In Disgaea: Hour of Darkness, Prince Laharl's servants are seen lounging around the castle lazily before and after every mission. However, during one mission, when you are attacked by an overlord so massive that he represents himself as 10 Lvl. 75 monsters, these vassals come to your aid; each at least 50 times your level.
Fate/stay night: For the first two routes, Rider comes across as a very mediocre Servant, losing to a half powered Saber in Fate and to a normal human (with Reinforced fists but still) in UBW. But then you get to HF, and it looks like she's dead again to Saber — and did she just curbstomp True Assassin, effortlessly turn Archer (who spent the previous two routes establishing himself as a badass) to stone, and fighting on near even terms with Dark Saber while not having a Master to draw energy from? Holy crap.
Of course, she had the misfortune of having Shinji as a master in the first two routes. Once Rider regains her true master, she shows what she's really capable of.
Both of the Kongol battles feature this. After dealing a certain amount of damage to him, he'll say "Kongol no need weapon" and start fighting barehanded, which is far more effective. The second one, if considered as a continuation of the first one, features this as well, since in this one Kongol wears armor that makes him much more powerful. Of course, said armor still doesn't negate his weakness to ice attacks.
Emperor Doel does this too. Once you beat him in his normal form, he'll activate his dragoon form.
You can even have your own characters do this with the "Special" combat action, which puts all of your characters into their dragoon forms AND teleports them and the enemies into a pocket dimension where the elemental attacks of the character who initiated the Special are more powerful.
Final Fantasy V: Galuf is a wisecracking old coot who makes bad puns and happily uses his amnesia to duck blame. This changes completely when he has to rescue the others, and particularly whenever Exdeath gets involved — he is quite a Badass, enough to defeat Exdeath with zero HP.
Dissidia: Final Fantasy: Bartz at the end of his story mode. Previously he's been portrayed as a happy-go-lucky mime wanderer who spends most of his time running away from opponents and making dumb jokes with Zidane. Then, when the time comes to show why he was chosen as a Warrior of Cosmos, he pulls a Crowning Moment of Awesome and tells Exdeath that this is the first time he's serious◊, while he duel wields Cloud's Buster Sword in one hand, and Squall's Gunblade in the other.
Final Fantasy IX: Steiner spends most of the first half of the game as the Butt Monkey and all-around buffoon, but when he actually gets into a fight, he's shown to be a pretty good swordsman. His general demeanor also starts to change when he helps rescue Dagger halfway through Disk 2, and he shows himself to be a competent leader and fighter alongside Beatrix during the invasion of Alexandria in Disk 3. This also happens every time he reaches Trance, where he goes from a knighty in rusty armor to a full on knight in shining armor. Since he's already one of the three melee monsters, this only makes him more dangerous.
Susano is presented as a cowardly middle-aged man, and throughout most of his character arc, this is played for laughs. He quakes in his boots at the thought of monsters, makes up a bunch of excuses to get out of doing work, and wages a battle against a sleeping bear. The moment when he stops being lazy, cowardly, and useless is at Orochi's cave, which he's seen cowering outside of at the beginning of the stage. When Orochi is about to devour Kushi, he says proudly and without hesitation: "Hold it right there, vile serpent." Then, with a little help from Amaterasu, he slays Orochi, delivering the final blow all by himself.
Reimu Hakurei. Perpetually selfish, terminally lazy, only solves incidents when she has no other option or another character convinces her to, only manages to find those causing any particular incident due to supernatural luck, and only wins because of (literal) impervious Plot Armor. Or at least, that's what most of Gensoukyou thinks. Then she unleashes "Fantasy Heaven" (aka "Hax Sign: You Just Plain F***ing LOSE"). Cue Oh Crap!.
A more specific Reimu example: in Urban Legend In Limbo, she's mostly content to let everyone else run around beating each other up when the Occult Balls begin appearing, and let the incident resolve itself. But when she realizes there's a very real chance that the Occult Balls could destroy the Hakurei Barrier, which is equivalent to completely destroying Gensokyo, she goes on the war path and fights with uncharacteristic zeal and urgency. This is among the first times in the series that we've seen Reimu at her actual job (protecting the Hakurei Barrier), and it turns out that when it comes to that, she's anything but lazy.
Yukari Yakumo is just a lazy, goofy youkai who's always sleeping and letting her shikigami do the work, right? Wrong. Not only was everything you did part of her plan, but there is a reason she was a Phantasm boss.
And, of course, there is Eiki Shiki Yamaxanadu, the annoying yama who lectures anyone and everyone about their faults. Her actual power is still not known because Yukari was convinced her, Reimu, and Yuyuko would be no match for her.
Dante in Devil May Cry both subverts and plays this straight. Dante is always wisecracking and arrogantly joking with his enemies in battle. However, he has every right to because he's a half-demon hybrid and is capable of pulling off spectacular feats even when not trying (such as being ambushed in his office and shrugging off being stabbed about five times simultaneously, nonchalantly eating a slice of pizza as his response). However, there have been occasions when Dante has cast aside his upbeat personality when the situation becomes critical enough. And if you thought he was a problem when he was quipping and smiling, it's going to be worse when the kid gloves come off. One moment from the first game comes to mind: after Trish pulls off a Heroic Sacrifice, Dante deflects an (alluded to be instantly fatal) energy beam from the Big Badjust by looking at it. In the following fight, he awakens Sparda's Devil Trigger form.
Grant Danasty in Castlevania: Judgment is regularly a laid-back guy who smiles in the face of danger. Then, when he uses his ultimate attack, that's when he starts to get serious.
Grant: I'm done playing around. (slashes opponent many times then summons many knives) Accept your fate. GO!! (hurls knives at opponent as he finishes the attack then lands) It's done.
An optional one in Mass Effect 2, we all know Shepard is basically a killing machine, but in Garrus's recruitment mission, one of the renegade lines is "Let's spill a little merc blood". You know things are going to die in large numbers when s/he talks like that.
Ah, from Sonic Unleashed comes the ever lovable Chip, one of the most God-damn annoying characters to ever come from a next-gen Sonic game (and that's WITH Tails' new voice actor being in the same game). On the last level of the game, he uses the Chaos Emeralds and his own powers to create a giant mecha created from temple ruins to punch out a literal apocalyptic darkness god-creature.
Sonic Battle: Sonic himself pulls this as well as a I Am Not Left-Handed, when he has to fight Emerl. Surprisingly, this is one of the few (if not the only) instances of Sonic not playing around with his opponent or in general. He goes from an adrenaline-pumped and cocky Kid Hero to (disturbingly) a deathly serious and utterly Pragmatic Hero. Then again, when you have 30 seconds on the clock (the previous 30 seconds spent trying to negate the Chaos Emeralds with the Master Emerald and failing) before the Final Boss (who happens to be a Physical God) blows your home planet to nothing with a fucking star system buster and the only way to stop them is to kill them (and it's someone you really care about), why would he play around? Damn; ladies and gentlemen, Sonic just proved why he is the fastest hedgehog alive and that he's got some serious brass ones. He's been holding back a lot more than what we believed he did.
Jak and Daxter: Daxter usually avoids violent confrontations like the plague, at least when he's directly in the line of fire. But when push comes to shove, he'll put his life on the line to do what needs to be done (especially in Jak 3), his racing skills and marksmanship rival Jak's (when Jak's riding a Zoomer, Daxter wields the gun), and hell, he's got his own game.
Let's not forget our hero, Sora. Cheerful, kind, caring, decent smarts,doesn't want to fight generally, a good best friend character. Except he's the lead. A lead who has saved the worlds multiple times, knows some very advanced magic, and has beaten eldritch horrors to a pulp with a GIANT KEY. And that is NOT touching on his ability to hold people in heart, which may end up saving the universe on it's own.
In Wild ARMs 4, when Gawn is introduced, he is portrayed as a bit of a goofball, albeit with great physical strength. To top it all off, his character design is much more subdued when compared to other characters in the game, especially the standard flamboyant villains. However, when he is forced to fight the protagonists and you learn he is Brionac's greatest fighter, he is so overwhelming, that his opponents are unable to get a single attack off on him, and he constantly one-shots your party members. The fight only ends because he runs out of bullets, and the protagonists somehow convince him that means he's the one who lost. Later, he easily shoots down missiles in mid-air with his dual pistols, and punches one when he exhausts his ammunition.
In Half-Life 2, throughout most of the game, the Vortigaunts serve as your alien allies in the fight against the Combine, providing some technical support and adding some interesting variety to the rebel fighters. However, you never actually see them in combat. This changes in Episode 2 in the chapter Vortal Combat, where the Vortigaunts show you the true power of the Vortessence along with an epic fight song against legions of ant lions.
Remember the Volus? The cosmic Butt Monkey of the Mass Effect universe? Turns out in the third game, they have a Dreadnought — a single Dreadnought — that according to a visiting Turian General happens to pack enough firepower to roast the surface of an entire planet three times over. There is a reason the Volus don't need more. The "Retaliation" DLC introduces the Volus as multiplayer characters. While they're incredibly fragile, they make for skilled support characters.
In Dark Souls, one of the recurring side characters is Siegmeyer, a bumbling Lord Error-Prone who frequently gets himself into trouble and has to be bailed out by the player. However, if you help him out every time he needs it, then he returns the favor in Lost Izalith, attempting a Heroic Sacrifice by charging a cluster of Chaos Eaters. Note 'attempting': there's a very real chance he'll survive the fight, even if you don't help him out.
Johnny Sasaki from Metal Gear spends the first few games being used as Comic Relief and a major Butt Monkey. However, in Metal Gear Solid 4, when his Love InterestMeryl was put in danger, he reminds the player and Solid Snake that he is, in fact, a 10 year veteran in an elite military unit.
A villainous example occurs in Chrono Cross. Quirky Miniboss SquadSolt and Peppor mostly serve as tutorials for the battle and magic system the first times you fight them. However, there's an optional sidequest that leads to the Infinity+1 Sword that starts by finding Solt and Peppor again. When you do, they accuse Karsh of betraying a longtime friend of his. In the ensuing cutscene, Karsh tries to dodge the question, and the two become enraged, attacking your party. This time, they're much stronger, and will definitely catch you off-guard if you're not prepared.
Phoenix Wright, Ace Attorney. He spends the majority of each case absolutely floundering and desperately looking for flaws in the witness testimonies. Then comes that brilliant moment where all the contradictions fall into place to reveal the truth, and he becomes akin to a force of nature. This is reflected in his appearance in Ultimate Marvel Versus Capcom 3, where he spends most of the battle with fairly underpowered attacks, until he collects enough evidence to enter trial mode, when he becomes a force to be reckoned with. He can even take things Up to Eleven by entering the even more powerful Turnabout Mode by landing an objection on his opponent in trial mode.
The Wardog squadron of Ace Combat 5: The Unsung War are Technical Pacifists at best, but mid way through the game, circumstances (Chopper's death) lead to them reacting as such, to the point the enemy buys into a myth about demons and they had taken over the pilot's bodies in revenge.
Link starts almost every game as a harmless youth from some backwater or another. But once his family, village, friends, etc... are threatened, he invariably saves them, and the world, within a few days.
Porky/Pokey Minch spends most of EarthBound avoiding confrontation with Ness and just being an annoyance. Come the final battle, and now he's got a spider-mech and he's fighting alongside Gyiyg/Giygas and he's a major threat. The music that plays during the fight is even titled "Porky Means Business."
Pac-Man: Most of the game, all the hungry little disc can do is run from the ghosts. But when he eats the Power Pill...
Sans of Undertale is super lazy and doesn't really care about much. But if you take the Kill 'em All path, he decides he can't afford not to care anymore, and faces you as the Final Boss — and he is the absolute most brutal fight in the game. It's implied that the reason he doesn't get dangerous in any other circumstance is that he knows you have the power to SAVE, and he can't bring himself to do anything knowing you can just erase it on a whim - and in fact, the only reason he fights you in the first place is to try to make you so frustrated that you just give up and leave his world alone.
Sans: all right. well, here's a better question: do you wanna have a bad time? 'cause if you take another step forward... you are REALLY not gonna like what happens next.
The Remake of Resident Evil has a minor, purely visual example with Chris who normally fires his shotgun from the hip. When you're facing a boss, however, he fires from the shoulder. The implication is that for creatures like zombies he's a good enough shot to take them down with a hip shot, but when facing a giant snake or the Tyrant they're deadly enough that every shot counts so he'd better aim properly and hit that damned weak spot.