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Comics are the easiest medium to accomplish this in, since you can have the narration saying one thing above the panel and the panel show what's really happening, whereas in Film, Western Animation, and Live TV you might have the narrator's speech conflict with the scene, necessitating a more "flashback" style to show this. It is very common to have a narrator say one thing and the below panel completely contradict it.
Rorschach in Watchmen is a good example of this, especially when he talks about himself. The artwork actually uses an unreliable framing device (one of many the work contains) to show "Rorschach" in the first person and Walter Kovacs in the 3rd person (walking around in the background of the same chapter), leading to The Reveal. This both misdirects the audience as to who Rorschach is behind the mask, and contributes to the sense of Rorschach's disconnection from "the man in the mirror", so to speak.
Ed Brubaker's Books of Doom miniseries tells the origin story of classic Marvel Comics supervillain Doctor Doom, seemingly narrated by Doom himself. However, at the story's end, it is revealed that the narrator is actually one of the Doom's Doombots, telling the story that Doom has programmed into it, leaving to question how much of it was true.
Dreadwing, the main antagonist of Gold Digger has a mymior, a magical journal of sorts for dragons. He lost his original one, but he was able to create a "new and improved" mymior for himself and it's clear that Dreadwing's jaded and evil mindset has heavy influence over his writing, such as putting everyone except him in a negative light, trying to justify his many crimes and giving questionable overviews of his relationships with other characters.
Word of God states that Delios of 300 is an unreliable narrator; all of the supposed inconsistencies with actual history are actually bare-faced lies, with Delios stretching the truth about who did what and how many there were. This naturally justifies the comic's explicit use of Rule of Cool and Refuge in Audacity.
Recent issues of The Boys have been about the backgrounds of other members of the eponymous group beyond Wee Hughie. Mother's Milk was relatively straight forward. Frenchie's was... not. This is partially justified by Frenchie being craaaaaaaazy.
The Scott Pilgrim series. It's revealed in the final book of the series, Scott Pilgrim's Finest Hour that Scott's memories of his past experiences with his ex-girlfriends were altered by Gideon Graves, meaning some of the events shown in the previous books may/may not be entirely false.
John Constantine from Hellblazer tends to get unreliable, especially if he's depressed or drunk. If there was a scene where he actually didn't see it (but we readers do), he will tend to second guess everything and can only imagine what could have happened. Although not an accurate description, John's gory imagination makes up one hell of a comic panel.
Done in Steelgrip Starkey and the All-Purpose Power Tool via thought balloons and dialog from Flynn "Flyin'" Ryan . Although he's secretly the tool's inventor and the mastermind behind Mr. Pilgrim, his thoughts often read like he's unaware of the big picture. Done particularly egregiously when he and a cohort are making plans, and he still refers to Mr. Pilgrim in the third person.
Vincent Santini, the narrator from Brooklyn Dreams, tells us in the first page he can't remember much from his past, so he'll tell us the best he can. The whole story is him telling us about his life the way he wants to remember it. He even says "I'll weave you some lies about my life, and who knows they might be true."
This is one of the rules governing the stories in Mouse Guard: Legends of the Guard.
June states that the stories can be neither "complete truths", nor "complete falsehoods." Exactly how much of any given story is true or false is left as an exercise to the reader, and they vary from the relatively plausible (a story of brief and unlikely companionship between mouse and bat), to the truly outlandish. (A mouse king who rode into battle upon a weasel, a Guardmouse who saved a town from a flash flood and drought by swallowing the flood waters then spitting them back out to serve as a reservoir.)
Amusingly, one of the most plausible stories — a play on "Androcles and the Lion" in which an African mouse manages to befriend a lion that's impressed with its bravery and resourcefulness (pulling the thorn out of the lion's paw is in there, but is outright established to be a secondary factor at best) — is discarded out of hand because the North American mice of the series have never seen or heard of lions or hyenas before, as well as the fact that it's told by a known lunatic who claims to have heard it from a beetle, which aren't talking animals in Mouse Guard.
An Annual had Iron Man villain The Mandarin telling his life story to a film maker, with the captions showing his version of the events, and the panels showing the complete opposite.
"Banjo Lessons": A man narrates, in increasingly detailed flashbacks, the circumstances that led him to have a psychotic break and murder his friends. He claims it's due to his suppressed rage over an incident where they killed and ate a dog while on their hunting trip, but a court sees through him and realizes the truth - "Banjo" the dog was actually their (black, while the men were white) hunting guide.
"Me An' Ol' Rex": A mentally disabled hick boy is beaten by his abusive father, but finds solace in "Rex", his dinosaur friend. Rex eventually grows bigger and begins eating people who the boy feeds to him. The boy eventually commits suicide because he knows he'll be blamed for the people's disappearance. We then discover that "Rex" is not a dinosaur, but his father, who was driven to cannibalism when locked in the shed for the boy's own protection. The dinosaur story was his delusion or lie.
In The Mighty Thor #356, Hercules and Jarvis are taking a stroll in the park, and a group of guys ask him if he's stronger than Thor or not. So, Hercules began to narrate their last encounter. Humbled and ashamed by the vast superiority of Hercules over him, Thor asked him for an arm wrestling, to see if he could regain the will to live. Jarvis laughed at the idea of Thor trying to defeat Hercules... but Jarvis, standing right there while Hercules made his narration, pointed that he did not remember any such scene. "Oh, of course, it happened while you were on vacation, dear Jarvis!". So, Thor was defeated in a second, attacked Hercules in his head with his hammer, began to destroy the city on a tantrum... Mr. Hercules, that doesn't make sense, aren't you making it up? Oh, this Jarvis may be a prince among butlets, but as a spectator he leaves much to desire. Where were we? Oh, that the fight got into the Empire State building which was destroyed... but such thing never made it to the newspapers, because the Avengers repaired it immediately! And goes on, on, and on... that is, until he realizes that the guy asking was not his fan but a fan of Thor, who felt sad for his hero. Where were we? Oh, that Thor was about to receive the final blow... and suddenly showed that he was holding his strength, beated the crap out of Hercules, and sent him to another state with a single punch. Yes, it really happened! Would Hercules lie to you?
The Sandman: Invoked with a story that Cluracan tells in a tavern. He tells of when he was sent as an envoy to an impoverished nation, imprisoned, and managed to escape as well as destroy the corrupt ruler. The other patrons call him on this, and he freely admits to adding and removing parts of the story to make it more interesting, though the only thing he admits to fabricating is a sword fight he had with the guards (he added that part to make the story interesting). He states they can choose to believe him or not. How much of it is true is left to the audiences interpretation, though in story Cluracan is still an amoral ditz and a drunk who get's himself in trouble, requires Dream to save him, and dethrones the ruler out of a revenge rather than duty, none of which is out of character.