Lots of people in the Southeast — and beyond — grow this plant as a shrub or hedge without really knowing its identity. It is a native evergreen, and it is widely cultivated as a popular yard plant, especially in the South.
There are several popular horticultural forms, various of which are excellent for use in topiary. Here in town I’ve seen a tall variety with weeping branches. Some of these forms resemble the common boxwood, with its slow growth and tiny leaves, but boxwood is completely unrelated to our mystery plant. (All boxwoods have their leaves occurring in pairs. Our plant has leaves alternating singly on the stems. Go ahead, take a look.)