The Pokémon Mystery Dungeon series is filled with this. In the Red/Blue versions, Gengar, the main antagonist, is very Genre Savvy. He knows just how to get rid of the villain and his plan works perfectly - almost.
Alakazam and Xatu also appeared to fit this trope, simply because of their ESP powers. Alakazam, however, was Wrong Genre Savvy.
In the second game, Grovyle, and each of the villains was dangerously Genre Savvy.
Misty from Pokémon Gold and Silver would also have a bit of this. It's more so if you enjoyed a curb-stomp battle against her in Pokemon Red Blue And Yellow, which is possible if you had Bulbasaur and Pikachu. In G/S/Crystal, however, Misty knew that you would bring in an Electric Pokemon, and brought out a Quagisire who knows Earthquake. She also knew you would bring in a Grass Pokemon as well, and has taught her Starmie and Lapras Ice-type moves.
Another one: Hope knows that tired old tale of "Revenge is not going to solve anything." He doesn't care.
Princess Waltz is a good H-game not just because of its elements that work, but because it gleefully lampshades its own cliches. It's really hard to hate this game for following the stock conventions of its own genres when they cleverly keep poking fun at them at the same time. In fact, the Big Bad and The Plucky Comic Relief are walking fonts of Genre Savvy hilarity.
Heroes of Might and Magic IV includes a sympathetic undead king who gets his underling to draw up plans for invading a neighbouring kingdom — and them sends the plans to that kingdom, so they can fix the holes in their defenses. He explains that even though invading his neighbour would make him the most powerful ruler in the entire world, that would just mean everyone else would unite their forces to take him down.
He later promotes a zombie to Captain and takes the trouble to learn his name for showing the sense and initiative to find out exactly what an enemy's Artifact of Doom did (saving his life in the process), and figures out that there must be a reason why no one has ever activated each of five MacGuffins. He then takes appropriate precautions.
The protagonist's genre savviness is what jump-starts the plot in the FMV game Brain Dead 13. Teen computer and video game ace Lance Galahad is sent to fix a computer at the home of Mad Scientist and brain-in-a-tank Nero Neurosis, and quickly identifies it as a typical mad scientist's lair. Dr. Neurosis flies into a rage after Lance refers to him as an "average villain", and he sics his homicidal toady Fritz on our hero.
Frankomatic points this out during the final battle between Lance and Fritz. You'd have to be REALLY genre savvy to know that the whole "rug whip" thing would actually work!
Almost all the characters in the Disgaea series, particularly Etna. Mao from the third game is dangerously so, concluding that the quickest method of kicking his dad off the throne and rule with his own iron fist is to actually become the hero of the game.
One example from Disgaea 2 that particularly stands out: Etna figured out that the Overlord Zenon she just defeated was a fake. How? The title of Overlord is transferred by Klingon Promotion, and she points out that her title on her status screen doesn't read "Overlord".
Also from Disgaea 3, after you have defeated Super-Hero Aurum he says "Wait! In these games the final boss always has to take his final form before you can truly defeat him!", to which Mao replies "Ah! Curse you, using that convenient Game Mechanic!"
In the Grand Theft Auto series, a pedestrian having a conversation about a nearby dead body will occasionally mutter "Don't worry, he'll respawn!" or something similar.
Many of the NPCs in the game tend to be genre savvy: civilians will complain about they can't walk down the street without someone trying to snatch their purse, kidnap them, or try to use them in strange rituals. And some of the villains are equally savvy; at least one fragment of dialogue for a low-level gangbanger references the endless-loop purse tug-of-war animation with a "No, really! I actually got the purse!"
In the same vein of the low-level gang member, a cry for help on part of the NPC struggling for her purse shows some degree of Genre Savvy as well, recognizing that since crying out about getting mugged won't summon help quickly enough, she yells that there's a fire instead.
This is advice given to people in the real world too.
Meanwhile, the game itself is very Player Savvy. "OK, so I know now that these apples will fall on me, and that the third one will fall up. Ah, but there's a gaping hole between trees there. I can use it to just jump between the two trees and avoid any apples! Alright here I- A SIDEWAYS APPLE?!". Or how about sequences with one insanely hard bunch of obstacles. Once you finally pass the apples/spikepit/enemies and you think you're home free once you reach the platform on the other side... the ground falls away, or a spike lands on that exact spot that you thought was safe, and you die just so that the game can teach you not to get complacent.
Arthas, aka the Lich King, of World of Warcraft, as of the newest expansion, has displayed some unexpected genre-savviness, going so far in one early encounter as to deliberately murder your character, simply to prove a point about his own power, knowing full well you'll get right back up shortly and keep coming after him anyway. Now that is Dangerously Genre Savvy.
Even more so when you finally do manage to face him; he reveals that he's been letting you kill all his best monsters specifically so that you will 'get stronger' — as in, get their loot — so that you, the player, will be a better, stronger minion when he turns you.
It should also be noted that Sonic himself is also this. With the amount of times he's lampshaded tropes in the games, he fits well. Example being in Sonic Colors he knew right away that the amusement park was just a front for Eggman's evil plot.
A perfect example; "Experience has taught me to investigate anything that glows."
Henry of No More Heroes is made of this trope. He correctly identifies himself as main character Travis' mysterious foil and just goes on from there.
Travis picks up some of it once Desperate Struggle starts, but the king of the trope is the final boss. When Travis can't figure out his motives, the boss snaps, pointing out that You Killed My Father is a staple of every genre known to man — "Shakespeare, for God's sake!"
Guillo of Baten Kaitos Origins displays genre-savviness throughout the game, questioning good guys who turn out to be villains, realizing when something has come "too easily," and knowing to run away before the inevitable "doomed to lose" boss fights.
In Metal Gear Rising: Revengeance, Jetstream Sam decides not to give a monologue unlike other bosses of the series, stating that both him and Raiden have heard enough speeches about ideals at this point.
"I can't get over how fast they all are! It's not even fair, I'm calling zombie bullshit on that, you know? They're not... allowed to be so fast!"
Unfortunately she's also Wrong Genre Savvy in the comic The Sacrifice she finds out that Her father was actually a carrier so when she shot him in a mercy killing after he was bitten, it was a pointless sacrifice
Bill: "You know who's going to survive this? It ain't the fella making jokes."
Nick in Left 4 Dead 2's Dead Center campaign asks the other survivors if they were bitten, knowing that the infection is being spread from zombies biting people.
Monkey Island: Guybrush Threepwood occasionally points out a trope during his adventures and tries to take advantage (generally by refusing to do something stupid).
The title character of Eat Lead: The Return of Matt Hazard is not only savvy about every genre he's ever been in, but he's savvy about every other game genre, too. He also has Medium Awareness, and these are half of what he uses to get through his situation. The other half, of course, is lots of guns.
Apart from the whole "evil unkillable vampires" part and stuff of which she is by necessity very genre savvy, Arcueid of Tsukihime also surprisingly displays some genre savviness in regards to relationships. Arcueid notes that Shiki sure is acting nice to everyone else, he says that he is nice to everyone... except her. You idiot! She's thrilled (but can't quite grasp why), because she recognizes him as being a tsundere — and therefore making her the love interest!
After a certain point, Max seems to have simply descended into being a Fourth Wall Observer. He suggests at one point switching to the Rhythm Game genre to take down the Samulacra, and instantly jumps on the opportunity to do a Fetch Quest later on.
In Neverwinter Nights, besides of making more explicable efforts to stop the plague, the Big Good and his minions set up an academy to train heroes to save the city. Of course, one of them does. However, this goes beyond any reasoning that might actually make sense in the game world, and seems more like a bad excuse to set up the Protagonist Without A Past.
Carth's smelling a rat about the whole mission in the first Knights of the Old Republic game could be interpreted as Genre Savviness, as could a lot of Atton's behavior in the sequel. In-universe, it's mostly explained as both of them being Force sensitive.
In Uncharted: Drake's Fortune, Nathan Drake invariably ends up in gunfights consisting of several waves of goons. Every so often, Drake will ask to himself "Where do these guys keep coming from?".
In the second game, Among Thieves, Drake in one level has to retrieve an ally from a broken elevator. As he does so, Drake tells himself "I swear to God, if there's a zombie around the next corner...". Mutant Spaniards, or "zombies", were a special foe from the first game, in a level where Drake again had to rescue a friend from a small compartment.
The girls in the Touhou games occasionally show that they are very aware of the tropes of Bullet Hell games. Not the least of which is the fact that they explicitly call their attacks Danmaku. One amusing example appears in Perfect Cherry Blossom, whose Stage 4 has an unusually long wait between reaching the boss's area, and the boss showing up. When she gets there, Reimu spends a few moments muttering to herself about what's going on, and when no boss shows up, she demands "Doesn't someone usually pop in with a response right about now?"
In Legacy of Kain: Defiance, Kain shows his level of savvy, likely stemming from several centuries of living, in the Citadel of the Ancients. He encounters a series of very well-proportioned statues with dangerous looking swords, and monologues to himself that there was no way in Hell they wouldn't attack at some point.
Batman: Arkham Asylum, When the player is getting close to completing all of the Riddler's Challenges, the Riddler accuses Batman of cheating, and that he is looking up the hidden locations on the internet.
In Call of Duty: Modern Warfare 2, in the second-to-last-mission, Soap and Price go on an assassination mission. Once the target realizes that Price is coming after him, he orders a full evacuation of his base and tells his men to simply hold off the heroes until he can escape. An entire military base vs. two men, and the guy knows it's futile to actually try to kill them.
In Singularity, Nikolai Demichev is smart enough to keep plans for the Singularity Reactor, and rebuilds it after the heroes blow it up. He also never forgets that time travel is possible. Thus, when confronted with two American Marines in modern-day uniforms even though there hasn't been an American military for about fifty years because the timeline has been altered so the USSR conquered the world in the sixties, he knows exactly what's going on, and doesn't waste time wondering how the two men have become crazy enough to believe the things they're talking about.
Devlin: Name, rank and serial number is all you're getting from us, Ivan. Now, I want to speak to someone from our embassy.
Demichev: You will find that impossible, for a variety of reasons...
In Brütal Legend, Eddie shows a degree of genre savvy right off the bat when he sees a Twisted Coil Battle Nun from behind. "All right. I'm supposed to think you're a nun, but I know you're really some big ugly demon, so let's have it! (she turns and roars in his face) HAH! I knew it! Big, ugly demon."
In Dragon Age: Origins, if you have the human noble story and tell Arl Howe that you're going to kill his wife and daughter, he will respond, "Isn't that precious? Is this where I lament the monster I helped create? Let me show you how it's done: I made your mother kiss my feet before she died, it was the last thing your father saw. Meet my sword, and change that." Unfortunately he's not genre savvy enough to know not to mess with the Warden.
In Dragon Age II, Snarky!Hawke repeatedly demonstrates throughout the game, that they are perfectly aware of what type of city Kirkwall is and what role they play.
Hawke: Someday I would like to go one week without meeting an insane blood mage, just one week!
Varric also demonstrates this throughout the game, though one has to wonder how much is embellishment on his part, since he's the narrator.
Merrill plays with this trope. On the one hand, she underestimates the dangers of Blood Magic, particularly the consequences they can have on other people. On the other hand, she is aware that Blood Magic is dangerous and that she is making a Deal with the Devil, which puts her light-years ahead of most blood mages.
In Command & Conquer: Renegade, after Havoc manages to board the plane and fight off Sakura just before take-off, Sakura immediately radios the crew NOT to attack him (too late, he has attacked them).
In Zettai Hero Project, pretty much everyone is aware of what cliches to keep track of, apparently because Henshin Hero shows are based on real life for them. But their Crowning Moment of Awesome comes when Darkdeath Evilman unleashes a series of energy blasts that land in countless cities across the world, causing mass destruction. Each and every one of those locations was evacuated, because they were all the buildings and landmarks that are always destroyed in movies. There were no casualties at all.
Kouin in Eien no Aselia realizes that being perfectly willing to kill to save his girlfriend makes him less sympathetic than the angsty Yuuto, which means he can't be The Hero. Yuuto himself edges close on occasion.
Mass Effect has Legion, a mobile platform for a race of artificial intelligences who download themselves into cyborg bodies. He explains the entire metaplot of the series in a single comment when he explains how his faction of his race have chosen to create their own future rather than use the technology of others. Adopting the Eldritch Abomination's seemingly benign technology will undermine their independence and cause their society to develop along lines someone else has chosen. It may be a metaphor for cultural imperialism or a Space Whale Aesop depending on your point of view.
In the first game on Noveria, the Peak 15 facility has suddenly been overrun by murderous insect. Even though he has no idea what they are and where they come from, the chief of security doesn't seem very suprised. After all, "Labs like these exist to do stupid crap that gets people killed."
There's also the DLC Lair of the Shadow Broker, and the banter between Shepard and Liara regarding merc tactics.
Liara: The drones are disorganized. They'd be more effective if they all attacked at once.
Shepard: Please don't give the mercs ideas.
Liara: The next wave looks like a big one.
Shepard: You just had to give them tactical advice.
Liara: But now there'll be fewer left to deal with inside.
Shepard: Keep dreaming, T'Soni.
One of the most genre savvy moments of the series comes after Saren's death, either from combat or a self-inflicted gunshot wound. After Shepard opens the relays around the Citadel, s/he sends the squadmates down to "make sure he's dead." One of the party members will then put a round clean through his skull, although it doesn't stop him from getting up again anyway.
A good example of Shepard's lapsing into Wrong Genre Savvy is during Lair of the Shadow Broker, when during a high-speed car chase, Shepard genuinely asks what kinds of guns a taxi has! In fairness, you could easily argue that all this does is prove that Shepard has become very much aware of their status as a Cosmic Plaything and become Properly Paranoid as a result. Taxi's armed with guns? Given what they've faced, that's the least absurd.
Double Switch: After being attacked by a mummy who turned out to be Eddie a few times, three people hurry to Brutus's room. Why? Because they decided that they need a gun to shoot their attacker, and since they know Brutus has had dealings with the Mafia, they figure who better to come to for a gun? They didn't get a gun, but at least they tried, didn't they?
In one mission in FreeSpace, you lead a raid on a Shivan supply depot. After the first two transports grab their cargo, two more show up to snag the last two. When the first one grabs his container, it promptly explodes, killing the transport. The other transport refuses to grab the last container, knowing that it's set to explode. Command forces the transport to do it anyway. Guess what happens next.
In Saints Row The Third, Loren captures Gat, Shaundi and Boss, and offers them membership in the Syndicate. They turn him down. He immediately tells his men to kill them. What's more, he doesn't stop even after the Saints jump out of the airplane they were in. As a matter of fact, he kills Johnny Gat and uses this information to enrage the Saints, possibly to get at their emotions and make them slip up. It works, especially with Shaundi.
Matt Miller is noticeably afraid of the Saints, and is well aware of what they're capable of, to the point where he wisely considers just paying the Saints off instead of fighting them in one mission.
The Saints as well, they often Lampshade and discuss tropes such as help arriving after two waves of SWAT teams and mentioning how they think Loren wouldn't be so cliche as to hide on the top floor of the tallest building of the city "like a criminal mastermind".
A lot of people in Super Robot Wars Z2 especially in Sasei-Hen are quite genre savvy, especially when events from the end of Code Geass happens. When Schneitzel reveals Zero's identity depending on your option somebody (Roger or Duo depending on player's choice) will point out why they should still trust him, not Schneizel and later, when in one route Lelouch becomes Emperor, almost entire cast knows him well enough to know he has a plan.
Blizzard showed themselves to be almost Dangerously Genre Savvy when it came to developing Diablo III - they knew that in the multiplayer option, just about every characters' stats would be the exact same as one another with little if any deviation at all. So they knew that since Munchkins would eventually force everyone to follow the "best" build, to simply make all the stats determined at level-up anyways.
They also knew that there would be shady gold selling and item selling websites out there to steal people's accounts, so they made their own version - the Real Money Auction House (RMAH) - to counter them, both undercutting shady "services" and allowing legit players to make a pretty penny.
In-game, the characters are very savvy. They typically notice traps before they're in danger of springing them ("This looks suspicious...") ...before the players spring them anyway, because they can handle it. The characters also pre-empt the reveal of the boss of Act 2 by basically saying to the child Emperor of Keijistan "we know it's you, Belial; stop screwing around".
White Bird "Use well. Or sell to curio trader. Either way, says much about you."
In the soon-to-be-released iPhone game Demon Souls (not to be confused with the Playstation title of the same name), you play as Thunder, a spear fisherman who lives in a small fishing village. He ends up fighting demons at every turn, grabbing artifacts, and the like. He actually becomes more genre-savvy as the story goes on, eventually saying at one point, "Anyone wanna bet there's going to be demons waiting for us right after I grab this artifact?"
He isn't surprised when he turns out to be right.
In Radiant Historia, Stocke regularly figures out plot developments and motivations like this, especially during sidequests. Among other things, as soon as Raynie starts explaining that "So there's this guy..." he immediately asks if she's in love with the guy, and when a very melodramatic soldier tries to send the party on a Fetch Quest but doesn't know the location of the targets, Stocke hazards a guess that the soldier pawned them for cash, prompting a "H-How did you know!?"
In the Silent Talon mission of Ghost Recon: Future Soldier, one of your teammates says that the mission is going well, which prompts another to reprimand him for jinxing it.
Mia in Duel Savior Destiny is rather genre savvy regarding tsunderes. During Lily's route, she tries begging her to treat Taiga as a normal teammate and to calm down the aggression against him. This isn't because she wants them to get along, but rather because she's perfectly aware that the longer Lily keeps it up the bigger the dere flip will be later, something she's convinced will win over her brother.
Mr. Torgue of the DLC bearing his name in Borderlands 2 is normally not the brightest bulb, but he's more aware of what's going on than youd expect.
Mr. Torgue: NOW THAT YOU'VE IMPRESSED PYRO PETE, HE'S GONNA GIVE YOU THAT SPONSOR HE KIDNAPPED, EXCEPT HE'LL DOUBLE CROSS YOU, AND YOU'LL HAVE TO KILL HIM, AND IT'LL BE AWESOME! ANYTHING YOU WANT TO ADD, PETE?
Pyro Pete: Uh, no, You, uh... covered it. Thanks... for that.
Geralt of The Witcher. He's well aware of traditional fantasy stories, and of course being the kind of person he is, sarcastically brings them up from time to time. He's also aware of the villain's excuses and lectures and tends to brush them aside in favour of cutting to the chase. That said, Geralt's knowledge of fantasy tropes aren't always Played for Laughs, sometimes they are very true: in one quest to cure a man of lycanthropy, he comes across a variety of cures ranging from the folk (Wolf's aloe sewn into a shirt) to the scientific (a potion brewed from alchemy) and the corny fairy-tale classic, true love. Rather shockingly, it's the corny fairy-tale one that works. Even better, Geralt, being a professional monster-slayer, has been specially trained to see through the schemes of intelligent monsters such as devourers and bruxa who are Genre Savvy enough to play on misconceptions of the common folk regarding their exact nature. So, he's double Genre Savvy.