Double-Sided Book

A book with two different stories- you read one side, then flip the book over and read the other one. The technical name for this type of book is tête-bêche; it is sometimes improperly called dos-à-dos, which properly refers to an even stranger book style that has two spines.

Examples of Double-Sided Book include:

One of the Ghostwriter books (and possibly more) was this- each side of the book told the story from a different character's viewpoint.
Mr. and Mrs. Smith, though the upside-down version only had the initial chapter in which they meet from alternating points of view.
Ace Books used the format in their Ace Doubles series from the late 1950s through to the early 1970s. Most of the Ace Doubles comprised one book by an established author and one by a relative unknown, in an attempt to boost the unknowns' recognition. It's also worth noting that because of the Doubles' fixed page lengths (usually between 256 and 320 pages) novels often had to be abridged to fit.
This is also the format of the large-format Monty Python's Life of Brian / Montypythonscrapbook.
There's a book that came out just before the last Harry Potter that offered the evidence for and against Severus Snape, with one side's arguments in one half and the other side's in the other half.
Only Revolutions by Mark Z. Danielewski.
One of the Star Trek: Deep Space Nine relaunch books, called Fearful Symmetry. The dualism implied was covering both one woman (Iliana Ghemor) who was surgically altered and sent into deep cover as another woman (Kira Nerys), and their mirror-universe counterparts.
Yin and Yang, a short play about Erast Fandorin, is like this. Each side of the book contains exactly the same criminal case with only a few key differences that lead up to a largely different conclusions.
The Strategy Guide for Ghostbusters. One side is the "Realistic" version for Playstation 3, Xbox360 and PC, the other is the "Stylistic" version for Wii and Playstation 2.
- Other cross-platform-but-different-for-each games have done the same thing; off the top of this troper's head this includes Star Wars: The Force Unleashed and Indiana Jones and The Staff of Kings.
Manga anthology magazine Yen Plus works like this, but slightly different from the usual; manhwa and OEL manga (which read left to right) are on one side, manga (reading right to left) on the other.
Brian Froud's Bad Fairies/Good Fairies. The critter in the middle could look like either, depending on which way up the picture is.
In-universe example: In Naruto, Sai has an art book featuring pictures of himself and his brother on their respective journeys through life, each tale chronicled from opposite ends of the book. The picture in the middle is not completed.
Split Screen, one of the sequels to Geography Club (about the members of a high school gay-straight alliance) by Brent Hartinger did this.
The Pirates! In an adventure with scientists and " " Ahab.
The Incredible Journey to the Center of the Atom by Trevor Day and Nicholas Harris is a popular science book which - depending on whether it is read forward or backwards - takes the reader on a trip from the vastness of the galaxy to the individual nucleons, or vice versa; and provides either scientific commentary, or poetic musings, depending on the way.
There was a tell-all book published about 12 years ago about legendary basketball coach Bob Knight, made in the upside-down way. One side was titled "What A Knight!" and praised his coaching prowess and talked up his skills on the court when he was in his prime. The other side was titled "Knightmares" and generally dealt with Knight's Training from Hell as applied to his players, and his General Ripper relationship with the media.
Comic Books example: the last issue of the anthology FantaSci, published by Apple Comics, was labeled "An Apple Turnover", with one story on each side, and a centerfold picture of an Eldritch Abomination that looked equally horrible either way up.

Tabletop RPG

Traveller Classic's "Double Adventures" were like this. Each book had two mini-adventures, printed upside down to each other.
Several Dark Sun adventures for Dungeons & Dragons used this format: DS1 Freedom, DSQ1 Road to Urik, DSQ2 Arcane Shadows, DSQ3 Asticlian Gambit and DSE1 Dragon's Crown.
The Call of Cthulhu (tabletop game) double adventure The Vanishing Conjurer/The Statue of the Sorcerer, by Chaosium and Games Workshop.
The third edition of In Nomine Satanis/Magna Veritas had In Nomine Satanis on one side of the book, Magna Veritas on the other.

Other

Many, many equipment manuals with English on one side and Spanish or French on the other.