Samurai by Stephen R Turnbull is a good starter.
Japanese Ghosts & Demons by Stephen Addiss is a good one with great ukiyo-e prints of, well...ghosts & demons (and kitsune and samurai fighting them).
Tales of Old Japan by A.B. Mitford which gives a good summary of The 47 Ronin amongst other classic tales. This is the bloody samurai one.
Japanese Tales by Rovall Tyler. A translation of a bunch of setsuwa bungaku stories from approximately the 11th-12th Centuries for the courtiers of Kyoto. This is the one with ghosts, spirits, (essentially) high-level monks, tengu, oni, and "yin-yang masters" i.e. wu-jen.
Samurai William by Giles Milton an excellent book about William Adams, aka Anjin-sama, the first Englishman to arrive in Japan and pretty much the only westerner to become not just a samurai, but a hatamoto, which is very high status. Also gives a brief account of Japanese mercenaries fighting on behalf of the Dutch in Indonesia.
I have, unfortunately, had the worst time finding anything for Korea. I found one book once, and I have never been able to find it after I had the money to purchase it. It was some university press, and I've forgotten everything. However, if you get the chance, do get to reading about Korea! If you get a chance to find anything about Admiral Sun-Yi, do so!
Romance of the Seven Kingdoms to get you started on China.
Chinese Fairy Tales & Fantasies translated by Moss Roberts is a collection of Taoist tales, much of which you might find useful for your campaign.
Ancient Tales and Folklore of China by Edward C Werner, which gives a good overview of some of the Chinese pantheon and includes the stories "The Eight Immortals," "The Guardian of the Gates of Heaven," "A Battle of the Gods," and "How the Monkey Became a God."
Genghis Khan and the Making of the Modern World by Jack Weatherford, provides an excellent history of the career of one Temujin, and gives a good look into the Mongols, and their contributions to creating a global society.
The Middle East...phew! There's a lot, lot, lot to cover! For pertinent areas, first begin with...well, the Bible, the Torah, and the Koran (obviously), then on to the Epic of Gilgamesh. If you can chase down some Persian tales that would be wonderful, as there's a few dragon slaying stories in there, I can guarantee you.
Then it's on to the Routledge edition of The Thousand Nights and One Night translated from the French translation by J.C. Mardrus by Powys Mathers, for the most complete edition of this classic that I've found.
Byzantium, a three volume series (or one abridged volume) by John Julius Norwich, which covers the history of that ancient bulwark of Christianity and a good study of an eight-century battle against Islam and other foes of the empire. Especially try the three volume series. For a history, there sure is a lot of reference to miracles, saints, and a bit about a "Jewish necromancer" who was in service to an emir of Syria (IIRC) and then poisoned one of the Emperors. Good stuff!
Hey! Don't forget Jade Dragons and Hungry Ghosts by Green Ronin! Great collection of Asian-themed monsters for 3.0.
