I'm in the same boat as you in that I didn't have pets as a youngster. Looking back I think it did me more harm than good as I was petrified of animals until I was a teenager. I'm still nervous around dogs and birds now, though have found myself at ease with almost everything else.
My little boy has only had hamsters so far- he is 3- and when we move house in a couple of weeks I am considering getting a cat. He is always so fascinated by cats in our current area and it has taught him to be gentle and quiet around them so he can pet them.
Obviously it is each family to their own, but I personally feel that not having a pet around the house when I was younger meant I missed out on something, and that isn't what I want for my son!