I think we're hard-wired to associate sucking with calm and comfort. It's meant to help a baby get enough nutrition when it's still young enough to need milk... if sucking were a neutral thing, the baby might not get enough food; so it's associated with positive feelings.
Interestingly, fetuses have been observed to suck their thumbs or fingers--since this is before sucking is even associated with gratification of hunger; it makes sense that sucking, in itself, is comforting for the baby before and after birth.
Some cats will suck on things well into adulthood or even their whole lives; it's theorized that if they are taken away from their mothers too early, they'll be more likely to suck. Or they'll knead with their front paws when they're being petted; that's what they used to do when they nursed, as kittens. So it's comfort behavior as well as social behavior... generally the cats who do this are quite happy animals; they just have some kittenlike behaviors.
I actually never sucked my thumb at all; but I do eat to comfort myself when I feel sad. Naturally this is much more unhealthy than thumb-sucking--I'm overweight--so I'd probably be better off if I did suck my thumb.
So, how long before somebody mentions Freud?
....Oops, I just did.