Herbs of various kinds have been grown and used in America since pre-Colonial times. Often, they were not grown in dedicated herb gardens but in vegetable or cottage-style gardens. Formal herb gardens were sometimes created as knot gardens, a form that has been common in Europe since the Renaissance.
An American herb garden might contain only herbs native to North America. These include native species of mint, members of the echinacea family, native sage, tobacco, purslane, chickory, monarda and St. John's wort. Native plant societies can often supply lists of native herbs.
A modern American herb garden might have plants native to many countries and parts of the world. Among the American Herb Society's "Top 10 Celebration Selection of Herbs" are: summer savory, sorrel, Italian parsley, Thai, lemon and Italian basils, cilantro, calendula, borage and dill.