Rabbits are found wandering in many areas of Middle-Earth. They are mostly harmless critters that scurry away to safety as they are approached.
Odd sightings have been reported in Wildermore. Rabbits have been spied in several places siting on a bear skin. The reason for this is as yet unknown. Some think there is a kind sole placing the bearskins around to provide a warm and snuggly place for the rabbit to live. Others think the rabbits acquired the bear skins directly from the Bears themselves.
Other places these critters have been sighted include the Vales of Anduin.