Crazy Awesome/Fan Works

Super Milestone Wars and it's sequel.
Adelleh from this Looking for Group fic. A cookie-eating, goggle-wearing undead priestess whose head is permanently in the clouds. At one point she actually convinces the other characters to throw themselves off a cliff, thereby saving their lives from an angry ghost!
Shinji and Warhammer 40 K. Too many examples to name, with mighty Shinji being only the most prominent.
And while we're on the topic of Eva fics, the version of Rei Ayanami seen in Nobody Dies is best described as a cross between Haruhi Suzumiya, Elsa Bloodstone, and all three of the Warner siblings. In fact, the whole fic is made of concentrated Crazy Awesome. For example, matchmaking between Shinji and emo-Asuka:

"Hook, line and sinker," Mana says, "Pretty Boy has fallen for the bait. Cancel plan B."
On the overlooking rooftop, Rei sighs and closes the radio detonator.
"I never get to do plan B."
Behind her, holding the bazooka, Kensuke shrugs.

Shadow Crystal Mage's Uzumaki Harry, from the Harry Potter/Naruto crossover of the same name qualifies. As the story summary states, "Uzumaki Harry is the adopted brother of Naruto and Sasuke, under the guardianship of Jiraiya. Anko is his sensei. He edits 'Icha Icha'. Can you picture how messed up this is going to be?"
The Angry Marines, a homebrewed chapter of Warhammer40K SpaceMarines, fought the Chaos God Nurgle to a near standstill, throwing everything they could at it. Then, when that was not enough, they threw what they couldn't: Their Battle Barge, The Litany Of Litany's Litany. That shut the demon up. Just long enough for them to hit it with a second battle barge, The Maximum Fuck. And the Angry Marines may or may not have been rocking out on it while it descended in flames upon the demon's head.
- One time, The Angry Marines, not getting to the battle fast enough, tore their own landing vehicle apart, and rode its engines down to the planet, raining down like meteorites of pure rage.
  - And they have a Predator Titan, as demonstrated here.
  - There is a tank called a Whirlwind. For most Chapters, it is a long-range artillery piece that shoots missiles. For the Angry Marines, it is a long-range artillery piece that shoots their own soldiers because that gets them onto the battlefield faster.
The Emprahsque
In the Mega Crossover fic, Kingdom Crossovers, the 8th chapter gives us Shego and Deadpool in a Gunman, with Shego using her energy to power the machine.
The Naruto Peggy Sue fic, Yet again, with a little extra help is fueled by this trope.
The AU version of Garrus Vakarian in Renegade. He is described, in the authors own words, as "An unholy fusion of Jack Bauer and the Kool Aid Man." His favorite tactics include kneecaps, excessive force (including hijacking a Hover Tank to capture an unarmed, injured mercenary), and crashing cargo haulers through warehouses. Several, warehouses.

"I've yet to encounter a potentially dangerous situation that can't be defused by smashing through a wall."

- It gets to the point where, when telling the story of how he found Shepard, she eventually realizes that after a certain point, the story has degenerated into an infinite loop of him smashing through merc-occupied warehouses with a garbage truck and shooting them all. She asks him to skip ahead to the conclusion.
One of the general themes of the Power Rangers fanfic "Of Love and Bunnies" is that being a Power Ranger turns you Crazy Awesome. Ten of these Rangers are the protagonists. These are people who can walk into a carnival and within two hours cause a fight to break out on the midway in which clowns hurl flaming pins at Adam Park. It's one of those stories.
- Within the story itself, there's the trio of Zack, Rocky and Conner, who provide 90% of the mischief by doing things such as hook up with a trio of hot graffiti artists and helping Bulk and Skull clean wash orange paint off of a chimp.
Harry from Oh God Not Again is this. Even the other characters admit it in-universe and it's considered odd when Harry isn't doing something bizarre and off the wall.
Every battle in Mighty Morphin Mecha Rangers is laced with some degree of this.
Ichigo in The First Guardian certainly qualifies. He purposely grows his hair to look like a shonen hero, actually tries to attach speakers to his Shinigami outfit so he can have his theme song (which is "Number One" of course) playing when he fights, constantly talks to his just as crazy Zanpakuto and chooses to do things based on "coolness factor". On the other hand, his crazy way of thinking allows him to enhance his Zanpakuto in various ways (from gathering spirit particles to strengthen it a la Quincy style, shaking the particles already in there to, temporally, turn his blade into fire, and to shape shifting it into different forms) without even showing shikai yet. And, no, his Zanpakuto isn't Zangetsu. And that's only a small sample of the crazy awesome stuff he does.
The whole genre of Crack Fics--provided the story actually works.
Everyone in Thirty Hs is absolutely deranged, but Harry himself stands out, killing astronauts with his Groin saw, eating people's eyes, fighting surf ninjas and rewriting history. And that's not counting how many planets he kills the fuck out of.
Absolutely everything Mosegi does in Valour and Mayhem.

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