Before we get into this whole belly rubbing thing, must say, gonna challenge you.  Dare you to send me a video of a cuter belly rub then this?

This run happened at LaSalle Park, one of the many Buffalo off-leash dog parks. 

 

So, why do they like it?  Well, it goes beyond feeling good.  Plus, it's different for cats and dogs.

According to VetStreet.com, to Dr. Margaret, DVM, says

"That although both cats and dogs expose their bellies, their reasons can differ.  Cats often lie on their backs in a defensive posture, which is not an invitation for a belly rub...Dogs expose their bellies as part of a submissive display, sometimes during play and with people they are comfortable with."

Adding, that sometimes you do have to come in with the belly rub, with some caution,

A different behavior occurs when a dog rolls on his back as soon as he is approached. “These dogs may be showing submissive behavior especially if it is accompanied by other submissive postures such as tucking tails or licking lips.  In these cases, attempting a belly rub is not the best response — at least not at first, as the pup could feel intimidated by someone leaning in for a rub. For these dogs, the best way to make them feel comfortable is to get low, as by sitting down, and call the dog over without leaning or reaching over them.

If only we could get our dogs to rub our bellies.  Do you think you'd shake a leg?  Ha!