Keep an eye on it
What it can look like. A general, vet-reviewed example — signs vary and this is not a diagnosis. When in doubt, ask your vet. 
Excessive licking in dogs
Clinical name: Acral lick / over-grooming
Repetitive licking, especially of the paws and legs, often to the point of wet fur.
Where it shows uppaws · legs · flanks · groin
Typical patternPaws and lower legs most often.
Linked allergy typesFood allergy · Environmental (atopy)
Food vs environmentalConstant, non-seasonal paw licking can point to food.
What you can do
Track which paws and how often; persistent paw licking is worth a vet visit.
Don't confuse it with
Other causes a vet will want to rule out: boredom/anxiety, joint pain, infection.
This is educational information, not a diagnosis or treatment plan. Always see your veterinarian about your dog's health.
Related signs
Itching & scratchingKeep an eye on it
Frequent, restless scratching that the dog can't settle from — the hallmark of allergy.
Chewing & biting at skinKeep an eye on it
Gnawing or nibbling at the skin, sometimes leaving damp or raw patches.
Face rubbingKeep an eye on it
Rubbing the face and muzzle on carpet, furniture or with the paws.