Science fiction and fantasy stories are familiar plot twisting grounds for the Möbius Band. "The No Sided Professor" and "A Subway Named Moebius" are just two examples. Literature also has some quite unsuspecting employments of the Möbius Band with "The Bald Soprano" by Eugene Ionesco and "The Gift" by Vladamir Nabokov given as examples in the web site "Math That Makes You Go Wow"
Flexagons have also been used in book art and here are some examples:
Children's books as flexagons - Chasing Your Tale, Ready or Not-2, I Like It Here, and Look Closely.
Voces de Mexico (Voices of Mexico) is a book with Mexican quotations appearing on a flexagon.
Idaho by The Book uses a tetraflexagon to produce a unique literary map of Idaho.
With the success of "The Lord of the Rings," maybe someone will write a sequel, "The Lord of the Flexagons." With the infinite varieties of flexagons and their applications, one could easily imagine series of both books and movies where flexagons flourish. There may be even 'one side' to a lot of the special effects in addition to a lot more sides!