Angora Rabbit

Angora is not simply one breed of domestic rabbit, it is many. French, English, Giant and Satin are all recognized by the American Rabbit Breeder's Association and are bred for the fine hair that they produce. A 5th breed, the German Angora, is recognized in other places, and was bred specifically to create a high yield, high density wool that could be harvested commercially. 

The English Angora is the one most commonly kept as a pet, and is the smallest of the breeds. It is characterized by large tufts of fur on the entire face save the nose, which is a trait that is more of less unique to that breed. Facial trimmings, as they are called, are found in other breeds, but not to the extent as in the English.

The history of the Angora Rabbit dates back to the 18th century, when it was believed to be imported to France from Turkey. (Ankara, the capital of Turkey, was called Angora from 1073 until 1930. This also the origin of Angora Cats and Goats) The rabbits appeared in the encyclopedia in France for the first time in 1765, and the French were the first to really capitalize on the rabbits commercially. Angoras soon became prized for their lovely hairs which can be easily harvested either with scissors, or by simply plucking out strands during their natural molting. Despite their long history in Europe, they didn't appear in the United States till the early 1900s.

All images from PlusPets

Unsurprisingly, Angora Rabbits require a lot of care and grooming to keep their coats in top condition. If you're up to that challenge, they do make very sweet and mellow pets, and are apparently pretty low cost to keep. (once you take out all of the grooming requirements) There are several sites out there about the care of these rabbits, as well as all kinds of information on their fibers and what you can do with it.

Thanks Austin for the suggestion!