The Transformers franchise has wound up with a number of these, generally being something fairly unremarkable when they're transformed.
A number of Transformers with helicopter alt-modes as of late have the ability to use the rotors as weapons in robot mode. These include Bulkhead from Energon, Evac from Cybertron, Blackout from the 2007 movie and Megatron from Animated (although he cheats by actually turning his blades into swords).
In what could be a deliberate inversion, the Animated version of Blackout shoots his rear rotor out as a disc weapon.
A great many Transformers with animal alt-modes can use their tails as whip-like weapons once transformed. Some even have something particularly nasty at the end, like a blade or a big spiked ball.
Engines forming guns. This happens a lot.
And, of course, anyone whose transformation leaves them with their alt-mode's head on one of their hands has a pretty nasty weapon. Not only can its jaws clamp down hard in close-range combat, but it can usually shoot some sort of beam attack as well.
The epitome of this, though, has got to be the Breastforce, from the Japanese-only series Victory. Their robot modes have chestplates than can be removed to turn into little robo-animal partners or hand-held guns.
Prowl; hubcaps into shurikens. Jazz; tailpipes into nunchucks. That is all.
The majority of the Transformers Animated Autobots use improvised weaponry (grappling hooks, wrecking balls, welders) to one degree or another. This is topped by Ratchet, whose most powerful weapons are essentially powered-up medical equipment.
In the Animated continuity, pretty much all of the Autobots are pulling this one off. They're a work force forced into war, so it makes sense that they would use the tools of their trade.
American Maid, from The Tick, uses her shoes as weapons. Unlike Jian above, she does throw them, and they apparently have some pretty pointy heels. She would occasionally use her tiara as a weapon, as well.
To say nothing of Captain Musilage, Babyboomerangotan and.... THE HUMAN BULLET!
Don't forget the woman who can shoot poodles out of a poodle gun.
The Box Ghost uses boxes, cardboard, and anything square. Although sometimes he will use contents inside the box, one of which had very, very sharp scalpels. He also uses bubble wrap. Ember McLain has many functions for her guitar, but when she runs out of option, it doubles as her choice weapon. Technus uses 21st century machinery at his disposal, including, but not limited to computers, cars, satellites, and even an online video game.
And who can forget Quick Draw McGraw's alter-ego El Kabong whose weapon of choice is a guitar... nothing special, just a regular guitar he that he uses to beat folks about the head and shoulders. Lampshaded in an episode of Harvey Birdman, Attorney at Law when Quick Draw is arrested for hitting a man with his guitar and is charged with assault with a deadly weapon, leading to a courtroom debate about the right to bear guitars.
Various episodes feature a mop, ballistic pies and dodgeballs used as weapons.
The French Peas of Jericho dropped slushies at the Hebrew veggies.
Wakfu has a few: of the mains, Ruel fights with a shovel, and Amalia has a vegetable doll. One of the minor characters fights with a baker's plate.
Shovels seem to be the Enutrof weapon of choice since it can also be used to dig for gold, and Sadida in general (both in-game and in the show) are infamous for using weird little veggie dolls to attack with. Or to put it another way, this trope as a racial trait.
An episode of Invader Zim saw Dib fighting in a cage match in order to see his father. He had a choice of improbable improbable weapons, including a giant corkscrew, and giant cotton swab. Dib, however, chose the giant Turkey Baster.
Bishop of Teenage Mutant Ninja Turtles is arguably a Badass version of this, as he uses everything around him as a weapon to even the odds in a fight. He goes from taking the turtle's weapons, to using a baseball bat, to using his own necktie.
Normally, a sword does not meet the standards for an Improbable Weapon. However, it does in the movie Tangled, where the wielder is a horse. And that's not even getting into Rapunzel's Frying Pan of Doom.
An episode of Futurama had Ben Franklin's Franklinator, which is essentially an animal (usually a badger) tied to a stick. However, Bender receives one with a small shark, and Fry gets a chipmunk.
In the pilot of Jackie Chan Adventures, Jackie beat off the Dark Hand Enforcers with a pair of windshield wipers.
In Adventure Time while Finn usually uses a sword, in the season two finale he defeats The Lich with a sweater, thrusting it through his eye sockets and ripping the top of his skull off. This was because the sweater had been imbued with the power of l-l-liking someone a lot.
The Settler Ponies in My Little Pony: Friendship Is Magic arm themselves with apple pies to fight a war against a tribe of buffalo. Not a play war or a game, mind you, but a sincere war over a parcel of land that both groups claim ownership over. It even goes into slow-motion when Chief Thunderhooves is hit, complete with tragic western music as he lays stunned with pie in his face.
Mad golfer Duff Killigan has been known to use golf clubs as weapons, as well as exploding golf balls.
The Mathther, an Expy of The Riddler only obsessed with math problems rather than riddles, occasionally throws grenades shaped like digits.
On one occasion, Ron's pet mole rat Rufus volunteered to let Master Sensei throw him like a throwing star. Ron's adopted ninja sister Hana once threw a cookie in the same manner, with destructive results.
Casey Jones from the Teenage Mutant Ninja Turtles normally counts, using a variety of sports equipment as weapons. But special mention goes to the Casey from Teenage Mutant Ninja Turtles (2012), who uses not just a hockey stick, but hockey pucks with very powerful M-80s taped to them and a taser hidden in a hockey goalie glove that's made from a potato masher.