In Seattle in the '80s, late night variety show Almost Live! had a send-up of kung fu movies and Public Service Announcements called, "Mind Your Manners with Billy Quan". In each episode, Quan and his opponent would use improbable weapons (such as sausage nunchakus, computer disc shurikens...).
Buffy the Vampire Slayer: Buffy certainly qualifies, since she frequently uses improvised weapons to kill vampires, especially in the early seasons. Most of these are improvised stakes, ranging in size from a pencil to a mop handle (and, in "Homecoming", she stakes a vampire with a spatula). She also decapitates a vampire with a cymbal in "The Harvest".
In Angel Harmony even stakes a vampire using chopsticks and Angel, to Spike's dismay, kills a opponent with a spoon.
In one particularly impressive example, Michael is attempting to keep a man alive while he is being targeted by a prison gang. Three gang members pull shivs and attempt to attack Michael in his cell, so Michael fights them with a small towel. And wins.
Chuck: John Casey is king of this trope, having weaponized: appliances as both melee and projectile weapons, part of a bed frame he was handcuffed to, a hotel room's heater/radiator unit, Chuck, his CrownVic, chairs and other furniture, and pretty much anything else he can get his hands on.
Chuck is no slouch at this himself, having used a broken CD and a scalpel as shuriken, a nacho platter as a discus, chair legs, a Dodge Challenger, Sarah, a clothing rack, "tranq gloves," a cane, the cast for his own injured ankle, another scalpel in a tiny weapons standoff, has disarmed bombs with internet porn and fruit juice, and is a crack shot with tranquilizer guns. This becomes especially prominent in seasons 3 and 4, when the Intersect can allow him to use pretty much anything as an improvised weapon.
Sarah gets in on the act as well, using hair pins as throwing knives, a broken CD as a knife, a car's air bag, handcuffs as brass knuckles, the carved head of a cougar, a tiki torch, and Chuck, among other items.
In Community episode "Epidemiology", Jeff, whose costume is David Beckham, uses his soccer ball to take out a zombie.
This was an homage to an ad-lib by Tom Baker that he made because he found what he was scripted to do too violent - he was meant to pull a knife on the alien and threaten them. The director was not pleased, but the writer absolutely loved it and decided to keep it in. In his autobiography, he described a little boy coming up to him, offering him a jelly baby and repeating the line, which he found to be a Crowning Moment of Heartwarming:
"Put down your weapons! Or I'll kill him with this jelly baby!"
The Twelfth Doctor uses a spoon to beat Robin Hood, of all people, in a direct duel! He makes it even worse by tapping Robin on the head with it as a taunt.
A funny version occurs in "A Good Man Goes to War" when Amy, fearing that an enemy was trying to get into the room, grabs what looks like a turkey baster and tries to threaten them. Turns out it's just Rory.
"Remembrance of the Daleks" ends with the Doctor allowing Davros to destroy his Dalek empire with what's essentially a piece of booby-trapped heavy industrial equipment. Stellar engineering heavy industrial equipment from the birth of Time Lord civilization, that is.
A Special Effects Failure-induced example is the Daleks, a terrifying genocidal alien race whose secondary weapon appears to be a toilet plunger (this is because it was — Classic Doctor Who famously had No Budget). Several attempts were made over the years to ditch the plungers and replace them with something more sinister like a claw, but reactions to it were invariably negative. In the new series, a character mocks a Dalek for its plunger and asks it if it's going to "sucker [him] to death", so it does, and it's actually horrible.
On Heroes, Mohinder has successfully used a rolling chalk board, microscopes, syringes, and a tuning fork against Sylar and the door of his taxi against Danko and his goons. He used a ceramic elephant statue against a hitman, but Eden saved him in time before the hitman could retaliate.
We can probably all still remember how Claire escapes from Sylar in Volume Five by stabbing him in the eye with a pencil...
Murder, She Wrote had a woman trying to protect herself in a restaurant freezer use a frozen swordfish as a weapon against a Jerkass Victim (the sharp nose acted like a knife) when he tried to kill her. Instead it was self defense (she killed him by accident when it caused a fatal slash wound).
Belle of Once Upon a Time has defeated enemies with a bookcase, an oar, and a mine cart. Usually while wearing five-inch heels.
Star Trek: Deep Space Nine: in "Empok Nor", Garak is accidentally exposed to a drug that turns him into a xenophobic, psychopathic killer. O'Brien does manage to stop him in the end, but not before Garak kills one of O'Brien's engineers with the engineer's own flux coupler.
O'Brien's own weapon in the final duel also counts, because although he used a phaser, he didn't use it as it was intended to be used but instead used it as a grenade.
Also the original Green Ranger's flute dagger. Given the fact that the Green Ranger's peers used a sword, a bow, an axe (that turned into a gun), daggers and a staff, as well as having pistols that turned into knives, the Green Ranger being armed with a flute is very peculiar (though still practical thanks to the blade).
In Power Rangers RPM the cast takes this to new heights. Although most weapons are one use only, the consistency cast's use of the unusual earns them a place on this page: suran wrap, a baby stroller (with a baby in it no less), a building, shopping carts, lawn chairs, beach umbrellas, bus doors, if it can inconvenience the mooks it's been used. And that's not counting Summer's Zip-Charger, which launches an RC car at foes. And, last but certainly not least, Dr. K's violin; the first time, it's just conveniently hooked up to a nearby amp, but the second time, she demonstrates that all of the technology is programmed to respond to her music.
Some Monsters Of The Week have also had odd weapon choices, such as Gnarly Gnome, who wielded a rake. That the Megazord wrenched from his hands and swung at him. He also used his accordion to confuse the Rangers and let him land some blows on the Megazord before it was punched out of his hands.
His younger brother Klaus did this numerous times. He attacked the Gilbert's house with a newspaper and pieces of picket fence before realizing it wasn't working and deciding to burn it to the ground (Damon and Stefan calm him down in time though).
Elena and Katherine both qualify during their fight in the season 4 finale. Katherine beats her up with a mop handle. Elena counter-attacks by ripping a locker from its' place and throwing it at her. It gets worse...
Glenn uses a piece of store shelving to get a Walker off of Maggie in season 2 of The Walking Dead.
Maggie also employs a No Parking sign at one point.