Females - spaying will stop the bleeding that occurs with every heat cycle and prevent any changes in your female's behaviour. Females that are not spayed, but who do not have litters, may develop false pregnancy or infection in the womb. Early spaying of females reduces the risk of them developing mammary cancer (breast cancer) later in life.
Males - some males develop antisocial behaviour when they reach maturity. This may be in the form of aggressive or sexual behaviour - mounting other animals or people! Uncastrated males, if left to their own devices, may patrol a wide area in search of a mate and can detect a female on heat over long distances. A male that wanders is more likely to be involved in a car accident. Castrating males also reduces the risk of them developing diseases of the prostate in later life.