If your dog could talk, odds are he still couldn't tell you the reason for his incessant paw licking -- there are too many possible sources. He may be allergic to a food ingredient or to pollen he picks up during his outdoor romps. If he's an active breed, long periods of inactivity can make him bored or anxious, transferring to a nervous habit of licking his paws or dewclaws. Arthritic or other body pains can also manifest in licking. If a few simple changes at home don't resolve the issues, take your pup to the veterinarian before he licks himself sore.
Rule out any obvious injury to his foot or toenail; he may have a hard-to-see scratch, or a tiny but painful thorn or sticker stuck in his paw pad. Check his toenails and trim them regularly to avoid painful breaks. If your dog's front dewclaws are intact, inspect them regularly and include them in your routine nail trimming. It's unlikely that the dewclaws will catch on anything and tear, but it's very painful when it does occur. Cracked or dry pads are also potentially painful; treat them with Vitamin E.
Oddly enough, physical pain in other areas of his body may cause your dog to lick his paws; certain on-leash habits and behaviors may actually cause muscle tightness that leads to foot pain. A veterinarian experienced in animal chiropractic or osteopathic care may be able to help.
Food or Skin Allergies
Try a dietary change and monitor your dog for any improvement in his licking. He may be allergic to grain, especially wheat, or even beef. If the licking is improved but not eliminated, ask your vet about adding a fatty acid to his diet to address any skin dryness.
Another logical place to address is your dog's paws. His paw pads contain sweat glands, so that moistness is a natural magnet for pollens and lawn chemicals that irritate him, causing dermatitis allergies, or atopy. Soak or wash them regularly with warm water; you can add povidone iodine or epsom salts to enhance the cleaning.
Boredom, Anxiety or Irritating Pests
Bored or anxious dogs can have almost-human responses; you might pace or chew your nails, and he licks his paws obsessively. Dogs confined in small spaces or chained may act out through paw licking, particularly breeds that need a lot of physical activity. Make whatever lifestyle changes you can to address those situations, and when he has to be alone, give him some chew toys to keep him occupied. If your dog isn't on a parasite preventive regimen, check carefully for fleas or ticks as the culprits behind his constant paw licking.
Obsessive Compulsive Disorder
If you and your vet rule out all other causes, you may be blessed with a canine companion that suffers from an obsessive compulsive disorder. Retriever and Doberman breeds in particular are more prone to this disorder that manifests itself in excessive licking, as well as some terriers and poodles. Boredom and a lack of physical activity can exacerbate it, leading to a condition called acral lick dermatitis and possible infection. If increasing his activity doesn't help, consult a trainer to help with behavior modification therapy. Your vet may also prescribe drug therapy. You may need to attach an Elizabethan collar until your treatment approach takes effect.