A Batman comic has Bruce Wayne sequestered to sit on the jury of a man he arrested as Batman trying to kidnap a baby. The prosecuting counsel asks whether there is any reason why he should not sit on this jury. Bruce calmly admits he's prejudiced in the case because he's Batman (hey, he's under oath). After everyone's stopped laughing, the judge tells him to stop screwing around and take things seriously.
During the initial run of Batman, Incorporated, Batman reveals his secret identity on an Internet message board, knowing full well that people will suspect Bruce Wayne of being Batman after he publicly announces his company's support for Batman's efforts. By putting the information on the Internet, he reckons people will dismiss it as just another crazy rumor. As if to prove his point, a troll immediately responds that Wayne is obviously a different person.
Catwoman pulled this off in her very first appearance in The Batman Adventures (1992). While stealing a necklace from a museum, she's caught by a security guard with a gun. Rather than panicking, she simply acts as if he doesn't have a gun, leaving the guard so rattled that he freezes up and is still babbling after Catwoman has escaped.
In Justice League International, Maxwell Lord introduces himself to the League by acting like he's already working for them, i.e. giving Dr. Light a League communicator and turning up at headquarters to introduce Booster Gold as their newest member.
In both the Post-Crisis and New 52 continuities, Superman keeps his civilian identity secret by pretending he doesn't have one. He reasons (correctly) that while a mask lampshades that you're hiding something, people will assume that a demigod who clearly doesn't need money or other material things does not have a day job and would not bother with the trivial nonsense of mortal life.
Note that this actually works. One story has Lex Luthor firing a scientist for daring to suggest Superman has a secret identity at all (though this also says more about Lex's own mindset than anything else).
Deadpoolis this. Like when he made 372,844 pancakes just so he could pull a joke on Domino and teach her a lesson. Or when he kicked Captain America in the balls just so he could save the world instead of Cap. Or how he shrank the Rhino down with Pym Particles and kept him as a pet/key chain. He doesn't hide in audacity—he eats, sleeps, and breathes it.
Exploiting this trope is one way you can get into Doctor Doom's good books. Examples:
Doom once gave Luke Cage a false commission as part of a bigger gambit, then skipped town before Cage got his fee. So Cage convinces the Thing to loan him one of the FF's vehicles, flies to Latveria, teams up with a group of insurgents, storms Castle Doom, beats up a bunch of guards... and politely requests his $200 fee. Doom bursts into laughter, pays, and asks Cage if he'd consider working for him again.
Doom treats villain Arcade like a court jester; he's apparently decided that Arcade is amusing enough not to be punished for addressing him as "Doc" or "Vic".
Loki: Agent of Asgard: In issue 1, surrounded by the Avengers and looking decidedly guilty of something, Loki takes their only remaining option. They tell them the absolute truth as to why they're there, namely that they're working for the All-Mother as part of a secret plan to protect Asgard.
The Punisher MAX villain Barracuda, in his spinoff miniseries, uses this to escape death by volcano. He and his group of mercenaries are working for Luna, a homophobic dictator who falls for Barracuda's Crossdresser second-in-command Fifty. Luna's sudden but inevitable betrayal lands 'Cuda and Fifty in a helicopter over a volcano with Luna about to make them jump in at gunpoint, leading Barracuda to make Fifty buy them some time...
Barracuda: Yo, Fifty! It's time to show this motherfucker your dick!
That time when Daredevil (who has a secret identity) showed up in a Christmas party in his civilian identity, with devil horns and a red sweater which said "I AM NOT DAREDEVIL".
Archie Comics' Sonic the Hedgehog: Prince Elias during the Sonic Universe arc "Secret Freedom" goes by the codename "King" while working with the Secret Freedom Fighters. Geoffrey St. John even lampshades it when he discovers his true identity.
Geoffrey: Agent "King", huh? Going for "so obvious it's overlooked?"
Over the years, Diabolik has pulled out quite the shit. We'll now report something he did early on:
Eva had been arrested, and between the prison being in a swamp with a train as the only way in or out and Ginko's surveillance, he had no idea how to break her out before she was sentenced to death and executed. So, what did he do? First, he kidnapped a top model leaving a wounded witness to make everyone think he had dumped Eva with the goal of getting Ginko to drop the surveillance or, at least, pity judge and jury into giving her a lesser sentence. As Ginko still kept up the surveillance but Eva had been sentenced to thirty years of jail, Diabolik went for his plan B: distract away Ginko while he caused a typhoid fever outbreak in the prison (Eva had recently been inoculated so she was immune) to force the evacuation, knowing that they would put the healthy prisoners in the back and reserved the forward side (that jerked less), and thus Eva would be safe when he derailed the train. That's not the most outrageous thing he did.
Neither Diabolik was the one pulling the most outrageous plan, that was Ginko. In "Mocking Diabolik" Ginko needed to escort ten ancient golden statues to the police station for safekeeping while the museum prepared a Diabolik-proof room to expose them, without Diabolik getting them. And Diabolik was spying on him, and he had no idea where the bug was (and, in another example of this trope, Diabolik had bugged the last round of Ginko's gun) So, what did he do? First, he and his men planted fake hints to indicate a certain mob boss was interested to those statues, then they stole those Diabolik's gadgets that had been confiscated after past heists, and used them to steal the statues. After which Ginko 'discovered' the fake hints and started putting pressure on the mob boss, getting Diabolik to surveil him while the Diabolik-proof room was completed and the statues then revealed. As you can see, the title of that story was quite justified.
A variant of the above is the second story where he faced a villain called theMaster of Disguise. In revenge for being unmasked at the end of the first story, the Master of Disguise captured Paperinik, unmasked him on live television... And then, two other Paperiniks entered the room and took off the masks, revealing themselves as Gladstone and Fethry, as Donald asked them before before being captured. End result: the villain got distracted long enough for Donald to free himself and lead his cousins into delivering a righteous beat-up, and everyone was convinced it was a bait from the actual Paperinik who enjoyed the show on TV from his lair.
Sometimes Donald is caught in possession of Paperinik's gadgets. How does he get away with it? Easy: as early as the fifth story, the entire city knows that Paperinik and Donald are friends (Paperinik declared such publicily, at least in written form), so it's not strange that the superhero forgot something at Donald's house, or the latter borrowed it. Even the cars, that, after all, are practically identical...
Daisy has a superhero alter ego too, Paperinika. How does she justify the fact she's apparently her spokeswoman? Easy: she told everyone they're friends, just like Donald did with Paperinik. Also, she gets away with her disguise (not as minimalistic as Paperinik's, but not really that disguising after all) because in her first story she acted so differently from usual she convinced Donald they merely looked alike, and Donald's poor opinion of the superheroine did the rest.
Why people think the Red Bat (alias Fethry) is competent and Crazy Awesome? Easy: no matter what, he acts as if everything was part of the plan, ever since his first story saw him accidentally foil the Beagle Boys with the help of Donald disguised as a headless gorilla (they were at a masked party as journalists, with Fethry wearing what would become Red Bat's costume and Donald a gorilla costume that was too tall for him), and when the journalists asked him if he had terrified and arrested the criminals alone he just quipped "No, this headless gorilla helped me" and left.
Fables: Prince Charming kills Bluebeard, walks out of the house carrying the body in a carpet—and cheerily admitting as much when people ask what he's got—and calls in the mayor to watch him dispose of the body. He correctly judges that he can get away with this, because a) nobody especially liked Bluebeard and b) all his money will now go to the Fabletown coffers.
In "Axiom of Implausibility", (a story from an issue of the magazine Heavy Metal) a firm is contracted to kill a witness who's holed up in the middle of suburbia. The first 3 attempts on his life fail after the hitmen, attempting to be inconspicuous and avoid witnesses, keep getting their covers blown by observant neighbors. So on the 4th try, they send in a Stripperific, Dual Wielding, bizarre One-Liner-spouting Action Girl to kick down the front door and make a total spectacle. The hit succeeds, and the eyewitness reports are so outlandish that the cops don't believe them.
Tommy Monaghan from Hitman tells his first girl, Wendy, that he kills (bad) people for money. Wendy doesn't believe him until he shows up, shot. Ironically, his next girl doesn't believe Tommy refuses to say 'bitch' because he kills (bad) people.
In The Sandman, Hob Gadling amazes his friends by insisting that mortality is for chumps and he intends to live forever by simply refusing to die. The ballsiness of the Insane Troll Logic amuses Morpheus enough that he convinces his older sister, Death, to make Hob The Ageless, and arranges to meet Hob for drinks once a century.
Scooby-Doo! Team-Up: Daphne starts suspecting the superheroes known as the Impossibles and the singing trio Impossibles are the same people but Fred dismisses her theory because "those would be the worst secret identities ever".
Once in a while Tex and his pards have pulled this. Such as the time they needed to go in a town controlled by a gang of criminals who were preparing an ambush just for them... So they went there with a stagecoach, disguised as a Mexican who didn't understand English (Tex), a preacher (Carson, who does look the part with the right clothes), a businessman (Tiger Jack. A Navajo Indian), and a woman (Kit Willer, Tex's son), and when the criminals stopped the coach the only reason they were discovered was that one of them tried to kiss Kit (the sheer surreality of the situation still left the criminals too stunned to stop them).
Once in a while it's them who fall victim to this. Such as the time Tex' archenemy Mefisto needed help with his overturned coach... And when Tex passed by, he asked him for help (Tex did not expect Mefisto to do such a thing and failed to check his disguise. It helped Mefisto was disguised as a leper, so Tex wasn't all that willing to come too close anyway).
In Wanted, there is a back story in which the supposed first supervillains of the world were a bunch of ass-naked bank thieves who get away with it for the longest time since the cops don't want to get into shoot-outs with a gang of naked men and superheroes don't want to be seen getting into a brawl with a bunch of big, burly men with their peckers hanging out in the open.
In Kyle Bakers You Are Here the main villain manages to serve only a year for murdering his wife due to "A good lawyer, bad evidence, worse cops and prison overpopulation" and then goes on to publish a book called "Yes I Did It and I'll Kill Again." After attending a press junket he says "I plan to kill the bastard who was screwing my wife" on air.