The West Wing: Summed up best by Lord John Marbury walking up to the First Lady while exclaiming "Abigail! May I grasp your breasts?" while she's standing next to the President.
Josh's Sassy Secretary Donna got her job by walking into the Bartlet for America campaign office and answering Josh's phone, claiming to be his assistant.
Donna: I'm your new assistant.
Josh: Did I have an old assistant?
Donna: Maybe not.
The X-Files episode "Jose Chung's From Outer Space" used this in the following way. So, you've seen a UFO, and that's semi-believable znd then The Men in Black showed up and tried to warn you from telling anyone, and that's stretching believability. Now, the Men In Black knock this over the believability threshold into the area where nobody will believe this by... looking exactly like Jesse Ventura and Alex Trebek.
Hilarious in Hindsight: Jesse later had his own show, Conspiracy Theory, with Jesse Ventura, which had him trying to find the truth behind conspiracy theories.
The parody book The Extra-Terrestrial's Guide to the X-Files, written as an instructional manual for aliens newly arrived on Earth, suggested this as a convenient way to discredit witnesses. "No really, after they abducted me and did their tests, the aliens stood together, sang some Broadway showtunes, forced me to drink a bottle of bourbon, and then dumped me on the side of the road beside a strip club!"
Downplayed in Seinfeld where Jerry, George and Elaine are waiting for a table in a Chinese restaurant. Jerry dares Elaine to go to one of the tables and snatch somebody's eggroll with no explanation. She goes, but chickens out, maintaining a ventriloquist's grin for Jerry's benefit while trying to talk the diner into selling her the eggroll.
Zig-zagged in another episode. George hits a pothole in Jerry's car, which starts making a clanking noise. Elaine makes up an elaborate story about how she and George narrowly missed an attack by thrill-seeking teenagers, and then mentions the pothole as an afterthought. At first, Jerry acts like he believes the story, but he scares a confession out of George later.
Psych: Shawn Spencer does this often. From naming his "psychic" detective agency Psych and defrauding the police department, to haunting Gus's boss's house to keep the team together, to arming a bomb, in the middle of a police cordon, to find out who designed it.
An episode of The Drew Carey Show has Mimi making Drew late for work by getting a cowboy to tie him up. Just as planned, Drew's boss doesn't belief his excuse. It's only when Mimi imitates the cowboy's "Ma'am" that he finds the real truth.
Doctor Who: The premise of the TARDIS cloaking system works on the fact that most people, when presented with a large blue police box incongruously parked in the middle of a major tourist attraction or thoroughfare, will simply ignore it. When you land said blue box in the middle of the Oval Office, and then while having a small army of Secret Service agents train their guns on you, what do you do? You sit in the President's chair and start barking orders like you own the place. And demand a Fez.
"Let's Kill Hitler", River Song's immortal line in Nazi Germany, right outside the headquarters of the Third Reich and surrounded by some Nazis:
Well, I was on my way to this gay gypsy Bar-Mitzvah for the disabled when I suddenly thought, "Gosh! The Third Reich's a bit rubbish. I think I'll kill the Führer." Who's with me?
In the Seventh Doctor serial, "The Curse of Fenric", the Doctor pulls a Bavarian Fire Drill to gain access to a naval base. While speaking with a scientist on the base, he borrows some pen and paper and begins writing. When some soldiers realize what the Doctor pulled and confront him he uses that very paper he wrote out in front of the scientist and presents it as proof of his right to be there.
In "Victory of the Daleks," the Eleventh Doctor successfully holds a roomful of Daleks hostage armed with nothing but a cookie, which he claims is the trigger for the TARDIS's Self-Destruct Mechanism.
In Legend of the Seeker, Cara is forced to impersonate a princess in the episode "Princess." The court she's visiting has a strict rule that any woman addressing the Margrave speak in rhyming couplets. Further, she's in a competition with another woman to win the Margrave's charms. About half way through she stops trying to win on the Margrave's terms, and plays by her own, starting by composing a poem about torturing a slave to death, then following up by shooting a man-eating beast in the face and eating its raw liver while wearing a pink, frilly dress. Naturally, it works.
In Burn Notice Michael, Sam, and Fiona get what they want through the audacity of Plan B, as Plan A never pans out.
Glee: Sue Sylvester' and her "Sue's Corner" news segments, where she advocates positions such as supporting littering and wanting to re-legalize caning. The fact that Strawman Has a Point is in full effect makes for some of the most surreal dialog ever to grace Public Television. Case in point:
"You know, there's a question I get asked a lot. Whether I'm accepting an honorary doctorate or performing a citizen's arrest, people ask me, 'Sue, what's your secret?' Well, I'll tell you my secret, western Ohio. Sue Sylvester's not afraid to shake things up. You know, I'm tired of hearing people complain, 'I'm riddled with this disease!' or 'I was in that tsunami!' To them, I say 'Shake it up a bit! Get out of your box! Even if that box happens to be where you're living.' I'll often yell at homeless people. 'Hey, how's that homelessness working out for ya? Give not being homeless a try, huh?' You know something, Ohio? It's not easy breaking out of your comfort zone. People will tear you down, tell you you shouldn't have bothered in the first place, but let me tell you something. There's not much of a difference between a stadium full of cheering fans and an angry crowd screaming abuse at you. They're both just making a lot of noise. How you take it is up to you. Convince yourself they're cheering for you. You do that, and someday, they will!"
A lot of auditioners for Britain's Got Talent, America's Got Talent, and so on try for this... some succeed. Memorably:
Fawlty Towers is often like this — Basil Fawlty, a hotel owner, gets away with a lot of what he says/does to his guests because he is so offensive that he either a) cows people into not complaining or b) they don't quite believe what they just heard
Major: No, niggers are the West Indians. These people are the WOGS!
The episode "Basil the Rat" uses this trope in the literal sense. The rat they've been trying to hide from the health inspector all episode long gets into a box of biscuits and is offered to the inspector as an after-meal snack. Basil very calmly asks the inspector "would you care for rat?" This seems to work, as the inspector doesn't respond, and Basil acts as though he'd simply declined a biscuit, and the inspector goes into a Deer in the Headlights BSOD. We don't quite know if it worked, because the series ended.
Alec Hardison on Leverage any time he has to improvise in character - throwing himself a birthday party to distract everyone in the office building in "The Mile High Job" and convincing the police that bank robbers want 25 large pizzas and the equipment to hold a tail-gate party in "The Bank Shot Job", to name but a few examples.
"Hello, sick people and their loved ones! In the interest of saving time and avoiding a lot of boring chitchat later, I'm Doctor Gregory House; you can call me "Greg." I'm one of three doctors staffing this clinic this morning. This ray of sunshine is Doctor Lisa Cuddy. Doctor Cuddy runs this whole hospital, so unfortunately she's much too busy to deal with you. I am a board ...certified diagnostician with a double specialty in infectious disease and nephrology. I am also the only doctor currently employed at this clinic who is forced to be here against his will. But not to worry, because for most of you, this job could be done by a monkey with a bottle of Motrin. Speaking of which, if you're particularly annoying, you may see me reach for this: this is Vicodin. It's mine. You can't have any. No, I do not have a pain management problem, I have a pain problem. But who knows? Maybe I'm wrong. Maybe I'm too stoned to tell. So, who wants me? And who would rather wait for one of the other two guys?"
Then there was the time he shot a corpse.
House: I shot him! He's dead!
Early on in the series House wants to continue a diagnosis that everybody else ruled out. He was on the bad side of every main character at the time (more so than usual), and each and every one of them violently objected to continuing the diagnosis testing. After Cuddy makes it violently clear to the entire staff to not let House perform tests on the patient, he takes a unauthorized sample anyway and proceeds to walk over and ask a lab staffer to run those exact tests on that same sample. House saying nothing of the sample's origins; the staff member just assumes that the unmarked sample can't possibly be the patient's (it's early in the series), and performs the tests anyway. House later has the sample reports on a clip board, so it's assumed the staff member reported back to him afterwards, and is to this day still oblivious.
How do you stop a surgery that's going to cause irreparable (probably fatal) damage to the patient? Simple. Spit on the surgeon.
Gene asks his DS Ray Carling to arrest the landlord of a bar so they can use the bar for a stakeout, telling Ray to 'make something up'.
Gene: In a bizarre twist of fate the landlord was arrested this afternoon... on suspicion of cattle rustling.
Ray gets a round of applause from the whole of CID.
Top Gear The guys engage in audacious cheating, including in that contest, passing The Stig off as James. It worked because they were losing, so no one really cared. (strictly speaking The Stig is credited as a Presenter of the show)
Father Ted has the episode "Kicking Bishop Brennan up the Arse". Due to a bet Father Ted has to do exactly that, and eventually Dougal suggests this plan: Kick him, then pretend nothing happened, because the bishop would never believe he would dare do it. The bishop spends the next several hours in a state of near catatonic shock before realizing what happened and storming out of the Vatican and back to Craggy Island, at which point Ted still manages to convince him that he must have imagined it until he sees the giant photograph of Ted doing it that he had drunkenly commissioned.
"PK Tech Girl" D'Argo is able to bluff some hostile aliens into backing off long enough to get a forcefield up and running, simply because the aliens refuse to believe a Luxan warrior isn't armed to the teeth. At the end the alien captain salutes his efforts. "You had nothing, but you used it well."
Another example is when Crichton is being abducted at gunpoint by Scorpius' right hand Lt. Braca. After listening to Scorpius wax poetic by radio about how "unique" Crichton's knowledge is, Crichton proceeds to escape by daring Braca to hurt him: "I don't think so, you know? I don't think Scorpy's gonna give you your badge of commendation if you shoot 'unique.'" Crichton proceeds to grab Braca's gun hand, hold it to his own head, and shout at Braca to pull the trigger. He generally acts like a madman until Braca drops his guard and Crichton clobbers him.
As D'Argo himself once put it to a flabbergasted - and deeply suspicious - guest alien of the week: "This plan is so bad, it has to be ours!"
Taken to its logical end in the three-part series finale, when Crichton and company gate-crash the peace summit of two alien empires—both of whom have previously mind-raped him and would like to try again—offering to sell his wormhole knowledge to create a galaxy-dominating superweapon. His insurance? A homemade nuclear bomb strapped to his hip on a couple dozen deadman switches. Even the Scarran emperor is kind of impressed.
It's actually even more audacious than that. See, that whole thing about auctioning off wormhole tech with a nuclear bomb as their insurance? That was all a bluff. The REAL plan was to break Scorpius out of the base so his knowledge wouldn't fall into Scarran hands (they didn't know what, or how much Scorpius knew about wormholes but they couldn't take chances). The entire plan, from start to finish, was a massive fakeout. Except the bomb strapped to Crichton's hip. That was actually real.
In Scrubs, The Janitor loses his job. He then appears working again, having dressed up as a doctor and told the replacement janitor that he was fired. He then continues working in the hospital, despite not being employed, under the philosophy of "everything will work out for me", and when the paychecks are handed out, he asks where his paycheck is, and the woman apologizes to him and goes off to get him one. When he does get it, he says that he was normally paid twice that amount, which evokes another apology.
The first episode, in which Gibbs steals Air Force One, and then later steals evidence (including the body of the victim!) in order to have his department head the investigation. They didn't think to inspect the body when Gibbs handed it over, because no one expected him to lie about who he was handing over.
In the season three episode "Jeopardy" The Team must rescue Director Shepard who has been kidnapped by a drug dealer demanding the return of his brother, who NCIS is supposed to have in custody. Unfortunately, the brother was inadvertently killed by Ziva earlier on. Their solution? Dress the corpse, slap a pair of sunglasses on him, and tape his hands so he appears to be driving while Tony hides and drives with his hands.
The Titus episode "Deprogramming Erin,". Titus tries to get Erin to love him again despite that his hot rod shop closed down, and comes up with a plot that involves kidnapping. He sends Dave over to distract her. When Erin asks what he wants, Dave deadpans "I'm here to distract you while Titus sneaks up behind you." Erin starts to laugh, until she notices he's not laughing with her. She turns around just in time to see Titus throw a burlap sack over her head.
The "Corbomite Maneuver"—getting an enemy to stand down by claiming that Enterprise is carrying a substance that would reflect any attack on the ship back at the attacker—from the eponymous episode was so effective that he even used it again in The Deadly Years.
In The Enterprise Incident, Kirk is assigned to recover a Romulan cloaking device so that Starfleet can study it. How does Kirk go about it? By convincing everyone that he's lost his mind, taking the Enterprise into the Neutral Zone so that he can get captured by a Romulan ship, steal theirs, and get it and himself back onboard Enterprise.
In Star Trek: The Next Generation: There is an upcoming social with a boring senior officer who is infamous for his small talk, but everyone in the senior Bridge crew feel obliged to bite their tongue and prepare to endure him. Suddenly, Lt. Worf suddenly outright asks to be excused and Capt. Picard gives him permission. Lt. LaForge, seeing that The Captain apparently doesn't mind people asking, immediately requests permission himself, but Picard cuts him off saying that he cannot excuse his entire staff and Worf beat him to it. At that, Worf beams with a smug "You snooze, you lose!" look.
Star Trek: Deep Space Nine has several of these. The straightest example would be the genetically enhanced "Jack Pack" escaping from their space age looney bin and traveling halfway across the galaxy to one of the most secure outposts in the quadrant in the middle of a war, simply by donning Star Fleet uniforms, making one of their own an Admiral and having him answer any and all questions with "That's a stupid question".
Played straight in "Emissary" when Kira claimed the station was heavily armed to scare away a Cardassian attack force. It worked, and the station turned out to be armed with sensor-deceiving illusions. Later inverted in "The Way of the Warrior" when a Klingon attack force is given the exact same warning, and the commanders assume that it's an attempt to intimidate them into leaving backed by more illusions. Unfortunately, they forgot that Sisko knows enough about Klingons to know you can't bluff one with a mere threat of violence. He's not bluffing. It goes POORLY for the Klingons.
Ariel. Simon is, at the time, a wanted fugitive engaged in the act of massively robbing the hospital he's walking through, but stops long enough to save a dying patient, then chew out the incompetent doctor to the point that he's begging Simon not file a report.
River in "Objects In Space". So, you've got a Bounty Hunter sneaking onto the ship and threatening your crew. You do the last thing anyone expects: you use your Psychic Powers to merge with the ship, read the bounty hunter's mind and screw with his head and flip over everyone's perceptions regarding reality. Then, just when he starts to realize that maybe you're feeding him a line of bullshit , you let slip a single word that makes him realize that you hijacked his ship right out from under him. The sheer audacity of the repeated mindscrews and flipping the tables on the hijacker is enough to turn him from a confident predator to a nervous wreck, but the real kicker comes afterward, when, despite being in total control, River surrenders, and the desperate bounty hunter is so off-guard that he takes this sudden swerve by the crazy psychic ninja-girl at face value, which leads him right into an ambush.
Season 4 episode "Monster Movie," which is an Affectionate Parody of old monster movies, the Shape Shifter does this by turning into various old B-Movie monsters, such as Dracula, The Wolf Man (1941), and a cheesy mummy. The murders are such a Cliché Storm that no one, not even Sam and Dean, can believe that they happened. Going even further, the shapeshifter wants to take on Dracula's identity by picking out a pretty blonde to be his Mina Murray (and calls her that); when Dean comes to the girl's aid, the shapeshifter dubs him "Harker" (Jonathan Harker, Mina's fiance); he calls Sam "Van Helsing" (like the Professor, not the Hugh Jackman character). He also built a giant dungeon out of wood and cardboard in his basement.
In another episode, the boys are in a mental hospital and break into the morgue. When they're caught, Dean drops his pants, throws his hands into the air and jubilantly yells "Pudding!"
On the sixth-season finale of Survivor, Jeff took the votes for the winner, went down to the shore and got on a jet ski. Then he's seen riding the jet ski past a freighter on the open ocean, then riding it up to Manhattan, where the reunion was about to be held. There's no WAY anyone believed he crossed the ocean on a jet ski, but that was the whole point. It was so audacious the audience couldn't help but love it.
The A-Team From driving a garbage truck through the wall of a Mob-boss' club (and dumping the contents on the floor), to turning a forklift into a tank that shoots lumber, to fashioning a hot-air balloon out of a vacuum-cleaner and trash-bags to break out of prison, all of the A-Team's plans go like this. As explained in-universe "Hannibal's plans never work like they're supposed to. They just work."
Boston Legal Most episode features the audacious antics of Alan Shore and Denny Crane. The latter of the two has come very close to having his name taken off the door because of his hi-jinx, despite being a founding partner, while the former wins most of his (usually unconventional) cases by "pulling a rabbit out of a hat" (Denny's "life advice"). As explained in-universe by Mr. Shore, "the conventional ones won't have me".
The crew of the Liberator in Blake's 7 repeatedly escaped sticky situations in space by flying straight though them. (Examples include pursuit ships, a gravitational vortex and a black hole.)
Community: Invoked by Vice Dean Laybourne when he kidnaps Troy to convince him to become an air conditioning repairman - he has an astronaut making paninis and a black Hitler in the room so that nobody will believe the kidnapped students if they try to tell anyone what happened.
In The bottle episode, the study group decide that Annie's pen was stolen by a ghost, since the alternative is believing that one of them is untrustworthy, which they conclude is less likely.
Law & Order. A mother confessed to murdering her infant daughter. The legal aid attorney assigned to her, his first murder case, starts pulling the most audacious stunts ever pulled by someone who isn't Jack. His opening statement: "My client didn't do it, it was God." In chambers, he then changes the plea to not guilty by reason of mental defect, then protests his own ignorance when told that such a plea requires 60 days notice. Then he tells the judge that, if this change isn't allowed, that his client will have grounds to appeal based on incompetent council, saying he'll write up an affidavit enumerating the 12 grievous errors he's already committed.
Jack: Legal incompetence as a defense at trial. You're kidding.
Judge Stein: Either you are a brilliant strategist, Mr. Feinman, or you are the biggest jackass ever to set foot in my courtroom.
Executive Assistant District Attorney Micheal Cutter forces the Governor of the State of New York to resign by threatening him with a blank sheet of paper.
Over on Law & Order: Special Victims Unit, the three ADAs who have been well received by fans are the ones who did this at some point. Alex Cabot acknowledged violating someone's constitutional rights with an illegal search and seizure, but still got the evidence admitted because she didn't violate the defendant's rights, though she did get a thirty day suspension. Casey Novak went on a crusade that culminated in her sending a subpoena to the United States Secretary of Defense, which horrified Arthur Branch. Rafael Barba got a defendant to throttle him from the witness stand.
The Haven 1st Season episode "The Trial of Audrey Parker", in which Audrey and Duke, unarmed, defeat two armed men, one of whom could read minds, by having Duke do outrageous things - such as stripping to his underwear and lamenting that he'd never done the Electric Boogaloo - all directed behind the scenes by Audrey. The poor psychic finally went crazy trying to predict what Duke was going to do next, and Duke and Audrey defeated them easily.
The Mentalist - Patrick Jane's twisted methods include interrupting a funeral to check a casket for a 'second' dead body; convincing about two hundred people, including Lisbon, that they are all going to die in a few hours, and to say their goodbyes and their prayers; getting a suspect thrown in jail by inciting him over the phone to bash up a police officer, so that he can question him because Jane himself is also in jail for illegal eavesdropping; and then breaking out of said jail using only a mouse, a pen, a Bible and a cranberry muffin.
Merlin gets away with the majority of his hijinks because of this. For example:
(Merlin is very obviously searching through all the keys to the castle right next to Arthur's bed. Arthur wakes up and stares straight at him).
Arthur: What on earth are you doing?
Melin: (beat) Looking for woodworm?
In The Crystal Cave, Arthur has just woken up and they're about to head out.
Merlin: Let's go.
Arthur: Don't you remember? I give the orders.
Merlin: *nods* Yeah. You ready? Let's go. *walks off and Arthur follows*
The guys of Impractical Jokers get away with most of their antics in this way. One such example is when the guys are challenged to cut the Broadway ticket line, attempts being made with pretending to know someone up front doesn't work, trying to insinuate into a group doesn't work, but walking past and saying "I don't do lines" miraculously does.
The Greatest American HeroEvery Man Ralph Hinkley has a bright, garish super suit that he doesn't know how to operate, so when he tries to fly he often smashes through windows or walls and ends up in rooms full of surprised people. To prevent this from looking strange he acts over-the-top; spinning and flourishing his cape in front of a crowd and shouts "Ta-Da!" and they all applaud. Another time he crashes into a hotel lobby and stands up and starts shouting "Call for Mr.Henderson, paging Mr.Henderson!" as he walks through the crowded lobby and out the front door.
In Sons Of Anarchy, when one of the Sons is accused of stealing a brick of cocaine, he sarcastically confesses: "Yeah, I walked in here, shoved a brick of coke in my pants and walked out. Douchebag". He did exactly that.
Jax responds to a character's threat to tell the authorities about the events of the second half of season 3 in Ireland by (among other things) telling them they'd sound crazy if they claimed any of it was true. Given the Sons' history, particularly that of Chibs and Clay, it actually isn't all that far fetched. Maybe not provable, but hardly a paranoid delusion.
The How I Met Your Mother episode 'Matchmaker' features Barney attempting to get Ted to join a Relationship Matchmaking agency to hook up with desperate women. Ted objects to the plan. But the next day, whilst Ted is relaxing in his apartment, Barney storms in:
Barney: Ted! Hurry you've gotta help me my boat is sinking!
Barney: My boat is sinking!
Ted: You have a boat?!
Barney: Yes i bought a boat last year at the police auction. I just got a call from a guy down at the marina and its leaning on a starboard at a 45 degree angle and if I don't get there right now its gonna capsize NOW C'MON!!! [both exit]