dan Marino should definitely buy this car. Well, not this one, cause I'm gonna fuck this one up. But he should get one just like it."
Also spoofed in the comedy film The Naked Gun when the car the cop commandeers is occupied by a student driver and instructor.
- The doctor, under mind-control, hijacks a car to get away first and exclaims "medical emergency!" before tossing the occupant.
Subverted a bit in Speed when the hero cop has to commandeer a sports car to chase the bus. The driver, thinking he's being pulled over for grand theft auto (since he's black in LA, this might not be a bad assumption), snarls that his car is not stolen. The cop, having no time to argue, responds by drawing his gun and saying "It is now!" before he takes the wheel.
- And in the sequel, the same guy ends up getting his boat commandeered by a member of the LAPD - in the middle of the Caribbean (The man points out how inherently absurd this is as it happens). But it ends better for him this time - not only is the boat still intact at the end of the movie, he ends up finding the parcel of stolen diamonds floating in international waters. Even if he doesn't get to keep them, he could probably demand a finder's fee from the original owners.
Done twice in one scene in The Rock. John Mason (Sean Connery) steals some rich guy's Hummvee to escape the FBI, so Agent Goodspeed (Nicolas Cage) grabs the Ferrari right behind it. After a chase down the streets of San Francisco (which itself follows the Rule of Cool to the letter), the Ferrari gets crushed by a cable car, so Goodspeed then grabs a bystander's minibike.

Guy on Bike: Whoa, dude. You just fucked up your Ferrari.
Goodspeed: It wasn't mine. Neither is this. (Steals the bike)

Parodied in See No Evil Hear No Evil when a bad guy pretends to be a cop and tries this. The driver of the car demands to see a badge. The bad guy just gives up and produces his gun instead. The driver gives up his car, complete with a whimpered "Please don't kill me."
Popeye Doyle does one of these to start the famous car chase in The French Connection.
Subverted in Rush Hour when Carter tries to "borrow" a motorcycle, and the cyclist refuses, prompting Carter to shove him off and take the cycle.
Live and Let Die. When Sheriff J.W. Pepper's car is totaled, he commandeers a Louisiana State Police patrol car and continues in pursuit.
RoboCop does this in Robocop 3. It doesn't end well for the car.
Hilariously inverted in Sin City in which an Anti-Hero violently commendeers a police car in order to flee the scene.
In Loaded Weapon 1, the detectives do this to commandeer a couple of bicycles (which promptly explode for no reason).
The chase scene in Police Academy 6 was conducted with the cops in a commandeered monster truck.
In American Gangster, Richie Roberts tries to get a taxi driver to give him his vehicle so he can follow a lead. The driver refuses, so Richie just knocks him out and takes the car while he's still unconscious.
In the comedy/thriller Foul Play, the good guy cop commandeers a taxi - as he tries to explain what's going on to the Japanese tourists in the back, the word Kojak registers with them and they thoroughly enjoy the chase.
Reversed in the comedy/thriller That Man From Rio as the hero, a guy on a weeks leave from the service, sees his girlfriend get kidnapped, he gives chase on a motorcycle stolen from a policeman.
the fourth Lethal Weapon movie played this for laughs during a foot chase. Murtaugh, unable to keep up with Riggs and their fleeing target, goes over to a guy with a bicycle, flashes his badge, and tries to commandeer the bike. The guy refuses to let go of the bike, and Murtaugh, having no time to waste, grabs a wad of 20 dollar bills from his pocket, shoves them into the guy's hand, then rides off. As soon as Murtaugh is off screen the guy who was standing by the bike pockets the cash and calls out to a friend "Hey Johnny, somebody stole your bike!"

Literature

Subverted in the novel Hannibal, when Clarice Starling witnesses Hannibal Lecter being kidnapped by Mason Verger's thugs and is unable to get a couple driving a car to even call for help. She spends the next few hours silently cursing herself for not throwing them out of the car and chasing the kidnappers herself.
In Aaron Allston's Doc Sidhe, the hero does not have a badge. But he chooses a car full of college students and shouts, "I'm with the Sidhe Foundation, follow that car!" and they are so enthused at the thought that they do.
In Dan Abnett's Warhammer 40,000 novel Brothers of the Snake, Space Marines hijack a Princess Royal's car. She tries to stop them, until the Inquisitor who summoned them intervenes, and she runs off.
- In other works in the 40K universe, an Inquisitor's rossette is possibley one of the most dangerous objects in the galaxy. Mainly because it gives them the authority to do pretty much anything they like up to and including forcing entire armies and fleets under their direct command or blowing up entire planets. This said, most of them are actually pretty careful in how they exercise such power.
  - To summarise, they can Flashed Badge Hijack superheavy tanks, entire armies, even planetary populations, if necessary.
Subverted in Jennifer Government where the titular agent tries to commandeer a car, only to be tied up in wrangling over how much she has to pay the owner for the right to use it (this being an ultra-capitalist society where the government isn't really taken seriously).

Live-Action TV

Done at least twice per season on 24. In one egregious example from season 6, Jack Bauer more-or-less carjacks a civilian, throwing him from his seat onto the ground and yelling "Don't get up" as he embarks on the chase.
The guys on Hustle do this pretty much whenever they need a lift. And they're not even cops.
The cast of Torchwood can hijack anything and not just cars, simply by flashing a badge and shouting "Torchwood!" That's a very well-known secret organization.
After one of his teammates is capture in Stargate SG-1, Lt. Colonel Mitchell commandeers a man's motorcycle to give chase. The man was even nice enough to give Mitchell his helmet.
In the Korean Drama Iris, the cars are commandeered with pistols, but it still works.
In the first episode of Power Rangers Time Force the Pink Ranger attempts to do this but the man in question refuses (perhaps law enforcers are no longer authorized to do this in the year 3000). However the Yellow Ranger (who possess superhuman strength) quite literally throws the man out of his car and the Rangers take it anyway.
The Real Hustle once showed how con artists would dress up as police officers and do this to steal people's cars. The guy they did it on did show some resistance, but mostly confusion. After a few seconds of protests the con artists were behind the wheel and driving off.
Played humorously in an episode of Psych. After Shawn and Gus get a lead on Lassiter's stolen car, Lassiter calls for action. Shawn and Gus teasingly remind him he has no car at the moment. Lassiter laughs along with them, then says "Oh wait. I just got a new car. (flashes badge) Yours!"
The Judoon Captain tries this on an Earth police car in The Sarah Jane Adventures. He gets away with it, not because the police recognise his authority, but because he's a seven-foot rhino-person with a ray gun. He fails to realise this, and thanks them for their co-operation as they run.
NCIS. In "Reveille" Ari pulls up alongside Kate on the street, knowing she'll commandeer the first car she sees to chase him. Unfortunately it's full of Ari's mooks.
Done in the MacGyver episode "The Prodigal".
On an episode of Flashpoint a rogue cop steals a random woman's car and uses it to transport his prisoner to try and negotiate for his daughter's release. He fails, and the SWAT team rescues her anyway.
In one episode of The Bill, criminals who are holding one of the police officers as a hostage get her to do this for them. Which was dumb, because the car's owner immediately contacts Sun Hill to find out what's going on.
Rebecca does this in the Season 1 finale of Alcatraz.
Kung Fu: The Legend Continues: Peter uses his badge to take a mother's baby carriage in order to use it as part of an improvised disguise.
Played with in one episode of Time Trax where two baddies steal Darien's wallet (with his badge inside), then steal a car by pretending to be cops and flashing the badge.
In White Collar one episode ends with an FBI agent commandeering a horse. As part of either the NYPD (or Parks Enforcement Patrol) the officer currently on the horse has no objections. Also unique is that while badge flasher is indeed an FBI agent in good standing, the horse is actually used by the currently suspended officer accompanying her (as the episode earlier established his history with equestrian).

Video Games

As the cops in the video games True Crime The Streets of L.A. and True Crime New York City you do this constantly with witty comments.

Nick Kang: My name is Nick Kang, and I'll be your carjacker today! The city of Los Angeles appreciates your cooperation.
Marcus Reed: I'm sorry. (drives away) NO I'M NOT!

The Space Marine Grey Knights in Dawn of War: Dark Crusade acknowledge an order to board a transport with "In the name of the Inquisition, we commandeer this vehicle!".
Grand Theft Auto IV features this as well. If you disable a cop's car, the driver and his partner will gladly grab the nearest vehicle available. Somewhat amusing being chased by two cops in a minivan.
- Or on a Faggio.
- The GTA cops aren't completely with it; sometimes they fight over the vehicle.
- In Vice City, the military bizarrely allows the local sheriffs (or at least you in a stolen uniform) to drive away with their stuff.
L.A. Noire, the player character does this to commandeer occupied cars. Unoccupied cars he will just steal without flashing his badge. Hilariously, this works even when you play as Jack Kelso, who is an insurance investigator... and you can do this to cops in a squad car!
APB: All Points Bulletin and Reloaded have this as a staple method of acquiring a vehicle for Enforcers. The civilians offer little resistance beyond sarcastic and snide comments, probably due to the fact that your character is likely packing enough heat to fight a small gang war, and likely on his or her way to do just that.
Your superhuman cop in Crackdown commandeers cars by tossing the original driver onto the street then driving off. One of the bug reports asked why he throws the occupant when he has a legal right to commandeer the car, the response was, "he's not that kind of cop."

Western Animation

Happens all the time in Fillmore! with bikes, scooters and, in one case, a floor buffer.
In one episode of American Dad, Stan proclaims "Official CIA business" to do this to a woman and her sports car. He grabs her and tosses her out of the car, then drives off. A moment later he returns and throws her wheelchair out next to her before driving off again.

Real Life

Truth in Television: Most states have laws which allow law enforcement officials to commandeer civilian vehicles, though the owners can refuse with minimal consequences; in addition, owners have the right to be compensated for the use of their vehicles, up to and including any gas used and damage sustained.
This trope also works as a very devious scam. Scammers have been known to run up to bemused people who are next to their cars, flash a fake police ID at them and ask (very forcefully) if they could use the car, giving the owners a phone-number to ring when they want the car back. It's only when the car owners ring the number that they find it's a fake, they've let someone steal their car, and there's nothing they can do about it.