While I have shelves bending under the weight of D&D books and books for other games (old: Warhammer Fantasy Roleplay, etc. and new-ish: Torchbearer, etc.), as well as TRPG magazines, I really only use three books as a DM: the 1979 Dungeon Masters Guide, the player core book for a clone of Basic/BECMI, and the original Fiend Folio, preferring as I do monsters that are a bit more 'out there.'

Most of my 'DM shelf' is made up of fiction from which I harvest inspiration for world building, etc. This is my personal APPENDIX N. Most of which can be found in APPENDIX N.

What have people read from the original APPENDIX N?

If you prefer more modern fantasy like that of Miéville—I love him; he does that 'out there' British interpretation of fantasy just right—and Jemisin, whom I hear is fantastic, please feel free to list authors you like who were not on the original list.

From the original list I have only read Burroughs' Mars series, Howard's "Conan" stories, Leiber's “Fafhrd & Gray Mouser” stories, Vance, Moorcock, Lovecraft, Tolkien, A. Merritt, and Zelazny.

Further inspiration for me that is not on the list includes M. John Harrison, Frank Herbert, C.L. Moore, Joe Abercrombie, and Miéville.

I have honestly never heard of most of these. If you had to pick just one book or series, which would you recommend as essential reading?

Quote from Lia_Black >>

I have honestly never heard of most of these. If you had to pick just one book or series, which would you recommend as essential reading?

 
So, it depends on what you want to learn about, and what aspects and influences you seek understanding on.

For the broadest overview of influences, i would say Tolkien's works, as there is a lot of 1 to 1 elements repeated.

To understand some of the oldschool mindset that has diminished a bit, Then Robert E Howard's Conan novels give you a good idea at the pulp sword and Sorcery aspects.

For the old way magic used to function, and how it was meant to interface with the story telling and planning aspect, then Jack Vance's Dying Earth novels.

Again, it is what do you want to find out about most. I haven't read all of these, so of the works i can't tell you which of the Appendix N works is the most entertaining.

Quote from Lia_Black >>

I have honestly never heard of most of these. If you had to pick just one book or series, which would you recommend as essential reading?

 Honestly, none of them are essential. Most or all of them are going to feel pretty dated to a modern reader.

I have read, and enjoyed, a number of them, but I'm an old. I also would expect to find that I'd notice a lot more racism, sexism, and the like that I hadn't really noticed at the time. (For the most blatant example: Lovecraft is hella racist -- not just in the "man of his time" sense, but in the "his peers, who weren't great themselves on the subject, were commenting on it in their correspondence" sense.)

Also, the bar has just been raised in terms of writing skill over the years. This may be more blatantly obvious in classic SF than it is in fantasy of the same era, but the expectations for characterization, prose style, etc. are much higher. (To justifiably pick on HPL, as a prose stylist, he's... unique.) Additionally, the cultural expectation of what "good" writing looks like changes over time.

As for what I'd recommend as "essential": are you looking for an entertaining read, or are you looking to learn more about where D&D came from? 

For the latter, Leiber or Howard are probably it, but I haven't read either. (I assume you're familiar with Tolkien, though the books are noticeably different from the movies.)

For an entertaining read, Zelazny is the one I've read that probably holds up best to modern expectations. (He really doesn't tell D&Dish stories, though.) The first Amber series is a fun, brisk, read. 

I am looking for two things. A good entertaining book and how that book fits within the roots of D&D?

I guess I am looking for a third thing which is to see which books people liked or have had an impact on the way they see the game. 

Quote from Lia_Black >>

I am looking for two things. A good entertaining book and how that book fits within the roots of D&D?

I guess I am looking for a third thing which is to see which books people liked or have had an impact on the way they see the game. 

 
Lord of the Rings i think ticks all those boxes. I think it had a greater influence than most of the books listed, and the influences are most obvious.

Moorcock would be my answer. At least his Eternal Champion series.

Those of Elric, Hawkmoon, and Corum have the pace and scale of a perfect D&D campaign. And it is in these series and in Poul Anderson's Three Hearts and Three Lions where we encounter the inspiration for Alignment in D&D. The Eye of Rhynn and the Hand of Kwll from the Corum books also gave us the Hand and Eye of Vecna. (Vecna's name is an anagram of Vance, whose Dying Earth series would be my second recommendation. With Leiber's tales of Fafhrd and the Gray Mouser being my third.)

Tolkien's influence is obvious: elves, dwarves, hobbits, orcs, and ents all making it into the game. But there is nothing at all Tolkien-esque about wizardry in the game. Other than Gandalf's appearance, itself inspired by that of Odin, the character had little to no influence on the game. Spellbooks? Before 'arcane foci' these were the defining accoutrements of those belonging to the class. And this and the academic nature of magic in D&D is found in the pulps. Not in Tolkien in which wizards are supernatural and angelic beings.

Moorcock is also a serious man of letters, having written literary works as well as sword and sorcery. And you won't find racism or sexism in his work. Like Ursula K. Le Guin he challenged many of the conventions in the genre in that regard. 

Worth noting is that Leigh Brackett was one of the cowriters of the screenplay for The Empire Strikes Back. She, C. L. Moore, and Andre Norton rank among the most important women writers in fantasy and science fiction.

Moore's Jirel of Joiry stories gave us "the world's first female sword-and-sorcery hero." One of emotional and psychological depth. And not what some might expect from stories written in the 1930s. But then this was the decade that followed the one in which we saw the publication of Virginia Woolf's principal works.

Don't be fooled into believing Howard's "Conan" stories are 'neanderthal'-ish because of the character's portrayal on the screen. They actually get quite philosophical. As do Leiber's “Fafhrd & Gray Mouser” stories. But both series manage this in tales that are very much focused on action.

Vance's prose borders on poetry in parts. Is more literary than most modern fantasy. It's not unlike M. John Harrison's. For which Vance was an obvious influence. Vance was influenced by Clark Ashton Smith, whose Hyperborea, Poseidonis, Averoigne and Zothique stories read a bit like classic D&D adventures. As do Vance's Dying Earth stories.

I should also mention Gene Wolfe's The Book of the New Sun. This is literature of the calibre of Frank Herbert's Dune and not mere genre fiction.

Thanks for the recommendations.

A little late to this, but Fafhrd and the Gray Mouser stories by Fritz Leiber are the place to start for D&D, not Tolkien. Tolkien's influence on D&D is present, but overstated.

As previously mentioned, D&D magic comes from Jack Vance. Alignment comes from Poul Anderson's Three Hearts and Three Lions and Michael Morcock's Elric series. A lot of the planes stuff has roots in Zelazney's Amber. The Thief class, with its use of magical items and the old shadow step ability is a mix of Leiber and Vance. Bard players should read Manly Wade Wellman's John the Balladeer, even if John took a 1-level dip in Fighter first. And the "Fighting Man" of 1e (now the Fighter) runs a gamut from Burroughs; John Carter, Howards' Conan, Anderson's Holger Danske and the entire Sword and Sorcery boom in the 1960s caught by Offut.

Looking for monsters? Take a look at Manly Wade Wellman and Margaret St. Clair.

Looking for why D&D has science fiction roots too? Leigh Brackett's sword and planet took sword and sorcery into the far future of Mars and Venus. Jack Williamson is more known for his science fiction than his fantasy. 

And anyone who has any interest in the history of fantasy needs to read Lord Dunsany and John Bellairs.

Generally, the older you go, the less constrained by modern ideas of fantasy and even genre the stories get.

The stuff on the list is stuff that influenced the writing of D&D, which means it came out no later than the 70s. My general advice is that anything hard to find is probably not worth finding other than academic curiosity, because things that are likely to appeal to a modern audience generally get reprinted.

Thanks to the advent of ebooks and the recent explosion of the interest in pulp, easily 90% of Appendix N is available and typically easy to find. What little that might not be is bound up in estate issues.