That's the question posed in this very interesting article from the International Herald Tribune titled "Prefer dogs to humans? You're not alone (or unbalanced) ". The article explains our association and attraction to pets and why it is normal, in their opinion, to love them so much.
As a pet lover I can certainly relate to the conclusions in the article although I think it goes a little too far when you read near the end that some people "marry" their pet! One person is quoted as talking about her pet as her "significant other".