three persimmon image by Aleksandr Ugorenkov from Fotolia.com. Different types of fruit trees grow wild in Kentucky. These wild Kentucky fruit trees produce fruit ranging in size from berries to a much larger fruit that resembles a banana. The trees vary in size, from just larger than shrubs to medium-sized specimens.hese wild Kentucky fruit trees produce fruit ranging in size from berries to a much larger fruit that resembles a banana. The trees vary in size, from just larger than shrubs to medium-sized specimens.