Hey, remember how Yuuno was in canon? In Blood That Flows, he's easily as Bad Ass as any of the main characters and can hold his own against Gods and Demons just as well as any of the other characters in the story.
In the stories written by Crossoverpairinglover on Fanfiction.net, virtually every character gets upgraded to a point they are badasses. Genuine Lockharts, super saiyan like Sakura's, Apollo's who create black holes, etc.
In No Gods Only Guns, Ambassador Udina becomes a full-on Guile Hero, humiliating the batarian ambassador in front of the Council, and also possessing an eyepatch and cybernetic hand. Also, Doctor Michel, who is a Distressed Damsel in canon, instead takes a buzz-axe to the goons threatening her.
While Naruto ultimately turned into a badass in his own series, Shinobi of the High Seas, Naruto is turned into a Showy Invincible Hero that manages to get through the Grand Line and using his Senin mode manages to barely fight Akoji, one of the Invincible Villain admirals in One Piece, to a stand still.
In Unfamiliar, almost every canon character (but especially Princess Henrietta) gets a massive competence boost and a power upgrade. Considering that they're expected to cope with AlexMercer, this is perfectly understandable.
The main Digimon characters from Digimon Fusion Kai can become beings that look like Super Saiyans.
Many canon characters from YuYuGiDigiMoon have given power ups: such as the Digimon Tamers receiving beast powers base on the Four Chinese Symbols, and the Sailor Senshi receiving the mysterious Valkyrie forms.
SeverusSnape has been spiking Voldie's father's grave with every dangerous drug and poison known to wizardkind (and LSD—because it might affect him), as well as every other grave in the cemetery on account of Voldie might have moved the gravestone, and the graves of every other ancestor of Voldie's that he and Dumbledore could track down, just in case.
Too badVoldemort foresaw this contingency and, since he couldn't move his father's bones if he wants the resurrection spell to work, moved the entire rest of the cemetery to an entirely different location and memory-charmed the local Muggles.
Daphne Greengrass and Neville Longbottom duel with (what are essentially) lightsabers.
Harry freaking Potter, in so many ways.
Note to self: overthrow government of Magical Britain at earliest convenience.
Quirrell. Word of God says he's possessed by Voldemort, but still. Let's see: Evil Mentor to Harry, is a sixth dan in an unspecified martial art, and, assuming the author's telling the truth about him being Voldemort, horcruxed the freaking pioneer probe! Oh, and then he went and tricked Harry into breaking Bellatrix Black out of Azkaban.
Blaise Zabini is a quintupple agent in a war with only three sides!
In Horseshoes and Hand Grenades, nearly every single character who ever appeared in Kamen Rider Fourze have gone into fighting mode. This ranges from Otaku Yuki Jojima using her Hayabusa Plushie as a punching glove, Butt Monkey Chuta Ohsugi fighting off against his former love interest, Sarina Sonada and minor characters like the ones in the Amanogawa High Glee Club consist of a sword wielder, a samurai and a ninja.
Aleph: Nanoha showed us that the Monsters of the Week could be a backdrop to the real meat of the plot, the character interaction, but then Madoka came along and showed us that the Monsters can still be legitimately, vividly scary. And Game Theory is very much a post-Madoka story, with the harsher rules and the scarier monsters and so on.
Also, pretty much all the characters over the age of about sixteen or so get a significant competence boost. Notably, they aren't any more powerful, but they use what they have much more effectively because they actually employ proper tactics. Especially Precia.
The Wolkenritter in particular have received a major upgrade in skill. They aren't any more powerful, but they show the experience and tactical acumen that would expected of centuries old combat constructs.
Yukino in Perfection Is Overrated. In the original series, her Child was only good for surveillance, and left her easily defeated by Shizuru. In this fic, she realizes that while she's not the best in a straight-up fight, she can use her powers to tip the balance of power in her favor at crucial moments, such as when she incapacitates Shiho, enabling Mai to win her battle without Yuuichi dying, and when she, in the final battle, uses her Child's abilities to immobilize one of the last remaining SUEs' Child long enough for Natsuki to finish her off.
The entire Mane Cast probably count, but Mimic from the Pony POV Series is said by Princess Luna to have been the first, and only, mortal pony to injure Discord. By kicking him in the face at supersonic speeds until she knocked his tooth out. He killed her afterwards, but still. Starsong probably also counts, managing to fend off Discord's brother Anarchy for a considerable time.
While Princess Cadence turned out to be pretty badass in canon, the version of her in this series was able to take on an avatar of Discord's father Havoc and not only survive, but it's implied note sadly, it's entirely offscreen so far that she won.
The Dashverse version of Zecora, while still being The Obi-Wan to the Mane Six like in canon, also proves pretty talented in ass-kicking. It's proved repeatedly over the course of the series, with such highlights as saving Rainbow Dash from the Shadowbolts, fighting Nightmare Moon one-on-one, and saving Dinky, Pipsqueak, and Alula from Sombra's bushwoolie Mooks.
Xenophilia turns Recurring Extra Lyra Heartstrings - usually depicted in fanon as a Cloud Cuckoolander musician and/or amateur cryptozoologist - into a grandmaster of the Still Way, the only Unicorn-exclusive martial art. She's described by Rainbow Dash as "probably one of the five or six most dangerous ponies in Equestria, even counting the Princesses," and the only pony in town other than Twilight who could beat her in a serious fight.
Lero: Wow. I had no idea. She's always been really friendly to me.
Rainbow Dash: (giggling) Yeah, I’ve heard that about her. Total sweetheart, you’d never guess that she could kill you in half a second from like three hundred bodylengths away.
Chapter 9 reveals her to be an auxillary Royal Guard, and we also see her in action.
In many Naruto fanfics the title character and his Academy teacher Umino Iruka tend to get an odd version of this. In the animenote In the manga, Naruto is painting on the monument in front of an assembled crowd of ninjas until Iruka calls him down, Naruto manages to dodge two low-ranked Chunin in the first episode before his teacher appears behind him once he assumes the coast is clear. In fanfics, he tends to outrun and outmaneuver Chunin, Jonin, ANBU (AKA Special Ops) and even occasionally the Hokage for hours, with Iruka being the only person able to catch him, usually within ten minutes of setting out. How Iruka catches the boy who makes Houdini look like an amateur is rarely explained.
In certain fanfics, the author explicitly labels Naruto in the description as "Smart", "Strong" and/or "Godlike.
Cosmic Warriors takes the normally cheesy Tuxedo Mask and has him wielding his cane like a real weapon with a hidden sword within. On top of that his cane seems capable of more tricks, like shooting five rechargeable red thorn darts from the base. So far there haven't been any cheesy one-liners either.
Clash of the Elements: Cackletta wasn't really much of a threat in Mario & Luigi: Superstar Saga, being an unimpressive mage with an easy boss fight halfway through her game. In this story on the other hand, she is a Manipulative Bitch of the highest degree, a two-thousand year old remnant of the Dark King's forces who caused the legend of the Shadow Queen just to extend her own life and she has also become a Chessmaster who successfully managed to outwit Alpha, the Star Spirits, and an omniscient trio of beings known as the higher-ups simply by hiding in an area that they refused to observe. Said area happens to be the Realm Of Darkness, which considering her appearance implies that she was strong enough to control The Heartless.
Yuuka is known to be old and powerful, but only slightly more than the regular heavy hitters of Gensokyo. It is very rare however for a fanon depiction that doesn't make her nightmarishly strong and pants-wettingly terrifying, and it is not uncommon for these depictions to cross into Humanoid Abomination territory.
Mokou is already an immortal powerhouse and EX-Boss. Touhou Ibunshu has her possess the powers of the Phoenix, giving her the strength to go toe-to-toe with Yukari after creating an army of thousands of kashoyo.