The reason why we say "God bless you" to people and animals goes all the way back to the Middle Ages! People back then believed that when you sneezed, your soul left your body. Remember, there wasn't much medical knowledge around at that time, and being as how a sneeze is somewhat of a violent body action, it's understandable that folks believed it wasn't a good thing. Saying "God bless you" was a way to ensure that the soul returned to the sneezer's body. I always say "Gesundheit" when something or someone sneezes because it's German for "health to you". For me, sneeezing means you've got dust or pepper up your nose or you're catching cold or have allergies.
Just a bit of trivia for everyone to think about.