This is not the Joke Character, as those are characters that are purposefully bad, nor is it the Lethal Joke Character, which is when a Joke Character utimately has some hidden utility. This is simply a character that just looks and acts silly without being a bad character. They may look wacky, have cartoonish attacks, and a goofy voice, but otherwise they play as well as any other fighter.
Keep in mind that, in order to be considered a fighting clown, a character has to be either:
In a serious fighting game, a normally silly character, or
In a silly fighting game full of wacky characters, a character even wackier than the other fighters.
If a game runs on Rule of Cool, this guy runs on Rule of Funny. Basically, fighting clowns are those fighting game characters that stand out from the roster because they're sillier than the rest of the cast without being a Joke Character. Look for them in any fighting game — you'll usually find at least one character that stands out due to this (unless the role of the game's silly character is already filled by the Joke Character).
Many a fighting clown uses Confusion Fu as his/her/its fighting style and/or is an Improbable Weapon User.
See also Lethal Joke Character. Compare Mechanically Unusual Fighter, which is about the actual mechanics rather than the character's whacky appearance (although the two may overlap) and Beware the Silly Ones.
Tekken has tons of these, and then some. Debuting in 1, we have:
Voldo is equal parts creepy and silly. After having spent so long in complete darkness, his eyes no longer function properly and his skin is pale-white. He also dresses in what can only be described as "some sort of bondage gear" and is the only character in which crab-walking (crawling face-up on one's hands and feet) is a large part of their fighting technique. Apparently he's gotten so good at it that he can easily and rapidly cover ground with it.
Practically all of Dampierre's moveset places him squarely in this trope. Some attacks cause him to land face first into his "Poker Bluff" stance and a particular kick can put him into the "Fake Pain" stance - both at random. To the uninitiated, this makes him seem like a throwaway character as it puts him in undesirable situations - until one finds out that's how he launches his most powerful attacks. If he wasn't silly enough, he has a throw were he spanks the opponent (regardless of gender), a Russian kick dance that causes him and the opponent to go up in the air, and moonwalks whenever you move back with him. And his One-Hit Kill involves him conning the opponent. In Soulcalibur V, his One-Hit Kill is replaced with a super move where he gives his opponent a kancho.
Faust (formerly Dr. Baldhead) and Robo-Ky in Guilty Gear.
Super Smash Bros. may have several, but Wario and Mr. Game & Watch especially. Mr Game & Watch fights by pulling out random equipment from his own games, pulling out things like turtles, flags, buckets, keys and other mundane things. Wario fights using a random assortment of wacky attacks and odd abilities, such as chewing on the opponent, punching them in the groin and farting.
As of the newest games, there's the Villager and the Wii Fit Trainer. The former uses a variety of tools and actions from his source game to do battle, such planting/growing trees, digging holes, and picking weeds, and his ability to store virtually anything in his Hammerspace pockets has been taken Up to Eleven, allowing him to Catch and Return even energy projectiles. The latter's moveset consists entirely of weaponized exercise routines and yoga poses, one of which has inexplicably gained the ability to gather the energy of the sun into a deadly projectile.
Most of the original Street Fighter characters have deeper motivation for fighting. Zangief, on the other hand, is a bear wrestler in a speedo who dances with Gorbachev in his ending.
Regarding Street Fighter, by the time of Alpha, Blanka seems to have solidly taken over that role. Among other things, he has become The Unintelligible in the storyline, he befriended Dan, and one of his super moves is shaking fruit from a tree.
Marvel vs. Capcom 3 brings Deadpool into the mix. While his moves are only slightly unorthodox, the voice clips that accompany them are hilarious... the first hundred thousand times, anyway. As of Ultimate, we also have Frank West returning, and lastly Phoenix Wright, who doesn't do anything you would expect from a fighting game character. All of his attack animations are of lawyery stuff, like reading documents. Even his level 3 hyper is merely accusing the opponent of a crime. They still do damage, though, and in the case of the latter it's the single most damaging move in the game.
He keeps this up in Injustice: Gods Among Us. He has silly weapons and deadly weapons, and uses his deadly weapons in a silly manner. His super move even starts by throwing a pie at the opponent's face. Despite his Monster Clown tendencies, it seems to be a completely ordinary pie, with the super animation, if it lands, having him clean it off... with a crowbar. And then when it's completely off and the opponent sees clearly, THEN he pulls out his gun, but waits a second before they realize what it is before firing. Then he finishes with a point-blank bazooka that he pulled out of nowhere to the face that ends up sending him flying as well. And if he wins, he douses his opponent with gasoline and watches them burn, but not before making a pun on the word fire. His partner-in-crime-and-maybe-love-as-well Harley Quinn is arguably even sillier, with much more of an emphasis on silly weapons and pulls out a giant mallet with no problem for several moves. There's also much less Black Comedy to go with her, she's one of the few villains who doesn't kill the opponent and just opts for a kick in the face and telling them to "lighten up".
Goblins in World of Warcraft have always been a wisecracking race of mad bombers and mad scientists who are relatively weak in combat, full of AI characters who offer you fetch quests while being liberal with jokes. As playable characters, they can now be as capable and hardcore as any other race, and are now parts of Horde raid groups taking down every Big Bad that has ever threatened Azeroth.
Suika Ibuki: A young-looking oni who is, at any given time, completely drunk. Her idle animation is swaying back and forth. Her crouch has her lying on the ground. Her dial-a-combo is a series of friendly pats. And so forth.
Suwako Moriya: What appears to be a little girl with a weird hat and a frog obsession (actually a god). She crouches on the ground be default and moves by hopping. Her dash has her move underground. Relatively normal attacks, though.
Mamizou Futatsuiwa: She's a tanuki boss, so most of her attacks involve hitting the enemy with her minions shapeshifted into various youkai or objects. Possibly an example in the shmup games as well; her patterns are bizarre.
Shaco is basically a demonic Serial Killer Clown. His fighting style and dialogue are mostly serious, except for his Jack In The Box, which lays a stealthed trap that stuns and attacks the first enemy (or group of enemies) to come across it and is shaped like... well... a jack in the box.
Bonkers, of Clayfighter, is both a literal clown, and is the wackiest character in the game. From Balloon Dogs to Teeter Tots, he'll make you laugh and cry.
Peacock, from Skullgirls. She's a malevolent, violent Toon with a wicked sense of humor. Her movements are funny and exaggerated and she drops jokes and references left and right, but her attacks are nothing to be sniffed at. Peacock utilizes a moveset chock-full of deadly keepaway toys designed to make the opponent pull their hair out in frustration.
In the show, there is an episode where the main characters get into a large fight against hordes of Mooks. Pinkie Pie starts off by blasting the bad guys with her Party Cannon, which is basically a cannon designed to fire out and set up a party on short notice. Assuming she hasn't changed the ammunition, she's basically blasting people with cakes and balloons. While work on the game began before the show, the episode made Pinkie Pies Fighting Clown style canon.
Mad Clown in Super Punch-Out!! starts out being a clownish expy of Bear Hugger, but come his second knockdown and "Show Time," he quickly proves himself to be one of the most aggravating opponents you will ever face.
Teddie in Persona 4 Arena. All other characters are either humans or things that looklike humans. He's a colorful walking cartoon teddy bear, who makes funny cartoonish expressions while doing comical looking attacks. He does have a human form, but only shows it in win animations.
Meepo in his DOTA 2 incarnation is a short guy with nets that beats you up with a shovel and the help of his clone, also wielding shovel. Rubick's possibly this given the oft-improbable animations for his stolen spells.