For many people, saying "Bless you" or "Gesundheit" following someone else's sneeze is a conditioned response or reflexive action. Whenever they hear a loud sneeze, the next words out of their mouths will be a blessing of some description. They do this, essentially, because of centuries of religion and tradition. By not saying "Bless you" or something similar, individuals may believe that they are setting themselves up for an even bigger problem down the road.
From some interpretations of the Judeo-Christian point of view, the heart and mind have nothing on the nostrils: when God decided to create Man from the dust of the Earth, He blew the spirit of life into Man's nostrils. In many other religions, the nostrils are considered to be a gateway between the spiritual and physical worlds. Whenever someone sneezes, he or she may be expelling some of the life forces or spirits sent by the Creator. By saying "Bless you," it is believed that evil spirits are prevented from entering the sufferer's body through the nostrils.
There is also a theory that, during the Dark and Middle Ages, a violent sneeze was often a precursor of dreaded diseases such as the plague. Whenever someone sneezed, those closest to him or her issued an immediate blessing to ward off the evil forces which led to disease and suffering. The words weren't so much for the health of the sneezer, but for the continued good health of those who came in contact with the expelled mucus. Some sources say Pope Gregory I popularized the common use of blessings as he reflexively blessed those who sneezed in his presence.
The very act of sneezing may also prompt a "Bless you" response from onlookers, especially if it is a powerful blast. Some common rumors about sneezing suggest that a person's heart may stop beating, the pressure could induce a stroke, or the eyes may be blown out of their sockets. The immediate response is thought to be an expression of gratitude that the sneezer did not experience any of those events. The German blessing, Gesundheit, literally means "May you be called healthy," and most likely entered the American vernacular following the immigration of the Pennsylvania Dutch and other German populations.