A few choice readings - not exhaustive. All of these are good, but a * denotes that you shouldn't miss it.
*Becker, Jasper. The Lost Country: Mongolia Revealed. London: Sceptre, 1993. A great book about recent Mongolian history, with a particularly chilling account of the Mad Baron. Though there are plenty of copies in Mongolia, it has been out of print everywhere else.
Beckwith, Christopher I. The Tibetan Empire in Central Asia: A History of the Struggle for Great Power Among the Tibetans, Turks, Arabs , and Chinese During the Early Middle Ages. Princeton: Princeton University Press, 1987. Interesting, though the names of historic personalities are a bit hard to follow. Many of the Turkish names are taken from Chinese, and all of the Tibetan names are taken from Tibetan.
Dunn, Ross E. The Adventures of Ibn Battuta: A Muslim Traveler of the 14th Century. Berkeley: University of California Press, 1989. This was the Muslim Marco Polo, a Berber qadi traveled all through the Arab world, Persia, India, Central Asia and China. Apparently his writing is so florid as to be unintelligible, so it's better to read about him.
Grousset, René. The Empire of the Steppes: A History of Central Asia, translated by Naomi Walford, New Brunswick: Rutgers University Press, 1991. A scholarly tome, which starts with lengthy descriptions of Sarmatian and Scythian weapon decoration. It's worth it. The book has excellent information.
Halperin, Charles J. Russia and the Golden Horde: The Mongol Impact on Medieval Russian History. Bloomington: Indiana University Press, 1987. A book that argues that the "Mongol yoke" was not as devastating to Russia as some people say.
Hopkirk, Peter, Foreign Devils on the Silk Road: The Search for the Lost Treasures of Central Asia. Oxford: Oxford University Press, 1980.
*Hopkirk, Peter, The Great Game: On Secret Service in High Asia. Oxford: Oxford University Press, 1991. The history of the Russian and British empires in Asia, and how they came to be only 20 miles apart.
*Hopkirk, Peter, Setting the East Ablaze: On Secret Service in Bolshevik Asia. Oxford: Oxford University Press, 1984. Amazing, though horrific story of Central Asia around the time of the Russian Civil War.
Jacob D'Ancona. The City of Light, translated and edited by David Selbourne. London: Abacus, 1998. A recently discovered manuscript of a 13th-century Jewish merchant who spends time in Zaitun in China. Some have argued that the book is a fabrication. Whether or not this is true, it's an interesting read.
Koestler, Arthur. The Thirteenth Tribe: The Khazar Empire and Its Heritage. London: Hutchinson & Co., 1976. A deliciously heretical theory that the Eastern European Jews are descended from a tribe of Turks who converted in the 9th century.
*Levin, Theodore. The Hundred Thousand Fools of God: Musical Travels in Central Asia (and Queens, New York). Bloomington: Indiana University Press, 1996. One of the best books I've ever read. Levin is an ethnomusicologist who works in Uzbekistan and Tajikistan, and he writes beautifully, with a dryly ironic style.
*Maclean, Fitzroy. Eastern Approaches. London: Penguin, 1991. The real-life story of a British diplomat who liked to find himself in the middle of the action. He toured Central Asia in the 1930's followed closely by Russian agents, fought in North Africa in World War II, and parachuted in on Marshal Tito to join the partisans in Bosnia.
Morgan, David, The Mongols. Oxford: Blackwell, 1987.
*Polo, Marco. The Travels, trans by Ronald Latham. London: Penguin Books, 1958. Everyone knows about this book but almost no one has read it. Some of it is pretty far-fetched and amusing, leading one to wonder whether Mr. Polo went as far as Venice. The tarantulas in India and the drinking bouts with sponges in Russia are particularly outrageous.
Ratchnevsky, Paul, Genghis Khan: His Life and Legacy, translated and edited by Thomas Nivison Haining. Oxford: Blackwell, 1993.
Thomas, Bryn. Trans-Siberian Handbook. Hindhead, Surrey: Trailblazer Publications, 1997. This is the book that everyone carries on The Trip. Has timetables, descriptions of all the towns that the train passes, and a lot more. A monumental bit of research.
Thubron, Colin. In Siberia. London: Chatto & Windus, 1999. A British author's trip through the region.