Cilan, in an episode of Pokémon, had his Pokemon incapacitated due to poisoning. So he had to fight off a Stunfisk with a fishing rod. He is able to keep the Pokemon at bay, and sufficiently weakens it enough to catch it.
Kirika from Noir is spectacularly good at this, able to take virtually anything at hand, even an item carried by her opponent, weaponize it and kill him in a second. On one occasion, she uses a mook's eyeglass earpiece as a shiv. In another, she takes apart a toy car at a dead sprint and drives the wheel axle into someone's spine. In yet a third, she slits an interrogator's throat with an ID card, while barely able to stand from blood loss after being gut-shot. The first time she snaps her opponent's neck with his own tie. And then there's the time when she piths a mook at a cocktail party by driving a martini olive skewer into his brainstem. And don't even mention the silverware. Probably her tamest improv gig features using popcorn as a field-expedient mook detector in a pitch black room (mook steps on popcorn, popcorn crunches, mook eats bullets). She also killed people with forks a few times, including Chloe.
Fate/Zero has Berserker whose skill Eternal Arms Mastership allows him to turn every kind of thing that can be recognized as a weapon in a Noble Phantasm. Due to this skill, he's also an Instant Expert, he can use any weapon as though he had trained with it his entire life, even if it isn't even a weapon he should be able to even understand. The Improvised Weapons are e.g. street lamp poles, enemy swords and spears, two MP5K machine guns and a fighter jet F-15J.
In one episode, Kenshin was asked not to use his sword while fighting. So, he used an umbrella.
Kaoru also tried to clock Enishi with a vase in the final chapters of the manga, but failed.
Saitou is probably the best example, as demonstrated when he used his belt to knock Kenshin's sakabatou out of his hand and later tried to strangle him with his coat.
In Detective Conan, Conan can kick anything at the bad guys and knock them out (granted, he does have power-boosting sneakers invented by his Gadgeteer Genius neighbor), and he was a pretty good soccer player anyway.
Subverted more than once, due to random effectiveness of the objects around him. Once, he tried to kick a cabbage, which promptly explodes. In a gaiden story, he had to resort to kicking a hospital bed since there was nothing else nearby, breaking his foot in the process. Luckily, one of the gadgets he gets his hands on later in the series is a belt that shoots self-inflating soccer balls.
Lucy of Elfen Lied does this using her vectors to throw things with blinding speed and accuracy, including pens on numerous occasions.
Which, while awesome, isn't nearly as improvised as Nana using her own prosthetic limbs for the same purpose.
David from Blood+ once escaped a tense situation by grabbing a hostage and threatening to stab him in the neck with a pen.
Kiri, the male protagonist of the manga Double Arts attempts this. He cobbles a sword together using a large number of much smaller knives thrown at him by the very guy he's fighting. Subverted in that, while impressive, Kiri's improvised weapon fails, breaking on impact.
Yomiko Readman of Read or Die lives by this trope, as she can turn any item made of any kind of paper into anything she likes. Notable examples include a bulletproof shield made from newspapers, a grappling hook and a Cessna-sized paper airplane from ungraded homework, a lockpick from a hair tie, a katana from $100 bills and several shuriken from 3x5 cards.
Inu-Yasha once threw a tree into the throat of a charging beast.
Kaname from Full Metal Panic!!, arguably. She knocked Sōsuke out using the second base from the school baseball field by throwing it and hitting him right in the base of the neck. Improvised Weapon Master, indeed.
Sōsuke does this sometimes. There was one occasion where he took down an attacking Savage by uprooting a tree and throwing it straight into the Savage's head. It counts because he did have a gun at that time. On another, he was forbidden from using weapons (in his interpretation, firearms) in a fight; he whipped out a fire extinguisher instead.
GUN×SWORD: Ray Lundgren's Vulcan was originally a mining machine his wife built. In the series proper, it's a Mighty Glacier with a lot of guns and seems to be capable of producing more power than an Original Seven armor.
In Ranma ½, there is a thin line separating any given martial artist from being a practitioner of this trope or an Improbable Weapon User. Of the main characters, however, Ranma Saotome and Akane Tendō are the ones who come closest to this, being ready, willing and able to pick up and use anything that is around as a weapon. Being practitioners of Supernatural Martial Arts may disqualify them though... how is a lawn roller (a large cylinder of concrete attached to an iron handle bar, used to flatten landscapes) an improvised weapon when you're strong enough to throw it?
Then there is Mousse, whose style is not only the ability to conceal all sorts of weapons, but to use any possible object as a weapon.
One Piece: Supreme Chef Sanji normally refuses to use knives in combat, despite being extremely skilled with them. He reasons that a chef's knives are tools for preparing food, not weapons. However, against one opponent that uses food as a weapon (which trips his Berserk Button, he hates people who waste food) he does not face this restriction.
Darker than Black: Hei doesn't use this trope excessively in season one, but come season two and he pulls out all the stopsnote since he suddenly has to be a little more creative.... He explicitly explains the concept of using this in combat, then demonstrates it by distracting Suou with a few thrown nuts and bolts, followed swiftly by a snowball flung hard enough to floor her and leave a mark on her face that persisted for the rest of the day.
Suou learns this trope well, and is shown using it with disturbingly effective results when rescuing July. She flings shards of glass like they were shuriken, hitting her target in startlingly vital and painful areas.
Things that Durarara!!'s Shizuo Heiwajima uses as weapons: crowbars, trash cans, traffic signs (up to and including those giant ones for freeways), guardrails, mailboxes, playground equipment, park benches, vending machines, motorbikes, van doors..the list goes on. If it has even a minor chance of breaking every bone in Izaya's body, he's probably going to use it as a weapon.
Shizuo is, naturally, not the only one to improvise weapons (although he is the only one so far to weaponize a Power Ranger) — others resort to more manageable items like pens (Seiji, Mikado), Jimmy bars (Kida), soldering irons (Walker and Erika) or garden trowels (Mika)
Though it usually uses more-or-less conventional weapons, Neon Genesis Evangelion had one example of unusual weapon choice. Specifically, Asuka in EoE. Battery of self-propelled rocket launchers, meet the frontal armor of a naval battleship.
That triangular tower shield first used in the sniper mission? It's part of a space shuttle.
In Black Butler, Sebastian fights a mafia group in a mansion using the dinner plates on the dinner table and the forks and butter knives he snuffed out of Ciel's home. Result = Major badass.
In the original Super Dimension Fortress Macross serie, Hikaru Ichijyo once used the gatling cannon of his Valkyrie fighter as a club after finishing all the ammos. In some circles this procedure is called "Ichijyo's maneuver".
In the novelizations, it is mentioned that many pilots do the same thing during the first battle with the Zentradi on Macross Island. May be considered part of their training or a carryover of actual training in Pistol-Whipping.
Edward and Alphonse of Fullmetal Alchemist frequently transmute spears out of stone when they need a weapon. On one occasion, Ed transmutes an elaborate sword out of a sea of blood. Roy using Havoc's cigarette lighter to make sparks when his gloves are wet (It Makes Sense in Context) probably also counts.
In Heroic Age, the Silver Tribe gets major improv points for using an exploding planet as a weapon. When humanity ignites Jupiter in the hope that the fireball will consume the Silver Tribe fleet, they respond by using their shields to collapse the planet-turned-protostar into what appeared to be a gigantic nuke, and directing most of the resulting explosion at the human fleet.
In the Hetalia Bloodbath 2010, Spain grabbed whatever he could to protect Netherlands from the ominious figure that attacked Netherlands. *squee*
Japan rolled up a poster and used it as a sword.
In The Movie of Hyakujuu Sentai Gaoranger, the GaoKong mecha (a giant red gorilla) arises from an erupting volcano, which sets all the trees in the area on fire, whereupon he grabs the burning trees, twirling them Hawaiian-style before hurling them at the enemy. This scene inspired the Hawaii setting in the fanfic The Ultimus Adventure (which gives this show the Power Rangers treatment).
Karakuridouji Ultimo's Mizho used a crutch to beak a guy's arms....after using Pocky to attack another guy.
In episode 5 of Bodacious Space Pirates, Marika, the main character, uses the solar sails aboard the Odette II to blind a ship that's attacking them using optical sights (their electronic sensors were down due to being hacked). She stops short of having the concentrated solar beams melt the enemy ship. Before the Lightning 11 can recover, several other ships arrive to perform a Gun Ship Rescue.
In a flashback in Naruto, Ino used a flower stem as an impromptu shuriken. It didn't actually hurt the person Ino threw it at, but she threw it into her mouth and claimed it was poison.
Talking of Ino, she even cuts her own hair, throws it on the floor and pretends to use her Shintenshin no Jutsu on Sakura. She actually flows her chakra in her cutted hair and ties Sakura's legs up.
The Third Hokage uses rooftile shuriken in one of his fights.
Tobi uses a broken pipe as weapon in one battle.
The grocery store fight in Ultimate Teacher features coins and bananas as projectiles and one guy gets beaten with the microwave oven he was hiding in.
In Maiden Rose, Taki's classmates come by on his first day to haze him armed with Broomstick Quarterstaffs, Taki promptly improvises with their improvised weapons, using the broom as a sword and tripping people over the buckets, other supplies, and their own comrades.
Rock of Black Lagoon used a combination of cleaning fluid and a swift hit to the head from a bowling pin to rescue Yukio from Chaka's grasp.
Sailor V probably used the most improvised weapon ever: when faced with a mosquito-based youma and his army of mosquitoes, she grabbed the mosquito-repelling incense she was carrying and infused it with the power of the Crescent Beam.