(Osmond 1979) Art Fleming's TV Game Show Fact Book by Art Fleming, Richard Chapin and George Vosburgh [Art Fleming on cover]
Mostly a quiz and fact book broken down into some three-dozen categories, plus a chapter of the original host's memories and the obligatory "how to become a contestant" info.  Not specifically a Jeopardy! item (the show had already been cancelled) but of interest to fans, and still somewhat useful to would-be contestants even today!

    (Harper 1990) The Jeopardy! Book by Alex Trebek and Peter Barsocchini [Alex]
    (Harper 1992) The Jeopardy! Challenge by Alex Trebek and Merv Griffin [Alex]
The first of these "official" books includes a lot of information about the show itself, along with many sample game boards and contestant tests.  The second book is almost entirely games from various tournaments.  Though Trebek and Griffin are credited as authors, their contributions are limited to a forward and an introduction.  The games, of course, were created by the show's team of writers.
 
    (Warner 1992) Secrets of the Jeopardy! Champions by Chuck Forrest and Mark Lowenthal
Hints, fact lists and quizzes prepared by former big winners and not endorsed by the show.
 
    (Northwest 1993) Inside Jeopardy! by Harry Eisenberg
    (Lifetime 1995) Jeopardy! by Harry Eisenberg
The two Eisenberg works are mostly the same book, but with some fascinating differences.  Eisenberg was a former writer and producer on the program whose first book was a behind-the-scenes account that included some pretty juicy revelations of what he considered to be improper behavior on the show, most notably his accusation that material was changed at the last minute to help specific female contestants.  The second book has mostly the same material, but with a lot of the more troubling accusations removed.  Even more interesting, the first book's publisher claims Sony Pictures threatened them with a lawsuit, while the second book is praised with a blurb attributed to "The Producers of Jeopardy!"
 
    (Citadel 1998) How to Get on Jeopardy! and Win! by Michael Dupee
Another book by a former champ ( the 1996 Tournament of Champions winner), this one offers a lot more in the way of behind-the-scenes details and wagering strategies.
 
    (Sony 2000) Jeopardy! Quiz Book (1-4) Four volumes
Also known as What Is Jeopardy! Quiz Book? (1-4), the first two volumes, each of which features 700 answers and questions from the series, were published simultaneously. A third and fourth volume were released together late in 2000.  The first two volumes were also released as a single, thicker book, and other combined versions may have been released as well.
 
    (Barnes and Noble 2004) This Is Jeopardy! [Foreword by Alex, who appears on the cover]
Sample qualifying tests, 400 Final Jeopardy clues, behind-the-scenes info, trivia and much more in this paperback "official companion" to the series.
 
    (Crown 2006) Prisoner of Trebekistan: A Decade in Jeopardy! by Bob Harris [Harris on cover]
Bob Harris was a five-time winner and Tournament of Champions finalist who, as he points out, has actually lost about as many games as he's won through various invitatrional tournaments that followed.  More a memoir (often a very funny one) than a how-to for wannabe contestants, though that's in there too.
 
    (Villard 2006) Brainiac: Adventures in the Curious, Competitive, Compulsive World of Trivia Buffs by Ken Jennings [Jennings on cover]
More than a Jeopardy book, this work by the show's longest-running champ is a study of trivia itself, and the people (like himself) who are interested in it.

    (Sony 2005) Jeopardy! - An Inside Look at America's Favorite Quiz Show [Alex on cover]
A handful of selected epiosdes (including the 1984 debut, Ken Jennings episodes and the three-part final of the Ultimate Tournament of Champions) plus behind-the-scenes features.