It's worth noting that multiple types of cotton were grown, most notably sea island cotton off islands predominantly in South Carolina. Tobacco was grown in the upper South, but was generally on a slow decline from the 18th century onward, Indigo was also on the decline. Étienne de Boré was basically the Eli Whitney of sugar cultivation which was largely limited to Louisiana and parts of Texas. Hemp was grown in Kentucky and Missouri. Rice was grown near the coast in the Carolinas and Georgia. As Tobacco declined in Maryland and Virginia plantations often switched to more traditional foodstuffs like wheat and corn, Maryland in particular was successful in this regard because of the demands from urbanization. Aside from these more popular cash crops I noted above it wouldn't have been unusual for smaller numbers of other crops be grown.
Before technological advances (the cotton gin) allowed the mass production of long-staple cotton, the only cotton that could be grown at a commercial scale in the South was short-staple cotton, which only grew in sandy soils very near to the ocean, mostly on sea islands in the Carolinas. It was the cotton gin that allowed cotton to spread throughout the Deep South in the first half of the nineteenth century. Before that, in the eighteenth century, the major cash crops were rice and tobacco, with indigo also commercially important. The climate in South Carolina is especially well-suited to rice, and much of the oldest money in Charleston was originally from rice planters.
In the Upper South (Maryland and Virginia, plus Delaware and parts of North Carolina) tobacco was the most popular plantation crop by far. It was actually much less labor-intensive than either rice or cotton, which is why plantation slavery was relatively more concentrated in the Deep South (not that there weren't large plantations with many slaves in Virginia, but by the nineteenth century such sites were more common in Georgia, Alabama, Mississippi, etc.).
In Louisiana and parts of Mississippi and Florida sugarcane (another crop that required a huge amount of labor) was grown, though this was never much competition with the huge sugar operations on Jamaica and other Caribbean islands.
Finally, all plantations would have featured food crops, especially wheat and corn (maize), as well as vegetables and fruit orchards. These staple crops were used to feed the household, as well as the enslaved labor (though sometimes slaves were responsible for some of their own vegetables, depending on the nature of work they performed on the plantation), as well as to make such products as beer, cider, and distilled spirits. There also would have been a necessity for animal feed.