"Wild basil" is a common name for several plants in the mint family (Lamiaceae):
the genus Clinopodium, in particular:
Clinopodium vulgare (Wild Basil proper)
Clinopodium ascendens (Ascending Wild Basil)
Clinopodium gracile (Slender Wild Basil)
Calamintha arkansana (Low Calamint, Limestone Wild Basil)
Ocimum gratissimum (African Basil), e.g. in Hawai'i
Perilla frutescens (Perilla)
Pycnanthemum incanum (Hoary Mountainmint), e.g. in the continental U.S.