Here's my list of non-RPG books that have influence how I play RPGs. I tried to mention the authors whenever they're known and whenever I can remember them.
Bulgarian folk tales, as well as Persian tales, Japanese, Hindu, Turkish, Russian and assorted other Fairy Tales. Tales of 1001 nights and Brother Grimm's stories deserve special mention, but I've also got the (translated) German tales they based their work on. They immediately reminded me of the Sea Tales book I had read earlier (most of them seemed to originate from the Northern countries).
"The little Mermaid" and everything else by Hans Anderson
Greek legends and myths, The Illiad and Odissey aren't all there is!
The Last Battle of Sandokan, The Last Flibustier, by Emilio Salgari. Scaramouche by Rafael Sabatini
Les Trois Musquetaires by Alexandre Dumas (and petty much anything swashbuckling I was able to get my hands on, if it's well-written)
Lord of Light, Amber and pretty much everything by Roger Zelazny. If I don't own it, I've probably at least read it. Same applies for the original REH stories.
Most stories of Jin Yong, if you can find a translation.
Romance of the Three Kingdoms by Luo Guanzhong
Many other mythological stories, including some currently designated as "religious". Mahabharata and Ramayana are among my favourites. I actually didn't know they're religious stories for some people when I found them on my mother's shelves.
The Hobbit, and the Silmarilion by JRRT. I like Lord of the Rings much less.
Pretty much anything by H.L.Oldie, but I'm especially fond of their (this is the pen name of two Ukrainian guys) Greek cycle, the Hindu cycle, and the space stories of Luciano Borgotta. If you're seeing a patter, it's because it's there!
Wiedzmin/The Witcher by Andrzej Sapkowski (and his next book, which is historical fantasy).
It's hard being a god by the Strugatsky brothers, if I have to single out any of their books. Because it shows how outside help might not be the best for you.
The Grey Mouser and Fafhrd's stories by Leiber, Fritz.
The magic of Volkhavar by Tanith Lee.
The Long War series by Christian Cameron.
The Fencing Teacher and the Captain Alatriste series by Arturo-Perez Reverte.
The Waylender and White Wolf seried by Davidn Gemmell are totally worth reading, too.
"The erotic side of folklore", can't remember the authors (and it's in Bulgarian anyway). But if you think nothing that has to do with sex has a place in a game, consider finding a book like this one and reading it!
Blood and Violence in Early Modern France, by Carroll, Stuart.
The Clash of Civilisations, but mostly by what I consider the author to be getting wrong.
Guns, Germs, and Steel: The Fates of Human Societies and Collapse: How Societies Choose to Fail or Succeed by Jared Diamond
My manual of Roman law, but I'm sure you can use any manual of Roman Law.
The Gift of Fear by Gavin DeBecker
The Art of Fighting Without Fighting by Geoff Thompson
Street E&E by Marc Macyoung
Balisong Iron Butterfly by Cacoy Boy Hernandez
Chinese boxing, masters and methods
Homo Ludens, by Johan Huizinga (1938)!
Paradoxes of the Defence and Brief Instructions Upon My Paradoxes of the Defence, by Silver, George.
The Flower of Battle, by Fiore dei Liberi
The Mabinogion and the sagas, if you find them. Le Morte d'Arthur by Sir Thomas Mallory. Beowulf.
For A Fistful Of Dollars, although it's a movie.
And then, there are gamebooks, which deserve special entry because they're stories with systems (at least, most of the good ones).
Fabled Lands, Bloodsword, Way of the Tiger, Talisman of Death, Virtual Reality are all series you might be familiar with.
"The Shadows of the Darkness" by Georgi Mindizov (pen name Bob Queen) is a title you're much less likely to know. However, it introduced a system of styles that "trumped" each other. "The Dragon Road", by the same author (different pen name), had sandbox elements like those I saw much later in Fabled Lands.
So, yeah, the gamebooks from back then introduced me to a lot of mechanical and setting concepts I saw in RPGs much later, up to and including stats as resource pools.
I might edit this post at some point, but fear not, I shall not remove anything!
So, here are my inspirations. What inspires you?
Let me offer you something, dear readers. If you ever write a post on this topic, post a link in the comments and I'd include it in the body of this post (along with your pen name for the blog). The only condition would be for you to post a link to this post as well. Although if I find your list interesting, I might add your link even if you don't post one.