Symmetry is supposed to be a natural attractive feature, and any deviation seen as ugly. Apparently, no-one told these guys, or their fans. They take Impossibly Cool Clothes to a whole new level. Why constrain yourself to pant legs of one length, or stockings that match, when you can wear one short and one long? It must be kept in mind, of course, that fashion is a fickle thing, and largely a matter of perspective. For every outfit listed here, some will fight to the death to say it looks cool, while others think it looks, in the words of Simon Cowell, atrocious. Keep squabbling about whether it's a "hot" or a "not" to yourselves, fashionistas.
Some medieval armour was actually asymmetric, often to lend extra protection to the body's dominant side, or to leave off armour for the side of the body that was already protected by a large shield.
One would expect cybernetic eyes to come in pairs, but as often as not a character will only have one cyber-eye (usually glowing), while the other one is still organic. This makes sense if the cyborg equipment replaces body parts lost to injury or disease — if you only lost one eye (or arm or whatever), why replace both of them?
Take this trope too far, and you can run into Rummage Sale Reject.
For extra bonus points, why not have mismatched body parts? Nothing says Evil like a hook hand, a horn on one side of your head, or an angel with one wing! And it doesn't have to be that complicated: both good and evil can enjoy the duality that heterochromia implies.
Examples
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Anime & Manga
Both of the top-level angels from Angel Sanctuary, Alexiel and Rosiel, have three wings. This is explained in the manga, as being twins the 6 wings of angels their level would usually have were split evenly between them — i.e., 3 wings each.
Several of Sakura's outfits in Card Captor Sakura have one short and one long stocking.
A lot of shinigami accessorise their uniforms according to this trope. The king of this trope is Yumichika (both before and after the time-skip), but also included are (before the time-skip) Byakuya, Chojiro, Isane, Renji (in bankai), Nanao. After the time skip: Rukia, Ikkaku, Shinji, Uryuu.
Several arrancar display this as well, but mostly in mask-fragments. Justified with Ulquiorra, who has something you could call bangs above his left eye, because of that stupid half-helmet he wears.
Uryuu's Quincy Final Form, Justified in that the Quincy are depicted as monk-archers based largely upon eastern martial-artists who specialize in the bow and who often leave one side of their bodies completely bare to avoid getting clothing tangled in their bowstrings.
Several of the Cloths in Saint Seiya, most notably the Aquila Cloth, whose upper body has an armored (left) and unarmored (right) side .
Many characters from One Piece, including the main casts have significant bits on their left side which range from minor things like earrings, combovers and tattoos to a Hook Hand.
Permanent asymmetries through all of the series are noteworthily Luffy's scar, Zoro's earrings, Nami's lock of hair in the left side of her face as well as her tattoo, Usopp's wristband, Sanji's exposed eye (changes from right to left side over the Time Skip) and Chopper's left antler.
Karin has hair that is long and straight on her left side, but short and unkempt on the other.
Killer Bee has a mark like an ox horn on his left cheek, mirroring the Eight-Tailed Ox that he is host to, which is missing the end of its left horn.
Temari wears two stockings: before the Time Skip the right one goes up from her sandals and ends just below her knee, and the left one goes from above her knee into her skirt. After the Time Skip, however, she starts wearing matching ones.
Sai has one sleeve on his crop top that's longer than the other.
The title character has that functionless spiral tie thing his pre-Time Skip outfit has on the left shoulder.
Guren (anime only) of the Three-Tailed Beast arc wore a green Badass Long Coat with a long left sleeve and a short right sleeve. Probably due to the fact that she was (from what the troper can gather) predominately right-handed and the Crystal Style Jutsu she used would have torn up the clothing she wore when she activated Crystal-Arm-Blade-Mode.
The standard uniforms for two of the five main ninja villages also feature this trope; Hidden Cloud flak jackets only have one shoulder strap, while most Hidden Rock shinobi only have a sleeve on their left arm.
The poster for The Extravaganza of Haruhi Suzumiya, featuring all the cast in fantasy outfits, shows Mikuru wearing one fishnet stocking and Haruhi wearing two fishnet stockings of two different lengths — one that goes far enough up to disappear under her skirt and the other ending just below her knee. Haruhi's gloves are also different lengths.
Mira, the Token Girl of Bakugan: New Vestroia, wears a Spy Catsuit that goes halfway past the knee on the left side and barely past the waist on the right. This explains a lot about why they usually show her from the right side when not showing her from the front.
In Soul Eater, Death The Kid has a fetishistic preoccupation with symmetry, to the point of OCD, making his naturally asymmetrical hair (which he's stated he was unable to dye) all the funnier.
The flight suits worn by the Simoun Sibylla feature one bare shoulder and a large off-center gem.
Kaori Kanzaki, To Aru Majutsu no Index's resident Action Girl, has a pair of jeans that go all the way down on the right side and stop just below her waist on the left side. Justified, though, because the spells she uses apparently require the asymmetry.
Iceman Hotty from Basquash! wears shirts and pants with sleeves and legs of different lengths and a glove on one hand. The shirt and glove may be to hide his cybernetic left arm.
She may wear essentially normal clothing, but one has to wonder how long it takes Setsuna to get her hair to look like that. Even after Chao takes her hairband away her hair still doesn't match!
Angewomon. The asymmetry of one glove has a reason, though; it forms the bow of her Celestial Arrow attack.
Most Digimons' design in general become asymmetric as they evolve especially at the ultimate level e.g. Zudomon's fur on one hand and not the other. But is averted by MegaKabuterimon and Lilimon.
Fairy Tail: Lucy's clothes are also pretty normal, but she mostly has that side-bun thing going on.
Nanael of Queen's Blade has one full-sized wing and one half-sized one. This isn't commonplace for angels in that series, it's more an indicator she's The Ditz.
Puella Magi Madoka Magica: Sayaka's Magical Girl outfit has a diagonal cut on her skirt. Her hair is also done in an asymmetry, her hair longer on her right side, while her skirt is longer on the left side.
Lind from Ah! My Goddess has asymmetric hair which is longer on one side than it is on the other.
Maximilian Pegasus from Yu-Gi-Oh!, with the left side of his face covered by his hair, which hides another asymmetric fashion in the form of his Millennium Eye.
Manami of Glass Maiden/Crystal Blaze has two outfits where one sock comes up to her thigh and the other only to her knee.
The Weird has a largely black costume with asymmetric red highlights, including a knee-length left boot, an ankle-length right boot, a wrist-length left glove and an elbow-length right glove.
Teen Titans: Plain Cyborg, with a metal plate on one side of his head.
It is a comicbook tradition for characters who can take on the properties of various elements to strike poses changing body parts into as many different samples at once. Say, Animal-Vegetable-Mineral Man. Ones like Metamorpho have it as their base look.
Deathstroke the Terminator with his mask split between black and orange. Underneath, one eye is cybernetic.
Psylocke's best known outfit with its varyingly placed strips. Though this can depend on who's drawing her.
Cable has one techno-organic arm and eye. His outfit tended to be a shifting mishmash of shoulder pads, pouches, and bandoleros.
His dad Cyclops' drifts in and out of this trope; while his original and X-Factor costumes, and Astonishing and post were symmetrical, one of his most iconic costumes (namely, the one from the 90's cartoon) had asymmetrical straps.
Shatterstar... oh dear gods, Shatterstar. One oversized shoulderpad, one eye with a starburst design around it... oy.
Mazikeen has half her face simply missing. Whether this is cool or not is a matter of perspective. However, on Earth, she wears a half-mask to cover this up, and the intent is very much that people will think "oh, she's just a normal woman in a funky outfit."
To say nothing of Delirium.
It's eventually established that fashion has nothing to do with it. When she finds her face "fixed" Mazikeen swears vengeance on the good Samaritan.
Spider Jerusalem of Transmetropolitan has asymmetric Cool Shades — a green rectangle on his right, and a red circle on his left. The machine that made them was stoned on mechadrugs.
Several characters in Strontium Dog. Johnny has a big pad one one shoulder, to which is attached his blasterbelt that goes across his chest to his over hip. Wulf has the same arrangement, and in an early strip starts also wearing a Gronk's skin across the other shoulder. Middenface has a big tartan pad over one shoulder. Evans' mutation means that one of his arms is in the right place, but the other is attached directly to the side of his head.
In the Dutch series Franka by Henk Kuijpers, former minor villain, now supporting character Uschi Undsoweiter (Gratuitous German for "and so on") always dresses and does her hair asymetrically, frequently by assembling her clothes from parts of two or more different sets. But then she is an artist who now works for fashion mogul Laura Lava.
Magog from Kingdom Come has a single shoulder pad, a scarred right eye, and a gold/metallic left arm. He was originally imagined as an unflattering pastiche of Rob Liefeld characters like Cable and Youngblood, who were (in)famous for their hideously cluttered and asymetrical costumes. Surprisingly, artist Alex Ross ultimately decided that he rather liked Magog's design, and the character went on to get his own series.
Films — Animated
Ralph in Wreck It Ralph is missing one strap on his dungarees. Likewise, Vanellope's stockings don't match. Appropriately, the race car they make together is similarly asymmetrical.
Films — Live-Action
Luke Skywalker's single black glove in Return of the Jedi, as a result of his prosthesis getting shot on Jabba's sail bark and him not having the time to repair/replace the burned-of synth skin.
A sharp-eyed viewer will note that the Tron Lines of some of the characters in TRON: Legacy are deliberately non-symmetrical for no apparent purpose other than aesthetics. Quorra has asymmetrical Tron Lines, and an asymmetrical outfit and haircut.
One piece of Alex's attire in A Clockwork Orange is a set of fake lashes on one eye.
Literature
In Larry Niven's Known Space stories, asymmetrical beards are cultivated by upper-class Wunderlanders as a fashion statement (specifically, the statement "I have the free time and money to cultivate this bit of elaborate grooming").
In The Mote in God's Eye, moties are described as being incredibly asymmetric. They have one large arm with a three-fingered "gripping hand" on one side and two smaller arms with five-fingered hands on the other for fine manipulation. The rest of their bodies are asymmetric to accomodate the design, including a much larger shoulder and no ear on the "gripping" side. The Gripping Hand is also the name of the sequel.
High-ranking Seanchan servants in The Wheel of Time series shave the hair off half their heads, then braid the other half. This symbolizes their dual nature (lower-class people have full heads of hair; nobles have mohawks or shaven heads).
In Talon of the Silver Hawk, in the Riftwar Cycle, Tal spends a few pages mentally mocking high fashion in the kingdom of Roldem, which, at the moment, includes a jacket specially designed to be worn on one side and slung over the shoulder like a cape on the other. He, quite frankly, thinks it's ridiculous... but not half as ridiculous as some of the other things he's seen there, like a woman whose only upper body garment was a necklace so huge it very nearly kept her completely covered.
Played for Laughs in A Tree Grows In Brooklyn: a character with a horrible burn scar on one arm consistently wins masquerade-ball costume competitions because while all the women's dresses are provocatively cut, hers always have one long sleeve, which the judges think symbolizes"something."
In R.A. Salvatore's The Cleric Quintet a young evil magician Bogo Rath shaves one side of his head while keeping long hair on the other. He believes it's fashionable, and also enjoys how it annoys the older magicians.
The Hyper Card talking Picture BookBob was about a man named Bob who became more and more unsymmetrical until he made hatred of symmetry a popular cause... until someone noticed that "Bob" is a palindrome and an angry mob descended on him.
The Original Series' episode "Let That Be Your Last Battlefield" gave us the Cheron people, who are all painted white on one side and black on the other... and get into a genocidal civil war over which side they're painted on.
Judging from General Martok, missing eyes seem to be the Badass asymmetry of choice.
Deep Space Nine's final season introduces the Breen ships, which use asymmetry in their design to look as alien as possible.
Power Rangers SPD: Emperor Gruumm has one horn, though it was revealed that he originally had two until Da Chief hacked one off in battle in his younger days. In his final appearance, Da Chief (now a Sixth Ranger) fights him again, and is poised to kill him... but instead cuts off his remaining horn, quipping "Now they match."
That same year, the Ranger suits themselves were asymmetric, with one side colored and the other side black.
Another example would be Sou Yagaruma. He even gets some good old fashioned badass-styled insanity to go with his asymmetry, and nifty psychological reasons behind it!
Daisuke pulls this too, while transformed into Kamen Rider Drake at least, with a single giant dragonfly wing on his chest.
Kamen Rider Double is all about this as the show's premise but special mentioned goes to the Cyclone form, which has a gray muffler on the right shoulder.
In an episode of Sabrina the Teenage Witch, Sabrina changes the color of one Libby's knee-high socks from black to yellow in an attempt to embarrass her. Libby avoids embarrassment by turning mismatched socks into a fashion trend amongst her friends.
In Serenity, River wears a dress that has one very long, poofy sleeve on one side, and no sleeve on the other. Its not made clear whether this is how the dress is supposed to look or if its a modification she made herself, but it looks pretty nifty.
Punky Brewster, mainly in the first two seasons. She has on a pink vest over a blue shirt over a red shirt, a bandana tied to one leg, a yellow shoe on her left foot and a red shoe on her right. Her pants leg is rolled up on her left.
Music
Ziggy Stardust. Happens quite a bit with David Bowie's stage outfits from the period - striped unitard with one short leg and one long leg, anyone? Plus the pseudo-heterochromia. From getting punched in the eye.
The StingRay. While things like the Moderne and X-Plorer tried to invoke this, the StingRay was the only one of the offbeat designs to not change the shape of the guitar itself, and to use asymmetricaly as an intentional aesthetic choice.
Love front-man Arthur Lee was said to have invoked this trope in an attempt to get recognized in the Los Angeles scene of the 1960s, walking in with a different shoe on each foot and sunglasses which had different colors on each side.
When Jack Casady auditioned for bass in Jefferson Airplane, he was told he could get the job if he shaved off his facial hair. Moments later, he came back with only half of the side of his face shaved, saying he could use that half for performances.
WWE's Zack Ryder wore one-legged tights in his ECW run. He has since reverted to traditional trunks.
WWE wrestler JTG often wrestles in baggy jeans with one leg cut off at the knee.
"Rowdy" Roddy Piper painted his body half white and half black for his WrestleMania VI match with Bad News Brown.
Several other wrestlers have elbow pads or wrist bands only on of their arms, usually for practical purposes as that's the arm they usually attack with.
Sports
Many American Football quarterbacks wear a glove on one hand and use the other to throw the ball.
If cars can count, the British American Racing Team in the 1999 Formula One Season. Initially the team's two cars had entirely different liveries (one for each sponsor), which was deemed illegal by the FIA. After a failed arbitration process, the team opted to have each their cars sporting one sponsor livery on one side and the other sponsor livery on the other side, resulting in the famous livery with blue on the right side and red-white on the left side. This was dropped next season in favor of the red-and-white livery (when the sponsor for the blue color was let go).
Former Benetton driver Alexander Wurz used to wear mismatching colored shoes when racing. Reportedly they were good luck charms.
The Third Edition Player's Handbook uses asymmetrical outfits for the iconic characters representing the Bard, the Paladin, the Ranger, and particularly the Sorcerer.
Agents of the Order of the Emerald Claw in Eberron wear half-helms as part of their uniform that cover the right half of their faces, leaving only an eye-hole.
Warhammer 40000: Tau Fire Warriors have an asymmetric helmet with a slightly off-centre lens, while Crisis suit helmets have different antennae and eye sizes.
Theater
For Susan Hilferty, the costume designer in the Broadway musical Wicked, this was one of the guiding principles for designing for the chorus, intended to give an otherworldly feel to the outfits of the Ozians. It helped win her a Tony Award for Best Costume Design.
Toys
Most of Mc Farlane Toys' original character designs fall under this trope. One particularly notable example is their obsession with peg legs; for a few years it seemed like every other figure they produced had one.
Mantax, the Toa Hordika, the Piraka, and two of the Toa Mahri, Matoro and Hewkii, from BIONICLE, had one arm shorter than the other. Lariska, a character not released as a set, had a mechanical arm as the result of punishment from The Shadowed One.
Bionicle's successor, Hero Factory, seems to have this as one of its signature traits, especially in the early 2011 sets. Nitroblast◊ is the zenith of this trait, with Drilldozer a close second.
Video Games
It's become so deeply associated with Final Fantasy that fashionable asymmetry is now considered the norm with JRPG's. Their outfits tend to be so busy (see picture), you can't help but wonder how long it takes to get into or out of them. How does Lulu go to the bathroom? While people seem to think pretty much entirely Tetsuya Nomura's fault, Yoshitaka Amano's clothing was never big on symmetry either. People blame Nomura because his were the first designs to keep their details in the games. Despite Final Fantasy getting so much flak for this, it's something of a Dead Unicorn Trope, as most Final Fantasy games have perfectly symmetrical clothing. Only FF10 and FF7 have much asymetry, and FF7 doesn't have much, mostly armored bits and shields. Final Fantasy VIII, curiously, tends to avert this, as everyone's clothes are generally practical and symmetrical.
Nightmare/Siegfried reaches new heights of this in Soul Calibur 2; one of his alternate costumes is his partially corrupted self, missing most of the armor but still having the giant monster-arm, one gold (pupiless) eye and one blue eye, and having a raised arc of flesh identical to the arm across his shoulders. Note that one arm is bigger than the other because that's the arm Soul Edge possessed, which is why it's different from the rest of his body. Ditto with the eye. It's not fashion, it's plot-related!
Certain costumes from Talim and Xianghua include leggings of different lengths.
Sheogorath◊, of Oblivion, wears a crazy purple-and-yellow suit with twisting designs so complex it would take another page to describe. This fits in quite nicely with his role as God of Madness.
Similarly, in the previous game Morrowind, the god-king Vivec had gold skin on one side of his body and dark gray skin on the other. Also, you and some NPCs can wear gauntlets and pauldrons on only one side.
The player can achieve this in Skyrim, when wearing various types of armour. The various types of Leather and Studded armour have different details depending on who you get them from (Bandits and Forsaken are notably asymmetrical) whereas the demonic looking Daedric Armour features different length spikes and horns on either side.
Kalas from Baten Kaitos. Born with only one (swan-like) wing, so his grandfather made him a mechanical one to go with it.
Not to mention Savyna, who wears one thigh-high boot and one regular boot.
Rita from Tales Of Vesperia has one a long boot and white stocking on one leg, and a short boot with a red-and-yellow striped sock on the other leg. She even gets a costume where she wears a long black pantaloon-thing (held up by what appears to be half a garter belt) on one leg and merely a shin-high red stocking under normal black shoes on the other. The really asymmetrical part, though, is that her pantaloon is on the leg that's usually bare, and her bare leg is the leg that's usually covered by her long stocking. It's honestly kind of disorienting if you've been using her original costume all game.
Extended to ship designs in EVE Online. Very few of the ships are symmetrical, though the amount of asymmetry varies widely.
David Nassau, Marquis of Athlum wears a coat like this in The Last Remnant. One side is green while the other is red, representing the colours of Calapeleis, Athlum's sovereign city.
The Kilrathi in the wing commander series are noted for their disinterest in symmetry and aesthetics in general. This is carried over subtly with their ship design.
Protagonist Kyle Katarn◊ himself has consistently featured a single reinforced protective pad on his right shoulder (presumably to absorb recoil from the various BFGs he uses and reduce the strain on his firing shoulder, which is also his sword arm) ever since the games went 3D. Manages to look reasonable rather than distracting, probably thanks to averting Shoulders of Doom.
In all Jak and Daxter games, Jak from wears a single plate of armor on his left shoulder. It presumably protects him from having his friend-turned-ottsel digging his claws into his flesh, though he wore it prior to having a passenger in the parrot pet position. Also almost always part of his outfit are a three-strap bag and uneven goggles.
The gunner armor in Monster Hunter. Most have heavy armor on the left side, and little to no armor on the right side. Justified in that fighting a giant, fireball spitting wyvern, one would want to protect the side facing the monster, while the little armor on the other side justifies Gunner armor's universally lower defense.
The Divine Dragon has 7 wings (3 pairs and a single wing with a stump opposite it). The asymmetry carries into Dart's Divine Dragoon form, and actually gets worse since one arm takes on a likeness of the Divine Dragon's head and neck (this is used for the form's strongest attack).
Rose's outfit, which shows some leg on one side and Zettai Ryouiki on the other.
There's also Dart's normal outfit: A suit of chest armor with a fully-armored left arm and hand while he wears nothing more than a simple glove on his right. However, this is a practical norm for medieval swordsman, who would often employ their offhand in some form of defense while leaving their swordarm free and completely flexible.
The (now removed) Herod of the Scarlet Monastery dungeon from World of Warcraft was quite memorable in design for three reasons - a Spin Attack accompanied by him yelling "Blades of Light!", inexplicably not wearing a shirt while otherwise being fully-armored in mail armour and a full-face helmet, and wearing an enormous shoulder-pad on his right-side◊. Since that time, the model for Herod's one-sided shoulder guard has been re-used as a piece of heirloom gear you can buy for your alts, and at least one single-shoulder piece of leather armor has been added that players can purchase in Pandaria.
Ezio Auditore da Firenze, protagonist of Assassins Creed II, has a comparatively subtle example with his assassin attire. Over his left shoulder he wears a half-cape, with the opposite shoulder not similarly covered. His left hand, meanwhile, is bare; his right is gloved. It goes even further than that; the bracer of the first blade is on his right arm, decorated with the assassin crest, and worn over the sleeve. The blade on his right arm is silver and with a finish that makes it look like a feather. The second hidden blade's bracer is concealed under the sleeve on his left arm, and the blade has a black finish.
It's worth mentioning that capes like that were in-fashion at the time for people of Ezio's social standing. It's also sensible for someone who does a lot of sword-fighting with his right hand — it keeps the hand protected and the arm free.
In Brotherhood, Machiavelli's outermost garment is missing a right sleeve.
Fallout. One-sleeved leather jackets (Mad Max-style) seems to be the norm. When you finally do find a jacket with both sleeves still on, the game remarks that you might make a fashion statement with that one....
Armour is asymmetric in the one way that actually makes sense. The left, or shield, side is heavier (more armour plates, bigger pauldron) to facilitate defense, and the right is lighter to increase mobility and make attacking easier but has a heavier gauntlet since the forearm would be vulnerable while striking.
Morrigan's outfit is probably patched together from junk she found in her swamp, but you do have to wonder why she didn't even try to make her skirt an even length.
Isabela in the second game has light armour on her left arm while her right arm is mostly bare.
The protagonist◊ of Pokemon Colosseum. Partly justified, as that is actually the machine used to snag shadow Pokémon on his arm.
This even extends to many species, such as Absol, which has a horn jutting out of the right side of its head, and Sneasel, which has a feather growing instead of its left ear and fangs showing on one side. Some fans dislike the latter's evolution Weavile precisely because it loses the asymmetry.
Team Fortress 2: Engineer wears one welding glove on his right hand, unless the player is using the Gunslinger or Short Circuit, which replaces the glove with a mechanical hand. Sniper also wears just one fingerless glove on his left hand.
In the pre-release beta-designs, the Engineer, the Spy, and the Medic all wore their class symbols on an armband on their left arms.
Skies Of Arcadia largely averts this; almost every outfit in the game is symmetrical. The only major exceptions are Vyse and Drachma's eyepatches, Drachma's (weaponized) bionic arm, and Aika's left-hand glove, which she uses to prevent her giant boomerang from taking her arm off when it returns.
Mad Moxxi from Borderlands is "ragdoll sexy" in her asymmetrical attire, most notably her stockings: one fishnet, one striped.
Realistic example in Drakan: Order of the Flame - Two of Rinn's armor, the Chainmail and the Plate Mail, had the left arm armored while the right (sword) arm was unprotected.
In Kingdom Hearts, Terra and Ventus each have a single armored pauldron on their left shoulder. In Terra's case, it also comes with bits of an armored gauntlet, and Fingerless Gloves. It's functional, though. Hitting hte pauldron allows them to summon the rest of their armor, which is symmetrical, so it's simply a matter of traveling light, as it were. Aqua has bits of armor on both arms, instead.
In both Borderlands and Borderlands 2, all Sirens have a degree of asymmetry in their clothing and, in the cases of Lilith, Steele, and Angel, their hairstyles as well. Asymmetry is also present in both Roland and Axton's clothes, where they've put together components of their old military uniforms.
A few of the sword-wielders in the Fire Emblem games, particularly Ike and Chrom, have a single pauldron or gauntlet on their left side, but not on their right. As mentioned earlier, as medieval swordsmen, this has a practical purpose of keeping the sword-arm free while still protecting the off-hand, but in Chrom's case it also shows off the Mark of Naga on his right shoulder.
SHUFFLE! has Asa, who has one long lock of hair on her left side which she ties together with a brown band.
Web Comics
In The Order of the Stick, Pompey is a half-elf. This is represented by his having one pointed ear (and no ear visible on the other side, since elves are the only characters drawn with ears).
Kevin, of Kevin & Kell, has one ear that flops down and one that remains vertical (he's a rabbit). A theory was given in the strip that it had to do with having one parent with each ear type. However, his sister Danielle does not have this oddity (both her ears are straight). It also varies as to which ear does which (explained by the cartoonist in the FAQ as being based on which looks better in that panel).
Equius, Vriska, and Kanaya all have mismatched horns. Vriska also counts thanks to her robotic arm and Eyepatch of Power.
Fefetasprite and Erisolsprite don't just have mismatched horns, they also have mismatched cheeks. They're both fusions of an aquatic troll and a non-aquatic troll, and as a result have one horn from each troll and a gill structure on their right temple but not their left.
And in bonus material (and at least one commission), Jigsaw has at least one outfit that's long-sleeved on one side... and a series of askew straps on the other. Points for color-coordination, though.
Dan And Mabs Furry Adventures: Regina has one skeletal wing which she hasn't regrown because she thinks it "looks cool"; Clan Leader Taun's ceremonial armour covers her left arm completely, but leaves her right arm completely bare; Quoar and Abel are heterochromatic, considered a good omen; and Cindy has a third eye on the palm of one hand, apparently as a result of her parents being exposed to too much magic.
Maxim, the Bishōnen Jäger from Girl Genius, wears a glove and a spiked shoulderpad on one side.
Western Animation
Teenage Mutant Ninja Turtles: In the 2000s animated series, the Shredder's wrist-worn blades are on one hand only.
Wilt, of Foster's Home for Imaginary Friends, has one wonky eye, and one arm waaaay shorter than the other. This is explained in the season four TV movie, and in the pilot he mentions it may freak people out.
On another continent, Venger from Dungeons & Dragons has the one-horn thing going.
A number of Transformers have transformations that give them asymmetrical robot modes, but some are asymmetrical just to be stylish even though their transformation does nothing to prevent symmetry, including all of the Transmetals 2 from Transformers: Beast Wars.
The Snake Armour from the 200X version of He-Man and the Masters of the Universe, though "Fashionable" is arguable; it looked daft. Given it was armour, one has to wonder why half of it appears to be missing...
Teen Titans villain Slade wears a mask that is black on one side and orange on the other, and has only one eye (because Slade himself is missing an eye, in an incident only detailed in the comics.)
The minor character the Mechanist has several marks in one eyebrow and High-Class Glass on the other, and Jet has a larger piece of armor on one shoulder than the other.
Towards the end, Aang changes up his robes and goes for the over-one-shoulder look, and even his belt is off to one side.
Many of the fashions in Jem and the Holograms are this way, especially for the Misfits. You can blame the '80s.
Discord from My Little Pony: Friendship Is Magic features body parts that can be identified as being from many different animals, all to go along with his general theme of chaos and, you guessed it, discord.
Code Lyoko: Yumi's Lyoko avatar in season 4 is a bit asymmetrical, with a shorter sleeve on one side, a buckler-like bracer, one stocking different from the other, and sakura petals on her thigh.
The Trishas from Rated A for Awesome are identical except for the fact that they're mirror images of each other. One has a single earring on her left ear and her hair parts to the right, while the other has a single earring on her right ear and her hair parts to the left.
In Kim Possible, Shego's supervillain outfit is a harlequin-dazzle pattern of black and green. Her heroic Team Go brothers wear similar outfits, with blue, violet, or red instead of green.
Kim herself originally sported a belt with a pouch on her right side. In Season Four, when she updated her mission clothes, she added a utility pouch strapped to her right leg.
Betty Director of JG wears an eyepatch over one eye. Not because she lost an eye(on occasion she has lifted her eyepatch, revealing an undamaged eye) but because it looks cool.
Real Life
This has shown up from time to time in world fashions, periodically disappearing and reappearing in different forms. Examples follow:
In Europe and America during the 1870s it became common for skirts to drape asymmetrically. Note that the silhouette was still symmetrical, but the details were not — for example, there might be an upper layer of skirt that hangs more to one side than the other, but the skirt itself was the same width and length on either side.
Asymmetry was very popular in the later years of The Roaring Twenties and in part of the early Thirties. These styles included uneven hemlines like the handkerchief hem, which zigzags from long to short in order to mask a longer hemline, and skirts that ranged from knee to mid-calf length at the front and ankle to floor length at the back to mask the recessive hemlines that would mark the sihouette of The Thirties. (These are in some ways similar to the "high-low" skirts popular currently.)
Aside from skirts, hats on one side, necklines that plunge from turtleneck to Absolute Cleavage territory, and waistlines via bias cut were all the rage in 1930s silhouettes.
Today asymmetrical styles are increasing in popularity, including single-sleeved tops and skirts with uneven hems (either longer on one side than the other, or longer in the back than the front). This has affected both everyday fashions and evening dress, primarily in the demographic of women and girls age preteen to mid-twenties.
Doublet sleeves and stockings of different color were common in medieval and Renaissance periods (well, at least for those who could afford such clothes)— the style was called "mi-parti". The colors of city or ruler's arms were sometimes reflected in the coloring of guards' livery. With two colors involved, the whole livery could be divided along the longer axis of the body, or the livery could be cross-colored (i.e. right arm and left leg in one color, left arm and right leg in the other).
A lot of cultural clothing (e.g. in parts of Sub-Saharan Africa) tends to be asymmetrical, due to being made of one piece of cloth that is wrapped or tied around the body.
Side-ponytails, single earrings, etc. are all examples of this trope.
Hallmark of fashionable ladies' eveningwear throughout the Noughties — from about 2000 to 2010 the red carpet showed gowns with some sort of asymmetric neckline- draped over one shoulder, one diagonal strap, one sleeve, etc.. The 2011 Oscars were the first in years not to feature this heavily, but the styles in stores still have this trend going strong.
Sometimes there are more practical reasons for asymmetry, since the object worn is actually a tool rather than simply an accessory of article of clothing, so having more than one is unnecessary:
Wristwatches. One is fashionably asymmetric, two will net you weird looks. Three would be overkill.
Often, people with mobile phones or similar devices have cases with clips on them, allowing them to attach the phone case to their belt or pocket. More often than not, people clip their phones on the left/right side and nothing on the other side. Unless they have two phones for some reason.
Many people have clothing of unusual cuts or asymmetrical patterns to hide physical deformities. Hairstyles can apply for facial (or back-of-the-neck) coverage. Of course, many don't bother.
Some gangs wear their identifiers on one side of their body. For example, the People Nation identify on the left. They might wear earrings on their left ear or roll up their left pant leg.
Urban bikers (and the Hipsters that imitate them) will roll up one pant leg to keep bicycle grease from accidentally getting on their jeans.
Mounted combatants' armor often had asymmetrical pauldrons, which helped them brace lances. Whether or not this is fashionable is left as an exercise to the reader.
Further, lots of styles where one uses different weapons in each hand (sword + shield for instance) would have the armor or protective elements take the weight and defense needs into account. For example, Greek hoplites would only wear a shin plate on the left shin, as that would be the one exposed to the enemy.
Archers have one shooting glove for their string arm to keep their fingers from getting cut by the bowstring when they draw, and a bracer for their bow arm to keep it from getting cut by the bowstring when they release.
Spartans who displayed cowardice in battle were marked by having half of their beard shaved. It was legal to beat up any man you found with a half beard.
Automotive designer Luc Donckerwolke loves to include a bit of asymmetry his cars, most notably in the Lamborghini Murcielago which features a larger than normal intake for its oil cooler on the left side (compared to the smaller brake duct on the right) as well as an asymmetrically designed dashboard.
The AMC Pacer used to have asymmetric doors. The left door was longer than the right door.
The 2nd and 3rd generation Nissan Cubes have an asymmetric rear window that wraps around one side of the car but not the other. (It might be an attempt to minimize the driver's blind spot.)
Lady Fiddler crabs find male crabs that have ONE claw much, much larger then the other one to be a fashionable as the males use them to compete for females, by waving in the air and fighting with them.
One species of Japanese snake feeds exclusively on snails, which requires an asymmetrical mouth. One of its curved lower jawbones has peg-like teeth to grip snail shells, while the other has hook-like teeth to penetrate inside and drag out the tasty contents.
Flounders, plaice, and similar bottom-lying flatfish start out life symmetrical, but become asymmetrical as they grow up. One side of the fish becomes smooth and colorless, the other textured with camouflage-patterns, and one of its eyes shifts from the plain side (which normally rests on the seabed) to the colorful side.
