1) Some say that the reason is to safeguard the sneezer's soul from allowing evil spirits a chance to take advantage of the soul leaving at that exact moment and entering instead. It is believed that by blessing them, the evil soul or the devil are barred from entering.
2) A similar reason dealt not with evil souls but with the soul of the sneezer. Since a sneeze was supposed to thrust out the soul, people thought it was imperative to bless them in order to prevent the devil from appearing at that very moment and snatching it away. You could think of it like a shield that would keep it blessed as long as it was outside the body.
3) On grounds like the above two reasons, another reason people answer a sneeze with a blessing is that this signifies an evil spirit's departure. In a way it is something like that legend where if you hear a bell ring it signifies that an angel has just received wings.
4) Another popular reason was the assumption that the sneezer's heart stops for a second when the person sneezes. Blessing them became a way to congratulate the sneezer for surviving.
5) A morbid and ancient reason was that during the bubonic plague, which wiped out a third of Europe, one of the first signs that a person was sick was when he began to sneeze. Thus, blessing them was a manner of asking the almighty to have mercy for the poor soul of the sneezer as they were definitely going to pass over into the other realm.
6) In an unlikely swing to an optimistic side, sneezing was also attributed with a sign of good luck. And in order to receive some part of this good luck, people retort bless you.
7) Manners. Or it other words, people bless you because everyone else does it and its considered rude if you ignore someone sneezing. Just like many other behavioral traits, no one actually knows how answering bless you became part of the fine arts, but nowadays, if you omit to say bless you when a person next to you sneezes, you would be considered very rude.
Sneezing is a physical action that is more a reflex to push out certain bacteria and germs from the body outside. The heart does not stop even for a second. (Though one could state that the heart stops between each heartbeat because that's the amount of time that passes between each beating of the heart.) In addition, most of the above are more based on superstition than on any real scientific research or study. So please do not take any of these reasons as medical facts. I have collected them merely for the sake of humor and laughs, and I wish you read them with a smile on your face.