Well, cotton was by far the most common export, so much so that most of what you will see mentions only cotton. There are exceptions though. When the Advance was captured by the Santiago de Cuba the load was mainly cotton (700 bales) but also contained turpentine, a useful solvent and medicinal made from the pines that are so plentiful in the American South. Tobacco was another important secondary cargo, of course. Then, as now, American tobacco was prized for it's high quality. Another one you will probably slap yourself in the forehead for not guessing is mail. Blockade runners carried mail and charged a premium to do so. .12 to .22 cents are some of the postal fees I have seen on letters heading from the Confederacy to Europe through neutral ports in the Bahamas.

Turpentine Tobacco and mail were a fraction fo the total both by bulk and by value. Cotton was king, as it was in most respects of the war. It was a critical cargo on all sides of the war, it was the basis of the economy of both the American South and a great piece of England's economy. It was also a massively important part of the North's economy. Cotton from the South fed Northern Textile mills, and cotton export revenues paid so much money into the Federal government's coffers Karl Marx referred to the American Civil War as a "tariff war" fought over control of this commodities trade: "The war between the North and the South is a tariff war. The war is further, not for any principle, does not touch the question of slavery, and in fact turns on the Northern lust for sovereignty."

Gray Phantoms of the Cape Fear: Running the Civil War Blockade by Dawson Carr is an interesting piece of reading on blockade runners if you want some additional detail.