Cats do not have nine lives. The idea that cats have multiple lives comes partially from myth as well as a cat's righting reflex that provides it survivability. The righting reflex gives the cat the ability to twist about and land on it's feet after a fall.
The myth of cats having nine lives is said to have come from Egyptian mythology, in which the god Atum-Ra was said to have visited the earth in the form of a cat to visit the underworld. As Atum-Ra gave birth to nine other gods, known collectively as the Ennead, religious worshippers began to associate these nine other lives with their domesticated cats. Another legend that contributes to the myth of multiple cat lives is that of Baldwin III, the Count of Ypres, which involves cats being thrown from a tower in a Belgian town and surviving.