Dogs lick their paws for a wide variety of reasons. Sometimes, the behavior is triggered by stress. However, it can also be due to skin infections, allergies, parasites and certain health conditions, such as hypothyroidism. In some cases, dogs may lick their paws out of habit or boredom.
Just like humans, dogs sometimes suffer from dry skin and may start licking their paws to relieve the itching associated with it. Since there are so many causes for this behavior, it's a good idea to have any new behaviors evaluated by a veterinarian, especially if the skin is swollen, inflamed or red.