In Austin Powers: International Man of Mystery , Oddjob spoof "Random Task" throws his shoes as weapons. When he tries this move on Austin late in the film, he only succeeds in giving the superspy a minor headache, prompting an incredulous response: "Who throws a shoe? Honestly! You fight like a woman!"
Twice during the film's climax he manages to use a garbage truck as a weapon. The films drop subtle hints that with his bare hands he's a poor fighter, but if given a weapon he's effectively unbeatable.
Part of Jackie Chan's signature style is finding novel uses for various improvised weapons collected from around the scene of the fight.
The hero of Pootie Tang uses his belt with great effect.
In the Sammo Hung film Magnificent Butcher, Wong Fei Hung fights another kung fu master with ink brushes.
Practically every main character in Mystery Men uses an unusual weapon. Examples include thrown forks, a shovel, a possessed bowling ball, and flatulence. The film also includes a weapon designer who only creates improbable nonlethal weapons.
TRON. Sole weapon: glowy Frisbee. With a controllable flightpath. Which could chop other characters in half or even split heads (though all we saw were jewel-like bits coming out of the helmet when this happened).
Anton Chigurh of No Country for Old Men has a cattle bolt gun, which uses compressed air to shoot out a retractable metal rod. He apparently uses it because it's good for blowing out locks, and not many people can tell it's a weapon.
Pam Grier as blaxploitation hero Foxy Brown: "I've got a black belt in barstools!"
In The Fastest Guitar Alive, Roy Orbison wields a guitar that conceals a rifle.
Among the many knives found in the Joker's pockets in The Dark Knight film, the police also pull out a potato peeler! You may cringe at the thought of how effectively he'd use it. He also makes effective use of a pencil.
The title character of the Japanese splatter film RoboGeisha is proficient in the use of weapons one would not normally expect to be deadly... with the most eye opening example being a pair of fried shrimp.
The killers in Gutterballs dispose of most of their victims with bowling pins, blunt ones for bludgeoning and sharpened ones for stabbing.
In Labyrinth, the goblin guards in the hedge maze sections use small, sharp-toothed critters tied to the end of poles, which bite whatever they are put near.
Elodie Yung's character in Banlieue 13: Ultimatum used knives tied to her long braided ponytail to dispatch enemies.
In Daredevil, anything Bullseye throws is a murder weapon (except when thrown at his Plot Armored nemesis). This includes semi-normal things like darts, steel needles, shuriken, and one of Elektra's sai. It also includes off-the-wall items like unsharpened pencils, Daredevil's cane (which to be fair is actually a weapon), paperclips, and chunks of stained glass. In one case he even manages to kill someone with a peanut!
Mike Howell in American Ultra makes use of anything at hand to defend himself: steaming ramen soup, the spoon he was eating said soup with, dust pan, canned goods, hammers, various knives, you name it. If it's within reach, he'll weaponize it.
The Winter Soldier is one of these whenever he doesn't have a strike team around to keep handing him loaded BFGs. The signs are there in the movie of the same name, which features him disabling a moving car by pulling out the steering wheel and throwing more than one person into a vehicle. But it doesn't really reach its apex until Civil War, where he uses (among other things) a railing, a mattress, helicopter blades, and Cap as weapons.