Spayed animals no longer feel the need to roam to look for a mate. The result is that they stay home and have less chance of being involved in traumatic accidents such as being hit by a car. They also have a much lower incidence of contracting contagious diseases, and get into fewer fights.
In males, neutering decreases the chances of developing prostatic disease and hernias, and eliminates the chances of developing testicular cancer. It also reduces problems with territorial and sexual aggression, inappropriate urination (spraying) and other undesirable male behaviors.
In Females, spaying decreases the incidence of breast cancer (the rate goes down to almost zero if the spaying is done before the first heat cycle!). It eliminates the chance of developing a serious and potentially fatal infection of the uterus experienced by many mature unspayed animals (pyometra). Spay surgery also eliminates the heat cycle and associated mood swings and undesirable behaviors, messy spotting (in dogs) and the attraction of all available males to your yard.