Seen in one of the Verizon "Dead Zone" ads. They Speak In Unison and try to be creepy, but because the guy has a Verizon phone...
Anime and Manga
Hansel and Gretel from Black Lagoon take this trope to a whole new level. While initially they are fairly distinctive (one is a boy, and one a girl) despite similar looks and personalities, it is later revealed that they swap the roles of 'boy' and 'girl' around as they please; Hansel wears his sister's clothes, a long-haired wig (both the twins actually have short hair), carries her weapon, and takes on her voice and personality, while Gretel does the same with Hansel's personality. The twins' gender is never actually revealed, which just adds to the confusion. Not to mention they just love killing people, just because they can. They also like to "play" with their victims. Is it surprising that everybody in the anime compares them to the twins from The Shining? In the manga, "Gretel" even sings the tune that plays over The Shining's end credits.
They also actively practice Twincest and were made to work as underage porn stars in snuff films. It's highly suggested that they just... broke... as a survival mechanism.
Not to mention their disturbing optimism which centers around the deaths of others, which they cling to even as they die themselves.
The twin girls Xia Yu Fang and Xia Yu Lan from Full Metal Panic! The Second Raid
The Liebert twins, Nina and Johan from Monster, at least when they were children. Nina has since grown up to be a hardworking and productive member of society, while Johan has grown up to be a sociopathic manipulator and mass murderer who has been compared to Adolf Hitler and the devil himself.
0010+ and 0010- in Cyborg 009. A small subversion, since the twins are * full-grown adults* and not children/teens as usual.
The Watahiko children in Mushishi. While not actually twins, they pretty much look the same, and share a single mind. Or more accurately drones/appendages of a single entity. The real Watahiko is a sentient fungus.
The Sonozaki twins in Higurashi no Naku Koro ni. Though they're not really creepy as a pair, they each have their own distinct creepiness.
Hisui and Kohaku from Tsukihime. Though they are faithful maids of the main character, it's as if they were hiding something...
Only Kohaku fits here: contrary to her cheerful demenor is in fact almost completely emotionally dead due to being repeatedlyraped by Makihisa Tohno and later SHIKI Tohno since she was 8 years old, something that caused her to hold a twisted grudge against the entire Tohno family. Despite her stiff behavior, Hisui is honest to a fault and completely loyal to Shiki, not to mention she actually has suffered quite a bit due to all the horrible crap that her twin sister had to go through.
Muhyo And Roji has Lili and Maril. They know too much, and behave suspiciously even after they help Roji fight some evil spirits.
Tsubasa Reservoir Chronicle, with the vampire twins Subaru and Kamui who are running away from a psychotic Seishiro for poorly explained reasons, and the "cursed twins," Fai and Yuui. When the latter twin became convinced that he killed his brother thanks to Big Bad's Mind Rape, he took his brother's name and became the series's biggest angst muffin.
Xxx Ho Lic: Moro and Maru, Yuuko's two assistants at the shop. It's revealed early on that they have no souls, and later, that they keep the shop grounded between dimensions.
Deadman Wonderland: Ichi and Hajime, who at first seemed to be a single, creepy Forgery kid with a lollipop.
Loveless: Yoji and Natsuo, who, despite not being actual twins, certainly fit aspects of this trope and usually act like one mind.
Kakurenbo: Inmu and Yanku. They never speak, have glowing red eyes and act together a lot. They seem to have supernatural qualities without being supernatural, such having a strong sense of smell and being real fast. Also, you don't even know who's who - it may be believed Inmu is the one in red, but that's never been verified.
Souya and Shirase aka (the cute boys who work as Sanetoshi's assistants) in Mawaru-Penguindrum.
In Yu-Gi-Oh! Yami Bakura's later deck includes a magic card called "Cursed Necro Twins", or "Cursed Twin Dolls" in the dub. The illustration includes two ghastly looking girl twin dolls holding presents. When one player chooses a present, the other player is forced to choose the remaining one. The card is meant to manipulate Bakura's card graveyard.
Space Runaway Ideon has the twins of the Buff Clan, a pair of short-lived villains who attempt to destroy the Ideon.
Arron and Gurran Schmittel in Armored Trooper Votoms, a pair of cryptic, cold scientist brothers who nevertheless take amusement in seeing how they can experiment in increasing Ypsilon's negative emotions. They even initially tend to finish each others' dialogue, when they're not engaged in sibling banter.
The series Kabuki featured twin assassins collectively named Siamese — former Siamese twins joined at the shoulder, and given cybernetic arms when surgically separated. They're portrayed in a fairly creepy fashion; although they do get a sympathetic scene at one point in the series, it's somewhat negated by the fact that the left-handed one is busy sewing all her stuffed animals' mouths shut at the time.
Fenris (the collective name of Andreas and Andrea von Strucker) had superpowers, but only when in contact with each other. As such, they were often found holding hands. As if that weren't enough, Andrea died, so Andreas had her skin tanned and made into a leather grip for his sword so that he could maintain his powers. Ick.
Later, Andrea was resurrected, so Andreas had the skin flayed from his arm and given to her. Those crazy kids.
At one time, Deadpool fought against two Britney Spears-esque twin sisters called "Mercy Sisters". They didn't finish each other's sentences, but they sure were creepy.
One of the most famous examples in the Western world would be the creepy sisters from Stanley Kubrick's film version of The Shining (though their ages are stated as different in the film — 8 and 10 years — they look identical and are actually played by twins). They were based on a photo of a set of twins taken by Diane Arbus.
Another well-known example from Western movies: "The Twins" from the Matrix trilogy.
Although, quite frankly, they'd be creepy even if there was just one of them.
In some instances, the creepy twin effect is caused by a split brain situation, where each twin has half of the same brain. Some examples include the film Slapstick Of Another Kind, and the movie The Nightmare Before Christmas. It also occurs in the novel The Singers of Time due to a set of conjoined twins sharing one brain at birth, who are then separated.
The Nicolas Cage remake of The Wicker Man features a pair of creepy old female twins.
The main characters of a creepy Japanese film called Wool 100%. They're at least 60 years old, live in an isolated junk-filled mansion, and still dress the same as when they were teens (one wears only blue kimonos, the other green western dresses). Them coming to terms with their It's All Junk - filled house starts when a little girl suddenly materializes from a ball of red yarn.
In Hellraiser Inferno there were the Wire Twin Cenobites, who also appeared as elderly human sisters.
Who were infinitely creepier than the bondage model cenobite versions.
There were also the Siamese Twins Cenobites from Hellraiser: Bloodline, who were fused at the head and only ever emitted growling noises.
There were two silent vampire twins in Hammer Horror's Vampire Circus.
Mu-rong Yin and Mu-rong Yang in Ashes of Time, brother and sister, apparently. They are very hard to tell apart, one time a character realizes only in the middle of the conversation that he's talking to the other twin. Both ask the same hitman to kill the respective other. Turns out they are two personalities in one body, eternally fighting
Harry Potter and the Half-Blood Prince has creepy twins in the background. They are not in the book. The movie adds them on to build a darksome atmosphere.
Troma's War has creepy Siamese twins, joined at the head, one with a high-pitched voice, the other with a low-pitched voice.
The 5,000 Fingers Of Dr. T features a pair of roller-skating twins who share a conjoined beard, with which they attempt to strangle the protagonists.
The eels Flotsam and Jetsam from The Little Mermaid fall under this trope. True, they may or may not be twins, (One eel looks pretty much like another.) but the scene where they talk Ariel into going with them to see Ursula is pretty creepy.
It should also be noted that one of them is blind in his left eye, and the other in his right.
The mages Beltira and Belkira from David Eddings' Belgariad have a tendency for finishing each other's sentences (This was retconned in the prequels, where they play a much larger role and speak and act normally). However, there is a slight difference between them, as Belkira would allow himself some ironic comments Beltira would never say. (Although they're good guys.)
[Meanwhile, the Weasley twins are taking bets on the champions’ survival:]
FRED (OR GEORGE): Three lads!
GEORGE (OR FRED): One lady!
FRED (OR GEORGE): Four go down—
GEORGE (OR FRED): —but do four come up?
The Carrow siblings aren't twins, but they are physically similar (squat, short). They also share a creepy wheezing laugh and are sadistic Death Eaters. And then in Deathly Hallows they become teachers at Hogwarts, teaching anti-Muggle propaganda and forcing kids to use the Cruciatus Curse against one another as punishment.
Emmeline and Adeline March in The Thirteenth Tale who speak their own twin language and don't realize that other people are real.
Violet and Verbina in Dean Koontz' The Bad Place.
Deek and Steward Morgan in Toni Morrison's Paradise are the psychic brand of creepy twins, seemingly never talking to each other, but always knowing what the other means, causing discomfort from the townsfolk.
An episode of Smallville featured mutant twins, referred to by the leader of their trio as the "Wonder Twins" for yet another comic book Mythology Gag. Not only did the two have identical grotesque appearances and Igor-like mannerisms, use their power by touching, and finish each other's sentences (to the chagrin of their leader), but they also shared pain.
In Joan of Arcadia's season one finale, God appears to Joan as a pair of twins (or does he?). It is pretty effing creepy.
Jekyll: Claire and Tom's twin kids are mostly normal throughout the series, but at the end, it's strongly implied that they've inherited the Hyde personality from Tom... and may in fact represent the divide rather than keep it lurking within themselves. Such as when they get bored and "switch" while confined in cells the size of beer kegs.
Doctor Who has played with the trope a couple of times:
In "The Eleventh Hour" Amy and Rory encounter a woman holding hands with two little girls. Although not twins, the girls look very similar and are dressed identically. The creepiness comes from the fact that all three of them are actually a single alien "multiform", who gets confused and starts talking out of the wrong mouths with the wrong voices.
Lampshaded in "Night Terrors". While searching an apartment building for a "scared kid", Amy encounters a pair of twin girls. She later asks the Doctor "I found scary kids, does that count?"
Zorn and Thorn from Final Fantasy IX are extremely annoying examples of this trope, as they are nearly identical in appearance (with the exception of their colors) and constantly repeat what the other twin says (only in reverse with the case of Thorn). It turns out though that they aren't twins at all, but are really one grotesque and horrific monster that somehow poses as Creepy Twins.
Alexia and Alfred Ashford in Resident Evil Code Veronica, who are seen at one point in a home video tearing the wings off a dragonfly and feeding it to ants. Let's not also forget that Alfred misses his sister so bad from her being in cryo freeze that he dresses up as her, and honestly believes he IS her, until he's caught half-way between identities and looks in the mirror. Think less Wholesome Crossdresser, more Psycho
Any of the Twins enemies in Persona3. It's that rattling sound they make, and the fact that they're skewered together.
Valkyrie Profile: Covenant of the Plume has Mireille and Mischka, a pair of twins who enjoy slaughtering people, are part of a mercenary group and display very good fighting skill despite being only twelve.
The twins Martha and Lindsay from Catherine, with their odd speech and unsettling amount of knowledge about the nightmares. In a variation for the trope they're old ladies.
Strange and True, the conjoined "Amazing Twins!", from Nightmare Ned bicker more act like each other, but they're still pretty damn creepy.
The Visual NovelMidori No Umi has Sorane and Rikuno, an unsettling pair who are almost completely indistinguishable from each other, aside from a few minor features like theireyes, are heavily into tarot cards, and speak every single word of their dialogue in unison.
Gwendolyn and Charlotte Somersett, imperiled twin girls from the Ravenhearst game series, are justifiably creepy, both because they're ghostly Single-Minded Twins, and because they spent most of their (brief) lives being browbeaten and terrorized by Charles Dalimar, who kidnapped them and their mother to be his ideal "family". Hearing them call the abductor who trapped their souls "Father" while speaking in synch with one another could creep anyone out.
The Cave has a set of twins as a playable character; and boy are they creepy constantly holding hands doing everything together, evil red eyes and extremely dated fashion sense. Turns out they're Victorian twins that belong to a loving caring family but because said parents never let them leave the house, they go to great lengths to kill their parents...and dogs...and ponies!
Rosalyn and Robert Lutece from Bioshock Infinite. They're actually parallel universe versions of the same person.
In Vocaloid, we have a few instances where twins Rin and Len Kagamine follow this trope to a T. Especially in Trick or Treat where they trick Miku to play with them and eventually eat her.
In the video for Oomph!'s "Augen Auf" (Hide and Seek), the group of Enfant Terribles includes two identical twin girls who are perfectly syncronized.
ThisDewey Defeats Tarzan strip features twin girls who are creepy even to their mother, and a reference to The Shining.
thingOne and thingTwo from The Motley Two don't really embody this trope (they finish each other's sentences, but it's annoying rather than creepy), but when they face Tetras, against whom they hold a grudge, they decide to invoke this trope for sake of creeping her out.
Sokara and Setesh Vu Noi in The Gungan Council are insanely creepy in the way their minds are linked.
A creepy parody: "The Delightful Children from Down the Lane" in Codename Kids Next Door are not identical, and there are five of them, but their manner of speech and behavior are dead on for this trope. One episode also featured their cousins, The Interesting Twins From Beneath The Mountain.
Sherri and Terri, the purple-haired twins of The Simpsons fame, have only occasional creepy moments.
Más y Menos from the TV adaptation of Teen Titans. They're actually good guys, but when Brother Blood had them under mind control, they definitely fit this trope.
Invasion America has Simon and Sonia, a pair of genetically-engineered Half-Human Hybrid assassins, complete with psychic link. What made them creepy before Sonia's Heel Face Turn was that half the time, they didn't even speak to each other. They just shared looks, and you could tell by their expressions that they were communicating through thought. Simon, definitely the scarier of the two, also had a habit of torturing Sonia through their link as well.