Folklore

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A trap for something with large paws.
 
I'm beautiful, no matter what they say!
 
Wood you like dinner?
 
Headless men
 
Spring Heeled Jack.
 
This Mule is on fireeeeeee.
1593 transported soldier legend Folk legend of a soldier who fell asleep in Manila and woke up in Mexico City.
Baltic Sea anomaly Looks like someone left their Millennium Falcon underwater.
Behind the sofa Where young British children hid from menacing scenes in sci-fi TV, now recalled humorously and nostalgically by British adults.
Bigfoot trap Believed to be the world's only Bigfoot trap.
Brites de Almeida A legendary 12-fingered Portuguese baker who baked a group of Castilian soldiers in her oven as part of the fight for Portuguese independence.
  Cottingley Fairies A successful photographic hoax in 1910s England which fooled Arthur Conan Doyle.
Count of St. Germain The original Tommy Wiseau, an eighteenth century polymath who made a number of contradictory claims about his origins, including that he was 500 years old. People have also claimed he is an important theosophical figure who many have claimed to have met years after his supposed death in 1784.
Easter Bilby How do you have an Easter Bunny in a country that has had a bad experience with rabbits? With an Easter Bilby of course!
Faxlore Forms of folklore circulated via fax machine.
Flying ointment A hallucinogenic ointment said to be used by witches in the Early Modern period.
Green children of Woolpit A tale of two purportedly green children who ate nothing but beans and claimed to be from a place where the sun never shone called Saint Martin's Land.
Headless men The most unknown, yet bizarre and intriguing, humanoid monsters in European mythology. Possibly more famous nowadays for having a cameo in Scooby-Doo! Mystery Incorporated.
Headless Mule They've got fire in place of their heads. Because regular mules are for weak people.
Heraclitus the Paradoxographer Before there were 14-year-old Internet atheists, this guy was saying "um, ACKSYUALLY" about Greek myth.
Icelandic Elf School Possibly the only school granting elf-spotting degrees. (Though certificates are also available from John Oliver.)
Josiah S. Carberry An expert on cracked pots, and one of only three fictional people to have won the Ig Nobel Prize.
Kaspar Hauser A German youth who claimed to have grown up in the total isolation of a darkened cell, and was once thought to be linked to the princely House of Baden.
Liver-Eating Johnson A 19th-century mountain man with a penchant for revenge and the consumption of livers.
Machine elf An entity that people claim they become aware of after having taken tryptamine based psychedelic drugs such as DMT.
Man-eating tree Hoaxes and unsubstantiated reports in Madagascar and elsewhere.
Mapinguari A cyclops in the Amazon rainforest.
  Mari Lwyd It's all fun and games until the horse skull comes knocking on your door.
Monkey-man of New Delhi Reports in 2001 of a strange monkey-like creature appearing in New Delhi at night and attacking people.
Nightmarchers One of the coolest creatures in Hawaiian folklore, a group of ghost warriors from the past that walk throughout the island, armed with oceanic weapons.
Panotti And you thought you had atypically large ears.
Phantom social workers Mysterious claims of "social workers" seeking to abduct infants and children.
Proverbs commonly attributed to be Chinese ...although they're probably not.
Pseudo-mythology The, very curious, cases of "invented mythology" in a few nations from europe.
Rods Photographic anomalies which some think are undiscovered flying creatures or miniature UFOs.
Russian reversal In Soviet Russia, Wikipedia edits YOU!
Spring Heeled Jack A mysterious character said to have existed in England during the Victorian age.
Telling the bees An alternative explanation for the declining bee population.
Tió de Nadal A log that defecates sweets for Catalan children on Christmas eve.
Titivillus The patron demon of scribes, responsible for many errors.
Tsukumogami According to Japanese folklore, if you keep a household item for 100 years, it becomes alive with a spirit, and may grow a face and teeth.
Vagina dentata The tooth, and nothing but the hole tooth.
Vampire pumpkins and watermelons In Balkan legend, an explanation for the blood-red streaks across these fruits: that they'd been left out on a full moon night, and thus turned by vampires.
Vril A book by the "dark and stormy night" guy that spawned rumours about German secret societies, a real master race living underground, and Nazi UFOs.
Well to Hell A 9-mile (14 km) borehole drilled by Soviet scientists uncovers the sounds of millions of damned souls. Hot stuff.
Witch window A superstitious practice in the State of Vermont to prevent witches from flying through open windows at night.
Yonaguni monument Between Japan and Taiwan lies the last remnant of the sunken continent of Mu (or rather, a natural rock formation that looks interesting enough to pass as it).

Mystery animals and animal folklore

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Looks a load of Bonnacon to me...
 
Pieter Dirkx's imagining of the Mongolian death worm.
 
That's either one fast-growing plant, or...
Bake-danuki Uses its testicles as a weapon.
Beast of Gévaudan A mammal(s) that went on a killing spree in southern France in the 1700s, causing significant and expensive Royal intervention.
Bird people The widely recurring motif in legends and fiction of birds who are people, or people who are birds.
Bonnacon A mythical ox which flings burning dung at its enemies from its rear and horn.
Cattle mutilation The alleged killing and subsequent mutilation of cattle, sheep or horses by unknown perpetrators. Some say they may be aliens.
Chupacabra A legendary creature in the folklore of parts of the Americas, generally reported in Latin America, that preys on livestock.
Cynocephaly A kind of human-wolf hybrid where only the head is dog-like.
Dog spinning Do Bulgarians really twizzle their domestic canines to foretell prosperity? The British Green Party thinks so, and they're not happy about it.
Drop bear A fictitious Australian marsupial supposedly related to the koala.
Fearsome critters North American lumberjack folklore, with Axhandle hounds and jackalopes.
Flying pig The classic impossibility has been officially proved possible by the Internet Engineering Task Force: "With sufficient thrust, pigs fly just fine."
Gef the talking mongoose A poltergeist-like creature which claimed to have been an 80-year-old Indian mongoose, alleged to have haunted a Manx cottage during the 1930s.
Humanzee A hypothetical(?) human/chimpanzee hybrid.
Jersey Devil A mythological creature said to inhabit the New Jersey Pine Barrens.
Liver bird A legendary cormorant or eagle that is the symbol of a major English city.
Living entombed animal Tales of toads and other creatures supposedly remaining alive encased in stone.
Lluvia de Peces It's raining fish in Honduras.
Mamlambo One of the most interesting beasts in Zulu folklore.
Mongolian death worm A large, bright red worm that kills using acid and electrical discharges – allegedly.
Montauk Monster Actually a decaying raccoon... or is it?
Pacific Northwest Tree Octopus An endangered creature, whose major predator is the sasquatch. Apparently.
Phantom kangaroos They're not just found in Australia.
Popobawa A bat-winged monster from Zanzibar said to sodomize people during election campaigns.
  Pig-faced women A lesson never to compare a person's children to pigs when pregnant, lest you be cursed.
Rat king Not the rodent monarch familiar from The Nutcracker, but a rare (some say nonexistent) phenomenon in which a group of rats grow up with their tails tangled in a knot.
Reptilian humanoid A recurring theme in fiction, especially science fiction, pseudoscientific theories and conspiracy theories.
  Rhinogradentia A fictitious mammal order documented by an equally fictitious German naturalist.
Sea monk An aquatic hallelujah.
Sidehill gouger Fictional creatures said to inhabit the Rocky Mountains of British Columbia and the southwestern sandhills of Saskatchewan.
Spherical cow "Consider a spherical cow in a vacuum..."
Squonk A Pennsylvania-based creature that cries constantly because it's so ugly. The most relatable mythical animal.
Tarasque One of the strangest mythical beasts in France.
Vegetable Lamb of Tartary Money might not grow on trees, but maybe sheep do.
Widow's man A strange myth that fishmen and seamen have been telling for centuries now.