Why do we bless those who sneeze?

As we were studying together in the library one afternoon my friend and fellow historian Brendan pointed out a wonderful little passage from the Essays of Montaigne that he was reading at the time:

Do you ask me whence comes the custom of blessing those who sneeze? We produce three sorts of wind: that which comes from below is too foul; that which comes through the mouth implies some reproach of gluttony; the third is sneezing, and, because it comes from the head and is blameless, we give it this honourable greeting.Essays of Montaigne Harvard University Press, 1925. p74

I see that it has received mention elsewhere on the net, including the excellent Language Log. You can read a different translation of the whole essay, “Of Coaches” here.