Belted Galloway

These are Galloway belted cattle, they are noted for their longer hair and odd band of white around their middle. They are often kept for meat, and it is said to be more tasty than from other cattle breeds. I don't know about that, but I know they look like Oreo cookies!
Zebu Cattle

Zebu cattle are from Africa, they can be very tiny, or medium sized, like this bull. They are not adapted to colder climates because they do not get winter coats, as such if you are in a cold climate, they must be kept in the barn for the winter. This is the most fuzzy Zebu I have ever seen. They resemble miniature Brahma cattle.
Naked Neck Chickens

These are also known as Turkens, they originated in Transylvania. One cannot help but draw a link between their naked necks and the Dracula legend, however there is no actual link. Personally they are not one of my favorite birds, their appearance disturbs me, but many people adore them.
Myotonic Goats

Also called fainting goats, they are usually kept as a novelty because of a genetic disorder known as Myotonia. When frightened their legs stiffen up and they fall over. As such they are very vulnerable to predation. As they get older the "fainting" spells do not happen as often. They are a meat breed.
Araucana Chickens

This is a rumpless breed of chickens, best known for their charming ability to lay colorful eggs. These are usually blue or greenish. Ameraucana is the name given to a bird that is half Araucana. I prefer the original.
Donkeys

Big or small, donkeys are really cool farm animals, generally kept for the purpose of guarding other livestock or as beasts of burden. The fellow in the photo is a miniature. They make great companions for horses, once the horse gets over their funny appearance, and sound. Yes, they are loud, and their bray can be heard from a long ways away.
Llamas

These animals first came on the market as "get rich" schemes, and were very expensive. Now, however, you can get into llamas for very little. In fact at one action I attended, they were paying people to take the male animals. Llamas are used as guard animals for sheep and goats. They are also used for fiber, meat, or as a pack animal. Although they may appear to be the snobs of the farm, they can be wonderful companions. Alpacas are smaller than llamas and often kept for the same reasons.
Guinea Fowl

This is a primitive looking bird from Africa. Their colors are plain especially when compared to the peacock, but it is their sound rather than their looks, which is why people keep them. They have a very loud call, which they use as an alarm. They are often kept as guard animals to scare predators away or to alert the farmer of strangers entering the property. They also gobble up a lot of insects, and people do gobble them up as well (the Guineas, not the bugs). Their odd appearance and quirky mannerisms make them an interesting addition to the farm.
Yak

Yaks are wonderful all purpose animals from Asia. They can be driven, riden, and are generally more pasture efficient than cattle. They produce milk, and can be slaughtered for meat. Although the ones in the photo do not show it well, they can get very thick heavy coats so are tolerant of cold. While they may look like smaller bison they are certainly easier to domesticate. Besides that, the look cool!
Hair Sheep

Most people only know of woolly sheep, but some sheep have hair that they shed seasonally, like dogs. The young ram in this photograph is a Barbado hair sheep. The main appeal of them is that you do not have to sheer them, as well they make excellent meat animals. Like all sheep, they are great for pasture control.
All the photographs are from Wikimedia, with the exception of the Llama, Donkey, Guinea Fowl, and Hair sheep, and you should check their licensing agreement before using these pictures. The other photos are my own and are not to be used without my permission.