If the dog spends time outside--particularly near water--he could pick up fleas along the way. The fleas that often live in grass are looking for a host, and they'll usually attach themselves around the dog's paws. After a romp in the grass, the dog may lick his paws to get rid of the fleas.
The dog could be allergic to yard or household chemicals, causing him to itch. His diet may also cause him to break out. This itching could lead to excessive licking, including the paws.
Even though a dog has tough foot pads, they can still get cut or scratched. The dog will instinctively lick the site of the wound to clean it, helping in the healing process.
A particularly smart or well-trained dog may know not to track dirt into the house, and he could be cleaning his paws before going inside. Dogs generally like to keep themselves clean, and their paws are usually the first things to get dirty. As a dog gets older, he may groom himself more; it's a low-energy way for him to occupy himself.
Although he may seem civilized now, the dog's ancestors are used to an active life of hunting and getting lots of exercise. A dog's life these days has little of this and can seem boring, especially when he's alone most of the day or kept in a crate. Excessive paw licking can be a sign of boredom.
Some dogs lick their paws to relax, or it could be a nervous habit--the canine equivalent of smoking or chewing gum. This may be more prevalent in high-strung dogs. Dogs may lick themselves because of anxiety or a traumatic experience. Gaining or losing a family member, or moving to a new home, may trigger more licking.
If the dog keeps licking his paws, particularly if he doesn't usually have that habit, a quick investigation may reveal fleas or an injury; otherwise, it may just be one of those canine mysteries. Yet, prolonged licking--particularly in older dogs--may cause the dog to lose hair on the site, open up skin lesions and invite bacteria. http://www.ehow.com/about_6399255_dog-continuously-lick-his-paws_.html