Not the first book I fell in love with, but one of the earliest, and the deepest. It was one of the first science fiction books I read after discovering the genre through a book report on Asimov and--wow. It's the book I re-read every couple of years, often during NaNoWriMo. It's probably responsible for the amount and intricacy of the politics that tends to work its way into my campaigns, as have its particular vision of transhumanism (both the Bene Gesserit and Tleilaxu varieties) and image of an unconquerable wasteland.
A Wizard of Earthsea
One of the few fantasy novels I've read; my tastes and habits have always run towards the science side of speculative fiction, though that's beginning to change. It's got a cultural depth that I've never quite been able to imitate, beyond working some non-medieval details into my worlds. It's also probably the reason that every time I really think about how magic works in my world, it ends up related to words in some way, though for me it's usually writing rather than speech.
The Chronicles of Thomas Covenant
Flawed heroes! Magic rings! Epic quests! The other fantasy novels I've read, besides Earthsea and Lord of the Rings. Magic tied to the land, wise and seafaring giants, the whole "white gold wielder" thing, prophecy--these things speak to me.
The whole teenagers with superpowers thing was a big deal to me, at the time, and probably still is. Especially teenagers whole honestly like having their superpowers; the Animorphs never complained about having their powers, they complained that they had to deal with evil aliens, and couldn't get any help because they might be anywhere. Being a long-running, ensemble based series, it's a good model for team dynamics, the right mix of tension and co-operation, and how to give each character the right amount of spotlight time. It's also very talky, which is more noticeable in my writing than my DMing, but my ideal games do have a fair bit of chatter, both between PCs and with NPCs.
The Elder Scrolls
By which I mean Morrowind and Oblivion, not having played any of the earlier games. Morrowind, particularly, defines my ideal fantasy tone, a blend of mostly normal medieval/roman and bizarre bug creatures wandering around in the desert. I've tried, with varying degrees of success, to create fantastic ecologies for me games, and especially to use weird domesticated beasts, mostly because there aren't any normal animals in Morrowind, and how cool this is in the game.
Oblivion's influence is the most obvious of any of the items on this list, because I lifted the core of the plot to provide a backbone for the Is This Fair campaign. It worked out very differently, and I had changed enough things originally to make it distinct from the video game, but having a guideline was handy. I did, unfortunately, end up having the plot revolve around an NPC -- which is how it works in the game, but I should have known better. Especially since thinking about Oblivion and its major NPCs helped me work out some basic principles on how to make them important without upstaging the players.
On a less embarrassing note, it's also had an influence on the kinds of game I want to run. A great deal of my interest in sandboxes, with ancient ruins and collectible locations, is due to enjoying exploring Cyrodiil. And I'd like to use a something similar to the Imperial Cult in a future setting.
The Lord of the Rings
Well, duh, right? For the most part, though, I'm not into any specific setting details -- none of the non-human races are crazy enough for my tastes -- except maybe the long-lived line of kings descended from ancient glory days bit. I like the setting in the book, but I don't have a whole lot of interest in emulating it in my games. What I do like is the comradery and courage of the fellowship and the people around them. It doesn't work in every game I run, but I like to encourage it, when appropriate.
Special Bonus Non-Influence: Anime
There's nothing particularly wrong with it, and I've probably incorporated a specific idea from a specific show I've seen a couple episodes of here and there. But a lot of my friends are really into it -- which is why I've seen most of what I've seen -- and I've just never particularly cared. Except for when I was seriously into DragonballZ, but I claim extenuating circumstances.
There are probably some other influences and non-influences I missed, but that's a pretty decent list of the things I'm aware of. Except for "history," I guess, which seemed a little vague to give it's own spot, but I really do love settings and stories based on ancient culture and myth.