Part of Jackie Chan's signature style is finding novel uses for various improvised weapons collected from around the scene of the fight.
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.
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.
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!"
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!
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.
Desperado had guitar cases that served as rocket launchers and machineguns.
In Once Upon a Time in Mexico, we get a guitar case with a flamethrower and another case that could be remote controlled as a rolling bomb.
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.
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.
The hero of Pootie Tang uses his belt with great effect.
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.
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.
In Trick 'r Treat, Sam uses a razorblade hidden in a chocolate bar and an ultra-sharp lollipop.
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).