The expression that a cat has nine lives originated in ancient Egypt.  There, cats were worshiped as gods and often embalmed and richly buried when they died.  Because the major gods of Egypt formed a trinity, three was a sacred number.

Since the multiplication of three by three is nine, crediting the cat with nine lives was the highest honor the Egyptians could bestow on the animal.  Because the cat’s swiftness and agility help it to escape with its life from many situations, the saying that cats have nine lives has endured.–Dick Rogers