In the movie Surf Ninjas, the mysterious guardian Zatch finds himself without a weapon against ninjas. So he reaches for the nearest object at hand... a skateboard. Which he uses as a Bo Staff.
A more popular example can be seen in Shaun of the Dead; the titular hero wields a cricket bat for most of the film. There is also a scene in which Shaun and Ed hurl albums at two zombies, as the zombies slowly meander towards them. In the scene at the pub, they fight the zombie bartender with pool cues, darts, and the jukebox. The swingball pole Shaun used to hit a zombie with the ball was ineffective, but then impaled the zombie to a tree with the pole itself (which stopped the zombie as a threat and helped the group afterwards when they learned to imitate zombies).
Jackie Chan's characters are considered masters of the form, squeezing it for all its slapstick value. Notable occasions include this sequence using paste tables, his own jacket, a box full of paper, his opponents' fighting-sticks, sheets of plasterboard, a Chinese lion head, a broom and, most famously, a stepladder. Also see Jackie trying a series of items in succession, after which the mook surrenders when Jackie gets to the 15-inch pipe wrench.
In Shanghai Noon, he used antlers like a bat'leth, made a blunt rope dart using a lasso and horseshoe, and "piss shirt bend bar"...
In one of the most memorable scenes from the original Teenage Mutant Ninja Turtles movie, Casey Jones takes out Shredder's Dragon using a golf-club found in the crime-wave warehouse. (Casey's motif is usually other sports equipment as weapons; this gave him a new respect for golf.) Casey is in fact an Improbable Weapon User, as in the battle described above, Casey spends the first half of the fight getting his ass summarily handed to him. The exact moment when Casey turns the fight around and goes from being a punching bag to being a badass, making quick work of The Dragon? When he finds the golf club in a pile of debris into which The Dragon knocked him.
Teenage Mutant Ninja Turtles: Secret of the Ooze: in an act of major bowdlerization, the turtles do this throughout the whole movie, most notably in the shopping center at the beginning.
The famous scene from Braindead/Dead Alive where Lionel slaughters a horde of zombies with a lawnmower strapped to his chest.
Oldboy features a toothbrush, a claw hammer, a screwdriver, and a broken CD are all used as weapons.
In Hot Fuzz, Nicholas Angel knocks out an assailant with a flowerpot, and in another scene Doris Fletcher takes out a mad stock girl brandishing a box cutter by whacking her upside the head with a "Wet Floor" sign. Later on in the film, a line of shopping carts becomes a battering ram. There's also the Shoplifter being KO'd with a lobbed spray can. Nearly all of the murders are committed without traditional weapons: part of the church roof, gardening shears, a car and a combination of natural gas and burning food. Only once the NWA is found out do they use guns.
In Terminator 2 Judgment Day Sarah Connor takes a psychologist as a hostage using a syringe full of cleaning fluid stuck in his neck, and threatening to kill him by injecting it if she wasn't left alone. The same psychologist comments how she had earlier stabbed his knee with a pen.
In The Bourne Identity, he is attacked by a switchblade-armed operative (who also knows kung fu), and has to defend himself with a ballpoint pen. He then disarms the assailant by brutally jamming the pen in between his knuckles.
In The Bourne Ultimatum, he kills an assassin with a bathroom. No, not things in the bathroom. The actual bathroom.
The best thing in the Daredevil movie was Bullseye's mastery of the Improvised Weapon. Killing someone with a paper clip or a peanut? Badass.
In Sweeney Todd: The Demon Barber of Fleet Street, the title character's first kill, in the heat of the moment, involved him laying into Pirelli with a metal teapot and beating him into unconsciousness before stuffing him into a box. He has to finish him off with his razor because the beating didn't kill the guy.
28 Days Later has Jim wielding a baseball bat (and later a crowbar), Hannah wielding what appears to be a vase of some kind in one scene, and makeshift Molotov cocktails wielded by Selena. Otherwise, real weapons abound.
Grosse Pointe Blank: Among his post-high school accomplishments, Martin Blank lists "kill[ing] the president of Paraguay with a fork." He later stabs an assassin in the neck with a souvenir pen, and smashes a still-plugged-in television over his business rival's head, electrocuting him.
Red Eye has a truly righteous incidence of this... with a pen. One of those punchy pens, with the little levers to push to make it punch... It doesn't kill the guy, but they are on a plane at the time and Jackson had already demonstrated how well he'd deal with Lisa's escape attempts. Later weaponry includes a pair of heels, too.
During the subway battle, the title character of the first Hellboy movie gives Sammael a good thrashing with a pay telephone.
In Die Hard 2, McClane kills a mook with a handy icicle. In the fourth film he runs out of bullets and has to take out a helicopter with a car.
The Chuck Norris movie An Eye for an Eye has Mako as Norris' sensei knock down one of several attackers, then render the mook fully unconscious by hitting him with a desktop telephone (rotary, no less). He growls, "The warrior uses what is at hand!"
The climax of Arabesque shows Gregory Peck killing the villains with a ladder — by jamming it down through the girders under a bridge into the rotor of their helicopter as they fly below trying to shoot him.
In Friday the 13th Part VIII: Jason Takes Manhattan, Jason attempts to shoot one of his victims with a harpoon gun, but due to being at the bottom of Crystal Lake for five years, he is unable to draw back the rubber bands to fire the spear. So he stabs the girl with the entire harpoon gun.
Serenity has Mal face off against The Operative in the final battle. The latter carries a sword so the former pulls out a screwdriver from a handy tool box.
The Transporter specializes in these, or indeed anything with Jason Statham in it. The best example is beating up a roomful of Mooks with a fire hose in the second film.
Then turning the hose on and leaving it to beat up the mooks by itself. Complete with Unflinching Walk.
Indiana Jones lives by this trope. And he's not alone. As Marcus says, the pen is mightier than the sword.
In The Last Crusade, Professor Henry Jones Sr. has killed Nazis with the following: a pen, an umbrella, a flock of birds, and a knowledge of the writings of Charlemagne. In addition to bashing his own son on the head with a vase.
There is a moment near the end of the original Stargate movie, when Jack killed Anubis using transporter rings. Yes, he used the local teleportation device to kill a guy. A really badass guy.
Smith, from Shoot 'Em Up, kills two people with carrots. He also has an interesting technique for firing bullets when his hands are busted up. He doesn't bother using a gun. He puts them between his fingers and puts his hand over a fire.
In Undercover Blues, Jeff Blue uses his daughter's stroller to beat up two muggers.
Blade Runner: Deckard is cornered in a bathroom with two broken fingers, no gun, and the villain Roy Batty has just walked in. His response? Wrest a lead pipe from the wall and beat Roy in the head with it. Roy's response? "Yes, that's the spirit!"
In No Country for Old Men, Anton Chigurh regularly uses a captive bolt pistol to not only kill people, but blast the locks off doors. He also strangles a deputy with handcuffs.
In District 9, the alien Christopher is able to improvise a bomb out some random pieces of alien technology left sitting around. Later on, Wikus uses the Gravity Gun on a prawn mini-mech to hurl a pig at a soldier with rather devastating results.
In Kill Bill, after her sword is knocked out of her hands, the Bride kills Go-Go Yubari with a broken table leg with nails in it. She also gets her revenge on the hospital orderly who pimped her out by putting his head in a door and slamming it.
Ip Man may be a Martial Pacifist, but if pushed has no qualms against using a feather duster, a long bamboo rod, wood pallets etc. to fight.
In The Incredible Hulk, the Hulk uses pieces of a broken statue to shield himself from the sonic cannons. He then uses the same pieces to take down one of the cannons and, later, a gunship. During the final fight, Hulk turns a police car into a pair of impromptu boxing gloves.
In Crocodile Dundee, the chauffeur who was driving around Mick yanked the in-car phone antenna off of the limo he was driving, and used it as a boomerang to take down a fleeing mook.
In If Looks Could Kill, Zigesfeld uses a gold serving tray to kill the French finance minister during his meeting with Steranko at the beginning, bashing him upside the head so hard he's knocked out of his chair and send sliding across the floor and into the wall.
In Thunderball Bond and Colonel Bouvar attack each other with chairs, bookshelves, upholstery, and a fire poker. (Bonus points to Bond, who only pulled the bookshelf onto Bouvar because his jacket sleeve had been stuck to it with a throwing knife.) Later, in the movie's climax on the Disco Volante, Bond frantically pummels several henchmen with what appears to be a radio officer's headset, repeatedly slams a small hinged door on a fallen goon, and hurls a heavy-looking chair at another one.
In The Living Daylights, Necros shows great improvisation skills, infiltrating a MI 6 safe house through the kitchen and taking out guards with a headphone cord, rolling pin, electric knife, cooktop, boiling water, and that old standby the cast iron skillet.
Sleeper - in a fight with a guard at a futuristic farm, Woody Allen knocks him cold with a strawberry the size of a medicine ball. Earlier he subdued another guard by asphyxiating him with a block of blue cheese.
Played for Laughs in Hot Shots Part Deux, Topper attempts to take out a guard using a bow and arrow. After missing every single shot (which the guard hilariously doesn't notice till he turns to look at the wall behind him), Topper then utilizes a chicken and shoots the guard with it. In another scene, he also "kills" a bunch of random Mooks by simply throwing bullets at them with his hand.
In The Raid: Redemption, a group of beleaguered cops blow their way out of a room by building a bomb out of a propane stove and a fridge. In about 10 seconds flat.
In the 1992 Brandon Lee movie Rapid Fire, he beats up a pair of crooked FBI agents with a kitchen. Fridge, drawers, doors, cooking implements... he pretty much uses the whole kitchen.
There was a reason Thorin in The Hobbit was called Oakenshield, as he literally used an oak branch to protect himself and win against Azog, as shown in An Unexpected Journey. In his second rematch with Azog, he has fashioned an armored gauntlet reinforced with iron fitting out of the same oak branch.
Also Gandalf when they were trapped in a tree and being attacked by wargs. He grabs nearby pine cones and ignited them as impromptu firebombs.