I can only recommend what I've read, so this listing consists only of the books I own, which I would recommend.
And yes, I do own all of the following books.  I am a book worm by nature, and reef-keeping is my passion, so a fully-stocked bookshelf is a given.  ;-)
"Natural Reef Aquariums"
by John Tullock
A Wonderful book.  One I always recommend to people just starting out with reefkeeping.  The book covers different filtration systems, with the emphasis, of course, on natural methods.  Other chapters cover lighting and maintenance, while others focus on different marine habitats (Florida Keys, Gulf of Mexico, Indo-Pacific regions).  The book also includes recommended reef species, planning guides, and a good amount of information on live rock and live sand.
A must have.
"The Conscientious Marine Aquarist"
by Robert Fenner
This book has a heavy emphasis on marine fish, but is also an essential book for the beginning (and experienced) reefkeeper.  The book covers setup techniques, species to avoid, disease prevention, and aquascaping.  Excellent information on many marine/reef fish, including Classification, Size, Selection, Habitat, Behavior, Reproduction, Feeding and Diseases.
"Aquarium Corals, Selection, Husbandry,
and Natural History"
by Eric Borneman
I refer to this book as the "reefer's bible".  Anyone who wants to keep corals should have this book.  Each genus is covered in detail, with information including Identification, Natural Location, Colors, Captive Care, Special Information, Collection Impact, etc.  The book contains excellent pictures for identification, and also concludes with chapters on coral Husbandry, Water Chemistry, Care & Handling, Coral Health, & Conservation.  Definitely a book you'll want to read from cover to cover.
"Corals, A Quick Reference Guide"
by Julian Sprung
This book contains excellent, though very concise information on corals.  As stated, it is a "quick reference guide", which gives basic information and care guidelines for each coral, along with beautiful pictures.  Information includes correct species pronunciation, Common names, Geographical location (region), a brief Description, "Similar Corals", and a bar graph showing Lighting Needs, Water Flow, Aggressiveness, & Hardiness.
"Invertebrates, A Quick Reference Guide"
by Julian Sprung
Identical in format to "Corals, A Quick Reference Guide", by the same author.  Information included is Common names, Region, Description, "Similar", Desireable/Undesireable Features, Food, Special Considerations, and Hardiness in Captivity.
"The Modern Coral Reef Aquarium" series
by Svein Fossa and Alf Jacob Nilsen
In my opinion, this series is an essential collection for reef keepers.  There is not much information about captive (and natural/wild) coral reefs that you cannot find in one of these volumes. 
Vol. I covers everything from natural coral reefs, setting up a coral reef aquarium, live rock, light, temperature, water chemistry and biological processes, filtration, algae, & conservation.

Vol II covers corals, corallimorphs, zoanthids, and anemones. 

Vol III covers Single-celled organisms, Sponges, Marine Worms, Crustaceans and miscellaneous other invertebrates (comb jellies, Sea Spiders, Horseshoe crabs, etc.).

Vol IV covers "The Future of Reef Aquariums", Molluscs, Echinoderms, & Tunicates.

"Corals of the World" 3-volume set by JEN Veron
A wonderful set of hardcover books covering all the stony corals of the world.  These books are not for the novice hobbyist - and are not written from the hobbyist perspective.  These reference books give you highly valuable coral identification, classification, and taxonomy.  Fantastic photographs.  Books comes in a nice slip-case.  Over 450 pages per volume.
"Coral Reef Animals of the Indo-Pacific" - by Gosliner, Behrens, & Williams
An awesome book for identification purposes.  This book excludes the "vertebrates", but includes all the good stuff.  ;-)   The book begins with an introduction to classification, and proceeds on to a discussion of coral & coral reef biology.  The bulk of the book contains pictures of Indo-Pacific invertebrates; each picture includes a brief text description of identification, natural history, and distribution. 
Looking to ID a sponge ... gorgonian ... anemone ... coral ... worm ... echinoderm ... bivalve, etc. - you'll likely find it in this book.
"Book of Coral Propagation ~ Reef Gardening for Aquarists" - by Anthony Calfo
An outstanding book on coral care and propagation.  The book contained far more information & advice on coral biology and husbandry than I expected.  The book includes excellent information on the transshipping process, how to handle shipped animals, quarantine procedures, as well as propagation "strategies", pests & predators, and troubleshooting. 
The information and writing style was creative, refreshing and very interesting.  
"Reef Invertebrates ~ An Essential Guide to Selection, Care, and Compatibility" - by Anthony Calfo & Robert Fenner
My new favorite book.  I received this book a little over a week ago, and have read it cover-to-cover once already, and find myself referencing it almost daily.  
I love the "critters" of reef-keeping - the snails, stars, shrimp, etc. - and all the cool hitchhikers.  This book covers just about all of them.  It starts off with an excellent section on "Living Filters", and proceeds on to selection, husbandry. feeding, and reproduction.  
Almost all marine invertebrates are covered; the text is very up-to-date, descriptive, and aimed at the reef hobbyist.  The pictures are excellent as well.  
A highly recommended book for both newcomers to the hobby, and salty old reefers.  :-)

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