This is not a 3-D-animation of a fictional creature, but an actual existing animal: the Angora Rabbit. Is this what happens when we over breed animals? Or, is this the result of having too much time on your hands?
Somehow I came across these pictures via this and site which eventually led to this curious source. Apparently there are four breeds of Angora rabbits: English Angora, French Angora, Giant Angora and Satin Angora. English and French were the original breeds, Satin and Giant were introduced in the late 1980s. Check the American Rabbit Breeder's Association's site for more info.
See also: Lifestyle Pets, Popple II.