The above link takes you to a video produced by the Mormon Newsroom for YouTube, explaining the sacred temple garments worn by worshipers in the LDS. Its primary purpose is to refute the idea of "magic underwear". This gets a great deal of play in the American Media, partly because of the popularity of Trey Parker and Matt Stone's popular Broadway musical The Book of Mormon and partly the historic tension the LDS community has had with American Christianity, playing off of religious tensions that America likes to pretend it does not have. While the official position of the LDS is that the garments are not "magic", other faiths have at times embraced the idea of the power of magic underwear.
In what some anthropologists believe to be a direct link to the temple garments of the Mormons, the Lakota warrior known as Kicking Bear introduced the idea of the Ghost Shirt to his people around 1890. He and another warrior, Short Bull, believed that the shirts would protect the wearer from bullets. This belief lead to deaths 153 Lakota, with another 50 wounded and 150 never found (estimates vary by source), at the Massacre of Wounded Knee on December 29, 1890. It should be noted that Wovoka, founder of the Ghost Dance faith, sanctioned neither the Ghost Shirts' supposed magic properties nor the use of violence in driving off the white man. Instead, he taught that God had given him a vision that if all the Native people's in the west would perform a dance that called upon the spirits of their ancestors the white man would be driven east and the lands would be transformed into a paradise of abundant resources. While popular among many tribes some, like the Navajo, never incorporated it into their practices.
Other faiths have their own sacred underwear as well. Based on Numbers 15:37-41 Orthodox Jewish men wear a garment called a tallit katan, a small rectangle of cloth with fringes at the corners, over their shoulders and under their shirts. The yajnopavitam is a thread worn by Hindu males under their clothing wrapped around the body. It is made of three strands representing mind, word, and deed and is typically given at a boy's coming of age ceremony as a sign of second birth. One of the five "K's" of the Sihk faith is the Kachera, or soldier's garmet, that is worn as underwear but can be outwear when playing sports or swimming. It represents chastity for the Sikh man. A cilcie is an uncomfortable undergarment ranging from course hair to barbed metal rings used to remind the faithful of their sin and need for atonement in several faiths but recently it is most popularly associated with the ultraconservative Catholic organization known as OpusDei. Do not get your information about them from Dan Brown, look it up yourself.
Personally, when I was a child I thought my Superman Underoos were magic.