Answer by Kath (1537). There are many kinds of wild rabbits including european, cottontails, amami, forest, swamp, marsh, eastern cottontail, brush type, desert, mexican, mountain and newengland cottontails. Overall there are about 30 different types.illy rabbit! There are many types of rabbits in the wild United States of America. There is the anami rabbit, the cottontail, the European rabbit, as well as the forest, marsh, desert and swamp rabbits, which are named and noted as living in the kind of conditions that describe them. add a comment.