Sluggy Freelance has exaggerated this, with characters thinking and arguing as if highly unrealistic conventions of various genres should apply to their situation:
In "The Sci-Fi Adventure", the otherwise-nameless Captain of a starship believes he'll be the sole survivor of an alien rampage because he's the "handsome masculine lead", but Torg questions the logic he used to reach that conclusion, calling him a "shallow, one-dimensional stereotype" and suggesting that Riff and Torg will be the sole survivors instead because they have the more interesting backstory. The captain shouts "What is this? A sci-fi thriller or a goofy buddy movie?" The alien promptly answers his question.
Zoe: I can't believe you hired scientists to raise the dead to be soldiers! I thought the military was made up of brave people. Where is your honor?
General Mayhem: Sorry, miss. You have to understand, there are basically two divisions in the collective we call "the military." There is the heroic military, as represented in most of your early war movies, and the conspiratorial military (filled with subterfuge and deception) as represented in bad sci-fi films and The X-Files.
Poor Piro from MegaTokyo thinks romance works like either a Japanese Dating Sim or a shoujo manga, and constantly beats himself up for not being able to live up to the kind of situations he figures romance should entail. It's hard not to laugh when he whines about how he should be an "expert" at the subject considering all the games and mangas he's played and read, totally without irony.
Largo on the other hand defines himself by Action Adventure Tropes, playing the hotblooded action hero in totally inappropriate situations. Ironically, his girlfriend actually finds herself oddly attracted to this, despite or possibly due to her own deep-seated cynicism.
When Yuki is awakened as a Magical Girl, she instinctively reacts by seeking out cute, impractical uniforms and acting as if she were the main character in a series of that genre. She gets this drummed out of her when the "impractical" part makes itself apparent.
Thankfully, the second thing she does is meet Largo, who immediately dresses her in something resembling tactical gear. Also a wonderful example of how Largo is both Genre Savvy and Wrong Genre Savvy at the same time.
The setting in MegaTokyo runs in multiple, overlapping genres at a time, and most characters have a Weirdness Censor for genres that don't overlap with their own. (Piro/Largo is only the most flagrant divide.) Most moments of Wrong Genre Savvy happen when a character wanders into an element of someone else's story or when the fantastic fails and Reality Ensues.
Othar Tryggvassen, Gentleman Adventurer! from Girl Genius. He's convinced that he's the leading man, Baron Wulfenbach and Gil Wulfenbach are the diabolical mastermind and the mastermind's fiendish right hand man respectively, and Agatha Clay is the leading man's beautiful young sidekick (even if she's not the Mad Scientist's Beautiful Daughter like he originally thought). Unfortunately he's completely insane and doesn't realise that he's wrong on all counts, so his genre-savvy plans are almost always inappropriate.
Once he realizes that Agatha is a Heterodyne, he changes on the last part and treats her as the Hero of Another Story (possibly with himself as some manner of Mentor Archetype) — which doesn't solve his problem, since he's still completely insane, and Agatha knows it and wants nothing to do with him. Word of God is that he's re-cast his delusion slightly, Agatha is now the tragic love interest (he's going to kill her last, in some sort of love-suicide pact).
One of the radio plays questioned whether Othar really is delusional — after all, having Sparks in charge has been almost always catastrophic for common Europeans, and it's not at all clear that the heroes will be able to break that cycle.
An odd example that may be both a subversion and a straight example occurs here. Lucy believes that she and the rest of the group are in a horror movie plot, which the current arc certainly resembles. This worries her because, due to the tropes associated with horror movies, none of them will survive. However, she isn't in a horror movie; she's in a webcomic. Given that the webcomic is Something Positive, her chances of survival might be even worse.
Shortly afterward Wil Wheaton gets his arm cut off because one of the survivors is acting like it's a zombie movie, and thinks a bite means infection... the catgirls don't work like that.
In Chainmail Bikini, a D&D webcomic, the players see the new players' character fighting undead. They stand around and watch, thinking it's the scene where she impresses them with her power and they ask her to join their team. When she turns out to be losing the fight, they figure out that they've "picked the wrong cliched introduction" and that this is actually the one where they save her life and ask her to join their team.
Ramgar: Hold up. I think this is the cliche introduction where we see the new character kick so much butt we ask them to come with us. It's a classic of the medium. Let her have her moment of glory.
Lucretia: Will you imbeciles get over here and help? I'm inundated with undead!
Sapphire: Looks like this is the classic "we rescue someone and THEY ask to join US" intro.
Ramgar: Sorry, I wasn't sure which cliche we are supposed to be doing!
Tarquin appears to have cast himself as the Big Bad and Elan as The Hero, unaware that it's Xykon and Roy respectively. Eventually Elan crushingly tells him that he's "not the real villain", and lets him drop off an airship, refusing to confront him in the epic showdown Tarquin wants. It is implied that Tarquin would be quite content being killed by Elan in a battle (the hero always defeats the villain, after all) but the anticlimax of being left in the desert causes him to lose both the plot and his cool, and he's left shouting "This is a terrible ending!" at his retreating son.
What makes him even more Wrong Genre Savvy is that he thinks that everyone around him are just characters in a story (which is true) and no one's motivations or feelings beyond what plot demands matter at all.
The rather odd Heroic Fantasy-High School RPG Class Of Heroes has as part of its official website a brief webcomic about a rather unobservant teenaged boy who plays the game thinking it's a Dating Sim.
In Platinum Grit, Jack Leaderboard was a private eye who thought and acted like the protagonist in a hardboiled detective story, going undercover as a removalist to crack a case. He thought he was uncovering a sordid tale of black magic and human sacrifice featuring Nils as seductive Femme Fatale and Jeremy as a cold-blooded murder with a perfect poker face. Nobody else even noticed his existence.
In this Dinosaur Comicsstrip, T-Rex attempted to re-create a scenario that always happened in cartoons, too bad he is actually in a webcomic that likes to play with tropes. It was even lampshaded in the end.
The unfortunate torturee in thisExterminatus Now strip gets it half right. He's spot-on regarding the comic's goofy sense of humor, but makes the mistake of assuming that that implies an aversion to violence.
In the fourth arc, a new player named Corey was introduced in the role of Luke. He keeps treating the game as if it was a video game rather than a tabletop game. For example, when treated with exposition about the plotline thus far, he responds, "Can I replay this cutscene later?" He soon grew out of this.
Corey falls for form of it when he reaches Dagobah in the The Empire Strikes Back arc. He goes in with no active sensors to avoid detection by the native population (for security reasons, assuming they're all Imperials). This leads to him faceplanting in a swamp because he couldn't tell what kind of planet he was actually landing on (he thought the fog was smog).
Tucker of Girls with Slingshots learned from romance comedies that stalking and persistence were the best ways to get girls. Clarice tried to set him straight by assigning him stories with more stable romances, but couldn't think of any.
The webcomic Sire has a force of fate known as The Binding which forces characters to stick to the narratives and morals of their Sire/Dam's story. The only way to survive is to learn lessons and not get caught in the same traps of their forbears. However, those who learn the wrong lessons or ignore them completely? They receive a tragic ending.
In Storm, Arche interprets the world in terms of the romantic adventures she's read. She thinks Eolill is a Knight in Shining Armor and wants to go on quests. Unfortunately, it's not that kind of world.