I agree with the other replies here. It could be allergies related to grains, etc in the diet. The licking and constant wetness of the paws can lead to another problem such as red yeast. If you see the fur on the paws starting to turn a reddish brown, then red yeast is present. A good shampoo to help with itchy paws is Paul Mitchell shampoo for dogs with tea tree oil.
This article addresses the diet
http://healthypets.mercola.com/sites...ike-crazy.aspx