As mentioned in other places, each breed of dog was created to fulfill some kind of purpose and the ideal characteristics of that breed, as outlined in the breed standard, reflect that purpose. For example, Greyhounds are thin and aerodynamic for running down fast prey, while Bloodhounds have long droopy ears to catch scent. Some breed standards call for docking, or the surgical removal of part of a dog's tail or ears; this practice seems to be quite old, dating perhaps back to Roman times, and was purportedly performed to prevent injury to dogs who could have gotten bitten on the ears or tail or had burs or thorns stuck on their tails or ears.
Today, docking of a dog's ears or tails is a highly controversial topic, especially for dogs that are used solely in the show ring. Opponents of docking argue that it is an unnecessary, harmful and cruel practice; still others claim that dogs rely heavily on body signals to communicate, and that since tails are an important component in the repertoire of canine body signals, tail docking severely affects a dog's ability for communication. Those in favor of docking argue that it is part of a breed's heritage and does not actually lead to any long term effects in a dog's health. In many countries outside the US, any kind of surgical procedure performed on a dog that is not necessary to the dog's health, including docking, is strictly banned and dogs with docked ears or tails are ineligible for conformation competitions. In the US, the practice of docking is still accepted and some breeds that have been traditionally docked have difficulty being shown if they do not conform to docking standards.
The Norwich terrier is a breed whose tail has been traditionally docked. It has been stated that because Norwich terriers often followed vermin into burrows, a docked tail was necessary for pulling the dog out of a burrow without damaging its spine. Indeed, Norwich owners that still hunt with Norwich terriers prefer to have the tails of their dogs docked to more easily extract them from burrows or holes. In the US, it is preferred to have the tail of Norwich terriers that enter the ring docked, though it is not a requirement. Indeed, the breed standard on the American Kennel Club website states that tail docking is optional for this breed, though there are strict requirements regarding how much the tail must be docked.
If you decide to show your Norwich, make sure that you carefully consider the operation and that it is only performed at the proper time and by a reputable veterinarian. If the tail is improperly docked, the dog could be ineligible for the show ring and so the procedure will have been a waste of time and money and you will have put your furry companion through unnecessary stress. If your Norwich is purely a companion dog with no intention of entering the ring, seriously consider leaving its tail natural.