Although he doesn't have a specific Weapon of Choice, Terrence of KateModern usually favours fairly improbable weapons, ranging from an ordinary stick to a freezer van. Occasionally these are improvised weapons, but more often than not they aren't, and you get the impression he's just enjoying himself.
Chaka uses regular playing cards and some forks. Lancer has a pair of paper swords (which he can cover with his PK field, making them incredibly dangerous). Generator has a Hello Kitty compact which is not at all what it seems.
Generator is too Crazy Awesome to stop there. She has weaponized hair decs! And a stuffed cabbit that has taken down grown men in armor!
A very popular phenomenon among fan-created characters for existing series. Yes, that double-ended scythe or windmill-blade-katana-thing your OC has for a Bankai/Soul Resonance/Innocence/whatever may look cool in that one picture... but it would be an absolute pig to wield in an actual fight.
Super-assassin Demise has this as a super-power. Literally anything, in her hands, can be used as a weapon. If she is armed with something that is already a weapon, she becomes the deadliest fighter on the planet. If she's armed with something that normally couldn't be considered a weapon by any sane man (in the past, she's killed people with a plastic spork, a comb, a snow globe, a smiley-face button, greeting cards, paperback books, chopsticks, cellular phones, toothpicks, paper clips, rubber bands, and music CDs) she also becomes the deadliest fighter on the planet. Of course, while she's a highly trained martial artist and has a body any Olympic-level athlete would love to possess, she's also just a Badass Normal. She tried to do that "deadliest fighter in the world" thing on Ultra-Man, and he just smirked and knocked her out with a flick of his finger.
Tom Foolery from the same setting uses weaponized toys, including machine-gun armed teddy-bears, explosive rubber balls, sharpened jacks that he throws like shurikens, acid-filled water-guns, and so on.
As her name suggests, Yo-Yo is an expert at using a yo-yo as a weapon. Lots of superheroes who laughed at her ended up bruised and battered.
Drake from New Divide uses a flute as his weapon of choice.
In Elemental Wind Elemental Selah uses the sharpened edge of her shield as a weapon. Another character fitting this trope is Corah, who wields a farmer's scythe.
Agents in the Anti-Cliché and Mary-Sue Elimination Society use a lot of different weapons: Claire uses pinecones (yes, you read that right), Marcus sometimes uses an umbrella, Tyler uses a three foot long Lego axle, Tom uses a shrubbery, and Stephen once beat a Sue into submission using a payphone.
In the fifth episode of the Stickman Can't Fight series, Black uses a hula hoop.