This page contains only a few of the books that I have read or am currently reading, so it is by no means exhaustive. For a more thorough list of interesting books, including a hell of a lot more ficiton than I habitually read, check out David Peterson's reviews.
Clicking on a book title will take you to the Amazon page for that book (if it exists).
Describing Morphosyntax: A Guide for Field Linguists, Thomas Payne. Commonly referred to as "the conlanger's Bible", and not without reason. Simply the best guide out there for creating/describing grammar. Like David Peterson said in a review on the Amazon page, what is conlanging if not "discovering" a previously unknown language?
The World's Major Languages, Bernard Comrie (ed). Gives enough description of fifty languages to sink your teeth into. It can get fair technical in places, but it depends on the author (the essays on each language are written by lots of different people). Quite an awesome resource, and a good source of ideas to
The Cambridge Encyclopedia of Language, David Crystal. A superlative introduction to all aspects of linguistics, and I really do mean all of them, from phonology to morphosyntax to semantics to pragmatics to cognitive to child language acquisition to socio to writing systems to abnormal/impaired. Written at a layperson's level. If you want to get an inquisitive teenager into linguistics, just hand them this book.
The Language Instinct: How the Mind Creates Language, Steven Pinker. I guess a lot of people don't like Pinker's ideas on cognitive linguistics, but I don't know enough to take a position in that debate. This book is really accessible and enjoyable. It gives a good informal layperson's Linguistics 101, though you have to prefix the entire book with an "oversimplified" evidential.
Women, Fire, and Dangerous Things: What Categories Reveal About the Mind, George Lakoff. The book to read for an intro to category theory and fuzzy logic. The beginning was a bit hard for me to get through, but that could just be because I've never studied any cogsci. Once I got past the beginning, it got a lot easier.
Metaphors We Live By, Geroge Lakoff and Mark Johnson. The intro book for Conceptual Metaphor theory. The first half can get a little draggy, but it's more than compensated when you get to the second half, "Implications".
Phantoms in the Brain: Probing the Mysteries of the Human Mind, V.S. Ramachandran and Sandra Blakeslee. A fascinating look at all different kinds of strange brain phenomena. Phantom limbs. Phantom other body parts. Blindsight. Hemispheric neglect. People believing they aren't paralyzed (when they really are). Really ridiculously cool, accessible, and well written.
Le Ton Beau De Marot: In Praise of the Music of Language, Douglas Hofstadter. GEB is supposed to be Hofstadter's seminal work, but I honestly like this one a lot better. It covers translation, philosophy, cognitive science, linguistics, AI, and all kinds of stuff, all centered around dozens of translations of a short-and-sweet French poem. Consider it a worldwide translation challenge (see, for example, Sai's interpretation in ASL).
Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter. I was tempted to file this one in Neuro & Cogsci, but it really defies filing. You could say it's about music, poetry, philosophy, cognitive science, mathematics, logic, art, patterns, and a whole bunch of other things. (Not technical; what terminology Hofstadter uses, he explains thoroughly.) This is a real brain workout, not light reading by any means. But if it's a workout, it's like having runner's high the entire time, and a huge endorphin rush afterward.
Five Quarts: A Personal and Natural History of Blood, Bill Hayes. This book takes a look at blood from all sorts of different angles. It's fascinating. Also includes a fair bit about the author and his lover's fight against AIDS.
Hunger: An Unnatural History, Sharman Apt Russell. Another one of those "look at X from all sorts of angles" books. This one is really well written, and stays fascinating/eerie/disturbing throughout.
Lord of the Rings Weapons & Warfare, Chris Smith. Gives descriptions and pics of all the weapons and armor used in the LOTR movies, plus schematics of the major battles. I can't comment on how realistic/plausible anything is, but there is a fair bit of post-Tolkien background conculturing, and if nothing else, yay pretty pictures.
Kodansha's Furigana Japanese Dictionary, Kodansha International. The best, easiest-to-use Japanese<-->English dictionary I've come across. Gives tons of example sentences, and some reference grammar stuff (conjugation tables and the like).
The New Hacker's Dictionary, Eric S. Raymond. Dead-tree version, with extras and illustrations, of the legendary Jargon File. Quite hilarious, apart from being a compendium of hacker (not cracker) culture.
The Abhorsen trilogy, Garth Nix: Sabriel, Lirael, Abhorsen. Excellently written, exciting, creepy fantasy about "the folk who keep the Dead down". One of the more innovative fantasy conworlds I've encountered, with interesting systems of death and magic. It has some of that feeling of "depth" that Middle-Earth is so often praised for.
Larry Niven's stories, especially the Known Space universe. I really like his voice: by turns creepy, exciting, snarky, whatever the story demands. Ringworld, N-Space, World of Ptavvs, Inconstant Moon, All the Myriad Ways, Convergent Series. Plus some newer stuff, which I haven't read, but which doesn't look as good. (Yay for fathers' old moldering book collections.)
Tamora Pierce's Tortall books: the Alanna, Daine, and Keladry series, plus my favorite, Tricksters. Pretty much your standard fantasy conworld, but with a lot of depth. And great stories, well written.
Tolkien, of course: The Hobbit, Lord of the Rings, The Silmarillion. Each of those comes in so many editions that I'm not bothering to linkto.
Old Possum's Book of Practical Cats, T.S. Eliot. (Link is to the free full text online.) A great, witty, clever, catchy cycle of poems about quirky cats and their hijinks. It was the inspiration for the non-lame parts of the musical Cats (the lame parts are what Andrew Lloyd Webber came up with).
Brave New World, Aldous Huxley. My favorite dystopia novel. I haven't read the followups (Ape and Essence, Brave New World Revisited), but I should.