In my mind cats and dogs form the best bonds with humans. I would agree that parrots also have a strong bond as Jen pointed out, but I can not pet or hug a parrot, and it simply doesn't feel the same.
Rabbits, fish, whichever animal you can think of, while cute or great to look at offers nowhere near the emotional satisfaction as a cat or dog can.
Having said that, there was a pig I loved when I was a young boy. My grandfather owned it, but he was "mine". I remember he loved me too, as I was afraid of most other pigs, but not this specific one. I could climb on his back, pet him, etc. Things that I didn't dare do with other pigs, as they always seemed to be close to hurting me.
