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.
Mukrezar is a quirky character. One of his plans to conquer an underworld city involved baking the world's largest cake. This was completely effective. His other plans, some involving suddenly-living-undead-food, are similarly off-the-wall.
"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.
Later on, it turns out that the Scrin think he's so crazy that they appended the "Insane" qualifier to their identifier tag for him.
In Negaverse Chronicles, Quackerjack is undeniably insane. He was even committed for a time. On the other hand, this is also the reason why he can make so many toy-like weapons that are effective enough for him to hold his own on a team of superpowered heroes. His insanity is also suspected to be the reason why he can see the Voice through the glamour.
Everyone in HHHHHHHHHHHHHHHHHHHHHHHHHHHHHH is absolutely deranged, but Harry himself stands out, killing astronauts with his Groinsaw, eating people's eyes, fighting surf ninjas and rewriting history. And that's not counting how many planets he kills the fuck out of.
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.
Xerosis runs on this— surviving the apocalypse and being the star of a Peggy Sue fic has warped Harry's mind and with Voldemort as his partner and Luna as his sidekick they come up with the perfect "muggle solution" to move all wizards to the moon and leave the Earth to the Puny Earthlings.
First off, when the Oni general of the first mask tries to double cross her she decides to EAT the mask and thus his essence, gaining control over his tribe, and it WORKS.
Then, in the 7th chapter (counting the interludes), she comes with an Indy Ploy that allows her to capture Tohru for Ikazuki, by attacking Uncle, KNOWING Tohru will protect his sensei.
Later, in Operation: Steel Lightning, she comes up with a Batman Gambit to infiltrate Section 13 and steal the masks back (and maybe the Talismans as well) that was a VERY close Near Villain Victory, only failing due to the OC Spanner in the Works known as Agent Wisker.
Hero, an Anthropomorphic Personification (one of many that reside in Jade's mind, and represent different aspects of her mind) also fits this trope, but with maybe a bit too much emphasis on the "crazy" part. In a later chapter, he rams his ship into the one that the Aspect of Jade's Super-Powered Evil Side took from him (it represents a part of her consciousness), KNOWING his ship is far to fragile to survive the impact JUST TO MAKE A DRAMATIC ENTRANCE!
In the chapter where Jade is being tortured by Lung, Left and Right not only MOW down an ARMY of Terracotta warriors but Left kills one of Lung's monsters WITH A CHAINSAW, and destroys a magic-proof door with DYNAMITE!
Adelleh from thisLooking 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!
Game Theory deconstructs this trope rather harshly. Nanoha's crazy, reckless plans tend to backfire horribly with serious consequences.
Aleph: One of the things that Game Theory has as a major theme is that Reality Ensues, and that doing something crazy-awesome and insane... is crazy and insane, and doesn't have to work just because it's the hero doing it.
In Mega Man Recut, Metal Man is a sawblade wielding lunatic who nicknames everyone and fights the mob with his blades. He doesn't attack people but only because he can't mess up his blades by getting blood all over them. At one point Proto Man, Cut Man, and Guts Man have to drag him to safety because he insists on having an epic Bonnie and Clyde-esque last stand against the cops.
Dust Man is a Cloud Cuckoolander who drives around in a creepy old van, fights pests and animals around the Skull Fortress, spends his time scaring the other Robot Masters with weird ghost stories and his general weirdness, and has a vacuum cleaner as a weapon.
One of the general themes in "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.
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. Their variant is dubbed, unsurprisingly, the Predator Angrinator.
Their Primarch, Temperus Maximus, did not land on a planet like the other scattered Primarchs, but was sent adrift through the void of space in a capsule, utterly alone save for a copy of Battletoads.