I have read of many goods that the western world desired from the east throughout history, silk, spices, jade, etc. But what goods, if any, did the western world have that interested the civilizations of the east throughout history?
In my reading there were a couple of rare commodities including:
Tin, found originally in Afghanistan, while sources shifted to Iberia and even Cornwall later in history
Byzantine/Roman silk
Weapons - if you count places like Armenia and Persia as Eastern civilizations. There are records of extensive arms transactions
Pottery (at some points in history), among other artisanal crafts - European craftsmen created at some points in history elaborate pots, and at other points cloths.
Textiles (in the late Middle Ages and Renaissance) - Some areas of Europe like Venice, parts of Italy, and the low countries developed booming textile manufacturing of the highest quality, which was actually in demand in the early Ottoman Empire, Samarkand (capital of the Timurid Empire) and perhaps China, though no record of that exists.
But the big thing, and the big problematic thing, was gold. Despite these rare exports West to East, most of human history before colonization and the military revolution involved extensive exports East to West, and huge net trade deficits from Europe to Asia.
During the Roman period, the flow of bullion East to purchase higher quality Persian goods and Asian silks was the cause of extensive hyperinflation and successive de-valuations of the currency, the most notable being under Domitian, the Severans, and Diocletian. In spite of the British conquest of India and centuries of mercantilism, domestic manufacturing, and imperialism, the British still had a trade deficit with China until they deliberately made up for this with the export of opium. Chinese Emperor Kangxi was quoted during the 18th century, responding to a British request for trade rights that he received such requests from "barbarians" far and wide, but that there was "nothing you can offer which we do not have".