To some extent, it depends on which part of the American South you're talking about...but let's make a generalization first.
European colonists throughout what would become the United States quickly adopted corn (Zea mays) from the Indians. They learned a technique invented in Mexico: soaking corn in alkali, which sheds the indigestible seed coat and allows the starch to form into a dough, thereby increasing the nutritional content. Corn treated like this is called hominy (see Ben Wagner's answer to What is the most important invention in human history) and is used in dishes across the United States. Common foods in the South include polenta (grits) and various forms of cornbread, including small thick pancakes baked or fried on a griddle, also known as cornbread.
That is, in areas such as southern Louisiana and the South Carolina coast, rice is widely grown and may be more common on the table than corn. Wheat is also grown here, and its flour is used to make biscuits (known to British readers as "scones", although if made correctly the biscuits have a much lighter texture). But wheat isn't grown as much in the Midwest, and it was a luxury food in the past.
There is a scene in "The Adventures of Huckleberry Finn" where Huck is watching the ferry boat searching for his body on the river because they thought he was dead, and the people on the boat throw bread-coated mercury on the side because they believed it would float around his body. Huck caught hold of one of the floating loaves, removed the mercury from it, and relished: "This is 'baker's bread'—eat the good quality; don't use your mean tortillas." "The rich like to eat wheat bread; the poor have to make do with corn.
Pigs were probably the most common domestic animals in the early days; they could thrive on a wide variety of foods, and they were the most efficient at converting food into meat. It is said that Southerners "used every part of the pig except the scream." To preserve as much of the meat as possible after slaughter, various smoking and curing techniques are used.