The World of Rare Cats and Dogs: Meet the Ashera and the Lundehund
The rarest cat breeds seem to be the Sokoke, the Egyptian Mau, and the Ashera. Of those the Ashera is the most expensive($20,000+), the Sokoke the most exotic (from the wilds of Africa), and the Egyptian Mau has the coolest history (lived with the Egyptians).
As for dog breeds, the one that keeps popping up on all the 'rare' lists is the Lundehund, or Norwegian Puffin Dog. Bred originally by the Vikings to hunt Puffins its most unique characteristic is its incredible flexibility in the joints. Other rare breeds include Otterhounds (about 350 in the US) and Stabyhounds (about 100 in the US).