An old Nintendo 64 commercial featured a man swinging around an N64 controller (which is very large, two or three times as large as the PS2's controller) by its cord, until he wound up hitting himself in the testicles with it.
At another point, Amiba, a self-proclaimed genius, Small Name, Big Ego, and Toki's Unknown Rival, attempts to pass himself off as Toki to smear his name. He also tries to copy Hokuto Shinken and press his own vital points to power himself up when he inevitably faces Kenshiro. It works for a few moments, as it causes his muscles to swell up, making him look like a luchador parade balloon. His failure to properly strike his own pressure points swings right into Bloody Hilarious as he deflates like a luchador parade balloon with a leak. Kenshiro rightly points out that Hokuto Shinken is not something a sloppy hack of a martial artist like Amiba can master.
In the third Naruto movie, Rock Lee manages to knock himself in the head with nunchucks, despite being an otherwise competent fighter.
In the last filler arc of Part 1, Matsuri has difficulty with weapons until Gaara helps her select one that she wouldn't injure herself with. Even then, it takes a few tries before she can get the hang of it, although she manages to save Gaara's life with it in the final battle of the arc.
Dino in Katekyo Hitman Reborn!, while a fully capable fighter when his subordinates are present, has absolutely no fine motor skills or coordination when they are absent. None of his allies are safe from his whip when his subordinates aren't around.
An episode of the Slayers OVA featured Jeffrey, a prince of sickly stature but assured of his utter dominance in every subject by his highly intimidating mother. This includes his swordplay, which can be generously described as "flailing enthusiastically in the general direction of... someone." He has thus far survived any and all altercations by the intrusion of his mother, who reacts violently and in Paper-Thin Disguise if someone sneezes at Jeffrey the wrong way.
An episode of Heartcatch Precure had Tsubomi and Erika take lessons from a martial arts enthusiast after their Curb-Stomp Battle first encounter with Cure Dark. Turns out the kid isn't that great at it and his confidence is shattered when two older students reveal the ruse. A fight with the Monster of the Week helps him regain his confidence and Tsubomi walks away with a very useful skill she uses from time to time.
In Tintin in America, a more "western" version of this trope appears when Tintin attempts to use his lasso, only to end up lassoing himself and his own horse instead.
Near the beginning of Flight 714, Prof. Calculus mentions that he practiced Savate in his youth and tries to demonstrate a high kick (lit. "face kick"), but only manages to fall on his back and empty all his pockets.
Whos Harry Crumb had the titular Harry trying to show off aikido, so he does a backflip over the couch (imagine doing that when you're the size of John Candy), and the landing causes the dinosaur egg to fall. His boss catches it, though.
The Big Bad in the James Bond movie Tomorrow Never Dies does this in front of the captured Chinese spy, making lots of karate chop moves and yelling Kiai all the while. He's supposed to be showing how "pathetic" her moves are, but it comes across as Narm. Which is kinda the point; he's mocking her since his Mooks have, y'know, guns.
Matter of fact, most of the film falls under this trope. Then someone hurts his clan brother. Cue Crowning Moment Of Awesome, when he suddenly becomes a real ninja.
Undercover Brother, in which the titular hero (wearing arm-shields) has a fight at the end with the villain's trusted lieutenant (who has sword-like blades strapped to both arms). Undercover Brother whips out some nunckaku and starts whizzing them all about, showing off, and then smacks himself between the legs. As the baddie smirks and moves forward for the attack, it becomes clear this was to lull him into a false sense of security - UB delivers a quick left-right-spinkick combo that nearly knocks him unconscious, before he is left behind by his Evil Boss, to go up with the exploding base. Bonus points for doing it all to Michael Jackson's "Beat It".
In Jet Li's Fearless, he is armed with a three-section staff and takes on the Japanese contender who comes armed with a katana. Halfway through the match, they unintentionally end up swapping weapons and continue fighting pretty well, until the Japanese man whaps himself in the back of the head with the three-section staff. Jet Li graciously offers to swap weapons back for the benefit of both.
In Return of the Jedi, during the Ewoks' miraculous comeback during the Battle of Endor, several of them are seen skillfully bringing down speeder bikes with well-thrown bolas. Then Wicket swings his own weapon and knocks himself out instead.
Enter the Dragon shows a Mook who has been given little training trying to use nunchucks while he thinks no one can see. His obvious mistakes give away his inexperience to Bruce Lee's character, who proceeds to demonstrate how it's done. This may depend on the edit/cut/version you're watching, though.
At the end of Stay Tuned, the main character applies one of his talents and opens a fencing school. When one of his students tries Flynning, he defeats her easily and calls her out on it.
In Get Over It the obnoxious antagonist Striker has pulled out a pair of nunchucks - prompting the comment 'Who keeps nunchucks in their pants?!?' - and is showing off with them when they fly out of his grip and hit a girl holding a rope in a place that's painful for girls too. Ouch. This means she naturally lets go of the rope she's holding and the guy in the harness that the rope is supporting crashes to the ground and lands on another guy. It's like Mouse Trap.
The Mask of Zorro features a swordfighting example. As the young thief begins his apprenticeship with the old Zorro, he shows off some flashy yet flailing maneuvers. The old Zorro then disarms him with one strike, and starts showing him how it's really done.
The Daily Show took it a step further: the Jon Stewart was digitally inserted in place of Antonio Banderas' character and proceeded to flail even more, while shouting "Come on, come on, come on! Right here, right here, right here!" before Diego casually disarms him as per the film.
In Bullet Proof Monk, Kar does a pretty good job using a steel pipe as a staff until he twirls it a little too fast and drops it.
Given that his "training" was done by watching wuxia films, this makes sense.
In Napoleon Dynamite when Kip goes up against Rex, his "cage fighting skills" aren't quite at the level he thinks they are, unsurprisingly.
Kick-Ass - Hit Girl and Big Daddy know what they're doing. Kick Ass himself, not so much.
Which is why Big Daddy always refers to him as "Ass-Kick".
Mook (waves his arms around a lot) I learned that from a Chinaman.
Jim West (Hits him with a shovel) I just made that up.
Also a subversion with Gordon, whom West wants to fight. Gordon starts making weird sounds and making odd gestures in a pathetic attempt to look Bad Ass. Turns out, he was just distracting West so that he could hit a button to activate a big mallet. He later does something similar against one of the Big Bad's female lieutenants, causing her to fall from a great height. Cue the President yelling at him to "stop dancing around".
In Donnie Brasco, Donnie's first "mission" with Lefty is to collect a debt from a guy who claims to have a Black Belt. Before he can get much farther, Donnie grabs him by the hair, punches him in the face and knees him in the groin, which convinces the guy to turn over his car to pay off the debt.
In The Adventures of Johnny Tao, Johnny grew up watching Wuxia films. He spends his free time training with the moves he saw, thinking they are real martial arts. While he can hold his own in a fight, whenever he tries an Awesome, but Impractical move like a flying kick, he ends up looking like a spaz. Later, when he is given real martial arts training, he becomes much more impressive.
In Ip Man 2, Big Bad boxer Twister mocks the "dancing" of the martial arts demonstration.
In Sourcery, Nijel The Destroyer, a barbarian hero wanna-be gives quite a swordsmanship show when confronted with multiple guards, culminating in the sword getting stuck in the ceiling.
In the Witches books starting with Witches Abroad, Magrat studies martial arts (because she's a Granola Girl seeking wisdom from around the world) but isn't particularly good at them. Leading to the priceless admonition from Granny Weatherwax of "Don't ninj at them!"
In Exile's Valour, two students try to show off using stage fighting. A thrown sword shatters a huge mirror.
In the previous novel Exile's Honour, Two students have been trained to do fancy court fighting. Alberich proceeds to kick their ass, since they were not trained to fight. It's mentioned if they were completely untrained, he'd have used all the padding he could lay his hands on, because they were liable to do anything.
One that's not played for laughs: in one of the Humanx Commonwealth prequel novels, the human protagonist Cheelo Montoya mugs a married couple at stun-gunpoint; the man attempts to karate-chop Montoya's gun arm, leading to the gun going off aimed directly at the man's heart. It's only a stun gun, so under normal circumstances, it would merely cause brief heart palpitations. The man, however, was born with a weak heart, which stops permanently.
Live Action TV
In an episode of The Fresh Prince of Bel-Air, Will Smith visited a dojo to learn martial arts. He finds a convenient block of wood on a stand and tries to hand chop through it. One hurt hand later he tries it with his foot and actually manages to break through it (though he still hurt his foot doing it). Then he finds a samurai sword lying around while waiting for the sensei. He picked up the sword and proceeded to strike dramatic poses with it while talking with his mouth out of sync with his words. The sensei came in while he was going this and asks him if he's having fun and tells him that everybody tries that. On the other hand, he wonders who broke his coffee table. 
Bulk in multiple episodes of Mighty Morphin' Power Rangers. In one episode called "A Star Is Born," there were auditions for a commercial about karate. Bulk entered the audition and showed of his "incredible karate skills" (read: making random movements while shouting). He passed the audition, but at the end of the episode we see the finished commercial; Bulk is the "before" and Tommy (who actually is a competent martial artist) is the "after".
In "Mirror of Regret", Bulk has Skull for company, and they end up on the floor.
He continues it in Samurai, as early as the first episode. Poor Spike, being taught to be a samurai by "Uncle Bulk".
On the few occasions they actually fought, Bulk and Skull proved to be quite effective fighters despite retaining their distinct lack of skill. Their random incompetence seems to function as effective Confusion Fu.
In one episode of R.P.M., Ziggy attempts to intimidate Dillon into coming back to the Garage with a display of martial arts that is so bad Dillon just gives up and goes back with him.
One episode had Tim attempting to break a board with his head. Take a wild guess what happens.
Al, on the other hand, has a rare Badass moment when he successfully pulls it off. (He achieved it first, which convinced Tim that he had to be able to do it, except that Al had studied the martial art in question.) Also a case of Al being the better handyman, as Tim tried to break it against the grain instead of along it.
Wesley from Angel managed to do this a few times in the first season. Hilariously, he once casually gestured with an axe to try to impress a girl, and embedded it in the wall. This was used in his sequence in the opening credits for years.
And again, much worse, in season four while amnesiac.
In a fifth season episode of Bones, Hodgins attempts to use nunchucks and almost knocks himself out. Luckily, Arastoo shows us how it's done.
In "The Vampires of Venice", Rory faces down a vampire with a broom, which he attempts to use to intimidate the vampire, by flailing it around wildly as if he was a master swordsman. Unfortunately for him, the vampire he's facing is a master swordsman. Cue Oh Crap on Rory's part.
In his début episode the recently-regenerated-more-than-slightly-insane Fourth Doctor chops a brick in half with his bare hand — recall that his previous incarnation Knew Karate. A few minutes later he tries it again, and nearly breaks his fingers.
One episode of Friends involves Phoebe spending the day with her younger half brother, Frank Jr. At one point (after having gone to Times Square to get ninja stars), he's on the Friends' rooftop patio thing flailing around with nunchucks.
In the fifth season premiere of Psych, Shawn gets into a fight with a Triad enforcer in a martial arts studio. Shawn had taken his first martial arts class earlier that day, and with little kids at that, but was genuinely extremely confident that he was going to win. He is knocked through a wall immediately, then spends the rest of the fight trying to survive. Eventually Juliet comes in and saves him, but he's still convinced he won.
In the Red Dwarf episode "Polymorph", when they go to face the creature, Lister Flynns with a baseball bat, and hits himself in the balls.
In the Blackadder episode "Born To Be King", Edmund challenges McAngus to a duel; he flails his sword around, trying to look like he knows what he's doing, then McAngus takes one swipe, cutting his blade in half.
Cheers. Cliff, a notorious braggart, claims to know martial arts. He busts a board in half and his friends are convinced. Quietly he asks Diane to take him to the hospital, for he has broken many fingers.
Invoked in Kamen Rider Fourze: In one episode the Monster of the Week attacks Ryusei, who defends himself with his considerable Jeet Kun Do skills. However, he realizes that Tomoko (a member of the Kamen Rider Club) is watching, and in order to maintain his cover as a Lovable Coward, he throws out a really clumsy kick that lands him on his butt, then runs screaming away from the monster.
A segment on The Daily Show had Jon Stewart digitally inserted into scenes from The Mask of Zorro; during the Training Montage, we see Jon swinging his sword like it's on fire, shouting "Come on, come on, come one! Right here, right here, right here!" At which point Anthony Hopkins' Don Diego disarms him with a lazy tap. Note that this is only slightly worse than what the character he's replacing actually did in the movie.
An episode of VIP saw Valerie Irons - who had a false reputation as a badass while the rest of her group did the fighting for her - forced into a fight with a highly skilled warrior who was doing the same thing on behalf of the unskilled villian of the week. She had to stall until one of the VIP group was ready to remotely control her body. When she managed to strike him once by fluke, her opponent believed he'd fallen for obfuscating clumsiness.
Rangi Jones from Footrot Flats learned all of his fighting moves from watching kung fu movies. Needless to say, this does not stand him in good stead in a fight against schoolyard bully Lex Murphy.
One episode of TNA featured James Storm trying to use nunchucks on his opponent, only to hit himself in the head with them.
In Pokémon Live!, Professor Oak tries to escape from a cage via martial arts training. It doesn't go well.
This also appears in Breath of Fire II, in almost the exact same context (this Ryu isn't amnesiac, but he's still just a kid at the time). It's not nearly as noticeable there though, since kid Ryu only fights a grand total of 2 plot-based battles and neither of them is winnable.
From the original Street Fighter game: Two bonus rounds involve Ryu/Ken trying to break brick pieces. It's possible to break all or some of those pieces, or fail altogether. The last part of which causes the character to look like this with booing sounds in the background to match.
The Talk-Radio track in Grand Theft Auto III features Lazlo, the host of the show, interviewing the owner of a martial arts dojo/vegan food store who embodies this trope. He tries to chop the host's desk apart ("I have already visualised the desk as two half-desks") with the expected results.
Double subverted with Forest Law from Tekken, who is very good at fighting. As soon as you give him a pair of nunchakus, however...
Critically failing the Test Your Might segment in Mortal Kombat 9 causes your character to just injure their hand instead (though they're still able to at least put a dent or crack in whatever they're trying to break, even if it's diamond.)
Whateley Universe: Generator tries teaching herself using her roommate's nunchuks and clocks herself. Even after she uses her powers and 'possesses' the nunchuks, she still gets hit. By possessed nunchuks that are trying to tell her something.
There are way, WAY to many videos of people failing at martial arts, unintentionally or otherwise, to even begin to list on this page.
Sokka of Avatar: The Last Airbender , when he was trying to find a good weapon. He kept falling over or smacking himself until he found a sword.
Kung Fu Panda played off Po's clumsiness in the beginning of the film.
The recruits in Mulan are guilty of this initially.
The Simpsons episode "The Monkey Suit" had a one-off gag where the family went to a museum exhibit about the history of weapons. They see a film called Nunchuks: Cool But Useless, which shows a Chinese vase depicting the invention of the nunchuks: the inventor smacking himself in the face, getting laughed at, and smacking the laugher.
Let's not forget Bart's "Touch of Death" technique, which he developed after skipping martial arts classes...
Darkwing Duck: Darkwing's means of proving his identity in the episode "Apes of Wrath".
The sword-fighting abilities of "Da Samurai" (don't confuse with the main character) in Samurai Jack, could be interpreted like this. Despite this, his fighting style served him well enough to take down a couple of robots in a tavern.
Jackie Chan Adventures: Jade does this in the second episode; she is Jackie's niece after all. She ends up high kicking a waiter's tray in a resturant causing a chain of events to occur that allows for the Rooster Talisman to end up in the soup she ends up drinking.
(The quarterstaff bounces off the ground, hits him in the face, and bends his beak)
In Kim Possible. Ron is the most notable example, especially when he is training with a staff in Japan and shows pretty impressive speed... accidently stripping himself to his boxers in the process. Pretty much every scene with Ron until he got in touch with his monkey powers, and even after that.
Antoine of the Saturday morning Sonic the Hedgehog cartoon attempts to learn martial arts ("King Fu") from Bunnie in one episode, but generally fails to do much other than spout Funny Bruce Lee Noises, damage everything in the environment but the practice dummy, and eventually send it flying through a window into Sonic's hut. He manages to save Sonic from a sneak attack with a flying kick late in the episode, though. That and a post-battle demo gain him praise, but he thinks the latter wasn't so good. He fumbles the second demo, lands on Dulcy's foot, and she wrecks the hut they're in.
Funny videos all over the Internet, the most famous of which is probably the Star Wars Kid.
Using any weapon without training can turn into this. Some weapons, such as flails, are known to be notoriously dangerous to their wielders even with training.
For example, Charles Darwin tried using bolas during his visit to Argentina. He was relatively lucky, and only tripped up his own horse. The gauchos with him reportedly found this very amusing.
Nunchucks are notorious for this, exacerbated by the fact that the physical properties of the weapon make it impossible to do the moves at anything less than full speed, as most other weapons allow you to get used to how it moves before trying to move it quickly. Averted early on, when people will use speedchucks (lighter and thinner chucks that are fast, but wont hurt much when hitting yourself) in training and presentation. Played Straight again when they switch to a thicker chuck later on in training, and haven't become accustomed to the weight.
Even training under the watchful eye of someone more talented than you doesn't make you immune to this. Ask anyone who has done any weapons training for any significant length of time and they will have at least one story (or more...) per weapon of accidentally hitting, cutting, stabbing, whacking, or otherwise inflicting pain on themselves.
In Martial Arts, it is often said that the most dangerous belt is a White Belt — God only knows how they could hurt you (or themselves)!