Mikey: "Then you can be my escort tonight before it's too late! You'll do it, right! It's important! I need it! And you love me, so you'll do it! Right!"
Breech: "I never agree to do anything without knowing what it is first. How do I know you're the real Mikey, and not some Dai-Oni possessing his body with the intent of making me promise to do something awful?"
When McGonagall tells Harry what really happened to his parents (Harry had been raised by his aunt and her husband with no explanation), Harry starts asking her which plot hooks might be left dangling, frequently making analogies to The Lord of the Rings.
Hermione does frame events around her as if she were in a story (early on, she wants a romance between her and Harry), but she's more often seen trying to convince Harry that he isn't in a story, and that he should stop trying.
Draco likes to compare his own behaviour to the heroes in the opera/play performances that his father takes him to see.
Daphne Greengrass, like most of the girls, views events like a romance plot, and tries to invoke her own romance with Neville during one of the battles between the first-year armies.
Dumbledore likes to frame himself as the wizard Gandalf from The Lord of the Rings, and conversations between him and students are often framed in "young heroes" and "mysterious old wizard" terms.
Quirrel and Harry often discuss the finer points of how to manipulate others, referencing stories and contrasting them with reality as they do so. "The role people play" is an element of Eliezer's writing that comes out frequently in this character.
Mike: "Ponies don't start randomly thinking about this kind of thing unless it's about to become some important plot point in a corny story they're in!"
Calvin and Hobbes: The Series has the titular duo, though in different ways: Calvin knows a lot about sci-fi movies, while Hobbes knows the outcome of pretty much any adventure Calvin drags him along on.
Calvin: Since that information is keeping us alive, I barely think we should tell you [who we are]!
One of the hallmarks of being a resident of Angel Grove in Of Love and Bunnies is that, living amongst Power Rangers for so long, they're used to the weirdness and can predict when strange things will happen and what effects they will have.
Pinkie Pie displays a brief moment of this in Ace Combat: The Equestrian War, while observing, along other ponies and griffins, the final duel between Rainbow Dash and Gilda. When Twilight asks her why is she excited, this is her response:
Pinkie Pie: Come on, it’s a fight between the aces! Whenever it happens at the end, it’s always awesome!
Jade in Akatsuki Kitten Phoenix Corporation Overhaul actually knows exactly which author she's being written by, and what the author's sense of humor tends to lean on. This leads to instances where she quotes a movie, and reprimands herself for being surprised at the outcome.
Jade: *waves hand* These are not the droids you are looking for.
In Queenof All Oni, Jade, after her Face-Heel Turn, is FAR more Genre Savvy than many (if not all) of the villains from Jackie Chan Adventures canon, partly due to her witnessing and/or exploiting their Genre Blind moments before the re-emergence of her Superpowered Evil Side, and she even exhibits Dangerously Genre Savvy moments. Some of her Genre Savvy moments include: taking Daolon Wong with when she breaks the Enforcers out of prison, remembering what happened when Shendu left loose ends lying around, cleaning out their lair before Section 13 can react on the info Valmont gave them, and one of her best was when she nearly managed to get the masks the heroes had (SOLO), in a Batman Gambit by remembering how the Dark Hand had used Jackie Dark to gain access to the captured talismans, and if it weren't for an OC Section 13 agent with Blackand White Morality (even to the point of FIRING a gun at her!), SHE WOULD HAVE PULLED IT OFF WITHOUT A HITCH!!
In one Code Geass fic, Lelouch, upon learning he's not the only one with Geass quickly realizes that the Emperor must have it as well. Why? That's the worst possible scenario for him.
A Naruto ficlet has Naruto attempt to use magic to turn Kakashi into a chicken. Why? Because Kakashi refuses to teach them anything even after Naruto warns him that he'll continue pranking Kakashi until he does. Sakura insists it's impossible to turn someone into a chicken. Sasuke on the other hand.
Sasuke: "It's insane, would take a miracle to pull off, and I doubt anyone else would even think to try it. (Beat) I'd say he has better than even odds of doing it."
Navarone from Diaries of a Madman is quite genre savvy, and is well aware of the cartoon logic the world sometimes operates on. It particularly applies during the Crystal Empire arc, where he recognises Sombra is carrying the Villain Ball, and takes full advantage of the cliched tactics of cartoon villains.
Harry in The Havoc Side of the Force fully expects people to screw him over the first time he does a job for them. Also, when his cover is blown after anonymously saving over a hundred slaves, he decides to leave immediately. Padme tries to reassure him that everyone present has her complete confidence, but Harry just dismisses that, saying that only meant the Hutts would learn his identity in hours instead of minutes. He's right on both counts: Bibble had the ship Harry was getting in payment stripped of almost all it's weapons, shields, and engines. And Aayla Secura (one of the slaves) sending a transmission to the Jedi Temple led to a ship trying to ambush Harry right where he should have come out of hyperspace (he had Anakin pull them out a little early so they would be ready)
Just before revealing his angelic nature in order to stop a mass relay from hitting them in Alpha and Omega Book 2: The Fallen Shinji remarks to Rei that she's about to learn something about "human ingratitude." Sure enough, immediately after two separate characters nearly kill Shinji before he's locked away to await execution.
"And the connection to that grav anomaly is?" Warragul gives me a funny look and I scoff at him. "Oh, come on, we all know that's where this is headed. Every time we or anyone else hit an unexplained anomaly like this in the past it's made something weird happen."
In Gensokyo 20 XX, the characters display this from time to time. This is mostly the case in in 20XXI and 20XXII, where they are imprisoned, where Suika is one of the first to pick up on the fact that their prison is meant to break them by depriving them of certain comforts, i.e good food, as well as things to tell time. Likewise, when Kaguya and Mokou are also imprisoned, Mokou also picks up on their captors and the warden are none too merciful, referencing the Scarpia Ultimatum, Morton's Fork,and Sadistic Choice tropes and how they applied to their setting. In that vein, Yukari noted she could gap herself out but then she could be found and thrown back in and it was also noted that where they were imprisoned was not a place where one could share suspicions and secrets openly.
In 20XXIII, Ran did note an inner core or refuge wouldn't protect anyone from a nuclear bomb or strike, stating that sort of the thing would likely be crushed or get someone pinned under a roof beam (which does happen), as the blast would be stronger and neither could it fit any supplies or at least a whole family, as well as pointing out that whole entire purpose for When the Wind Blows was to criticize that sort of thinking. Unfortunately, neither Yukari (going insane) or Chen (being a child) listen to her and they build said inner core or refuge right under a roof beam, as she advised against it. In that note, after the nukes were dropped, the characters did note that survival in the aftermath would be difficult and that life would not be as ti was and neither do or would emergency services arrive and neither do the characters, save Sakuya, expect for them to.
In Bond Breaker, the main character Shade is well aware of this sort of thing, frequently averting classic anime tropes like walking into a bathroom in use, and even manages to manipulate some rules of the world he's in at the time to the advantage.
In the Buffy the Vampire Slayer / Power Girl fan fic story Origin Story, Xander Harris was a comic book geek. Alexandra Harris has all of his memories. She is thus often able to predict what the various Marvel Comics heroes will do before they think of doing it. She also knows a lot of secret identities.