Pit bull Hagrid and the anonymous Canadian dachshund are proof that just about any responsive dog with sufficient prey drive can be used to move tame stock in a controlled environment. Why the American Kennel Club doesn't open its "herding" contests to all breeds just beats me.
One of the handsomest dogs I know is a friend's AKC CH. Rhodesian Ridgeback, a top lure courser, pictured here during his first time on sheep:
Notice how he covers the ewe that breaks away:
That's prey drive. The great challenge with "non-traditional" breeds is maintaining their interest in the work. Working drive --- the will to keep at it come hell or high water --- is so low in so many cases that pointing a crook at a dog's shoulder can make him say, "No more of this for me."