Hair is a powerful thing in folklore, whether it's the long hair of a great warrior (or beautiful woman) or the tanned fur of a powerful beast. Anyone familiar with the Old Testament of the Bible will have heard of the story of Samson. He was a warrior granted super-human strength by God, but his power was tied to his hair--cut his hair, and he would lose strength, which was exactly how he was finally defeated (and re-growing his hair allowed him to get his revenge). In the Swedish folktale "The Magician's Cape," an evil magician gets a tear in his magician's cape and the heroine sews it with her own golden hair--it glows so brightly that he can't sleep, and has to mend his evil ways and undo his evil deeds to get it to stop shining.
There are also many stories about magical garments. There are invisibility cloaks such as the one called the "Mantle of Arthur" in Cornish folkore or the "Tarnkappe" of Sigurd from Norse myth. The brothers in the fairytale "The Thirteen Swans" (it's had other titles, as well) were returned their proper human shape by shirts woven of nettles by their sister, and the Persian hero Rostam had a coat called "Babr-e Bayan" which was fire-, water- and weapon-proof.
Shapeshifters often used a magical skin to take on animal shape--an example is the selkies of Celtic folklore who can be forced into marriage by stealing their sealskins while they dance on the beach.
And the power of many magical garments derives directly from their origin as the pelts of legendary creatures. In Greek myth, the hero Herakles (or Hercules, in its Roman form) fought the Nemean Lion and discovered it was immune to weapons due to its golden hide. To defeat the beast, he had to strangle it, and then discovered that no weapon could skin it either--he was finally able to collect the pelt by using the lion's own claw. The hide then became a protective garment. Similarly, the Biblical Leviathan had a skin that was supposed to be good for making impenetrable armor and protective clothing.
The myths, legends, and fairytales of all parts of the world are full of such stories of amazing creatures and the heroes that battled them. The hero-monster encounter was often part of an "impossible task" set by the hero's enemies in order to defeat him, or by his prospective bride in order to test his worth. Frequently, as with Herakles, the hero had to bring back the hide of the animal, which retained some of the creature's legendary powers and gave the hero even more strength.
Two such magical garments have appeared in manga (and through manga, anime)--and if readers know of more examples, I'd love to hear about them--the chanchanko vest worn by Kitaro in GeGeGe no KitarĊ and the kimono or robe worn by the title character in InuYasha.
KitarĊ is the last member of the yokai Ghost tribe, and he wears a black and yellow chanchanko vest woven from the hair of his ancestors. This is no hair shirt (an itchy, chafing undergarment worn as penance by followers of various religious and philosophical traditions), but a powerful artifact in the form of a garment.
A chanchanko is a kind of vest or jacket lined with down or other fibres usually worn by the very old or the very young in Japan. Traditionally, when a man turns sixty he is considered to have reached old age (many years ago when people's lives were shorter, the age was even younger than sixty), and he is given a red chanchanko that symbolizes a return to childhood--the red color represents warmth--and is supposed to ward off evil and bad luck. Essentially, you might say, a chanchanko is a protective garment, whether it's protecting from the cold or from harmful forces.
KitarĊ's chanchanko is also protective, and it even turns red when used. Its power presumably derives from the yokai who donated the hair for its weaving and it protects the wearer from danger--it can even help a friend or hinder an enemy when KitarĊ isn't around to control it.
InuYasha is a half-demon who has a robe made from the fur of a fire rat, inherited from his human mother who was given it by InuYasha's demon father to protect her. The Robe of the Fire Rat, like KitarĊ's chanchanko, has protective qualities and is red in color. InuYasha's robe can protect the wearer from normal weapons and may even reduce the effects of magical weapones, but it is especially effective against heat and fire. Any spells and barriers against yokai, however, will turn the robe to normal cloth, as it was created from the fur of a yokai.
The Robe of the Fire Rat has its origins in the 10th century Japanese folktale "The Tale of the Bamboo Cutter" in which it is one of the items in a series of impossible tasks set to test the suitors of a magical woman. In this folktale, it was said that the robe had been transported to China by a priest from India and was kept in a temple in the western mountains. In one version of the story, it was made of bluish-black fur tipped in shining gold and kept in a box inlaid with precious stones, while in another version it was of a silvery color that was supposed to become even more silvery each time it was exposed to fire. When tested for authenticity by being placed in a fire, however, the robe burned to ash, revealing it as a fake. In the tale, the true robe was never found, if it ever existed.
Like KitarĊ's chanchanko, InuYasha's fire-rat robe derived its magical properties from the yokai it was made of, just as magical pelts and garments in other cultures are powerful because they are made from magical creatures.