The US show (conformation) standard for Norwich terriers calls for "Tail medium docked. The terrier's working origin requires that the tail be of sufficient length to grasp". The Norwich standard is owned by the Norwich Terrier Club of America, and only a vote by its members can change the standard.
In Europe, it is illegal to dock tails or show dogs with docked tails. This was passed by the European Union as it was felt that it is cruel to dock tails on dogs.
I have heard of two (historical) reasons given for tail docking.
The first is that in England during the 1800s, a docked tail indicated that the dog was owned by a working farmer - and thus was exempt from tax. I have not seen any historical evidence for this, only modern references. (I would welcome seeing any evidence that dates from the 1800s.)
The second reason given for tail docking is so that a Norwich could be pulled from a hole by the tail. There are historical references to Norwich being carried along in saddle bags on fox hunts, and being used to flush the fox. (This seems to have taken place more in the US than in England.) Other than this use I can find no evidence that Norwich were ever used to hunt down holes, as many other terriers breeds did (and still do). And many of those terrier breeds that naturally hunt down holes do so with full tails. So a docked tail is obviously not necessary for hunting down a hole.
There are stories of Norwich being used to kill rats. In the late 1800s Norwich terriers were fashionable among Cambridge students - and one can imagine Norwich being used to keep down the rat population in the medieval colleges (dorms) of Cambridge. However for this purpose the Norwich would sit by the hole or crack, wait for the rat to come out, then pounce and kill the rat by shaking the rat until the rat's back broke. So there was no pulling out of a hole.
Today I know of no Norwich used in fox hunting, nor any Norwich whose primary function is to kill rats. Rather companionship has become the primary function for Norwich terriers, as it has for most dog breeds.
Several European-tailed Norwich have earned their AKC conformation championship. So clearly some US judges have decided to overlook that part of the standard that says "Tail medium docked". And if you look in the show ring you will see that the majority of Norwich have short tails that most men would have a hard time grasping if the dog is moving around. So clearly tail docking has become more of a fashion statement, than an actual necessity.
I have watched Norwich puppies having their tails docked. Docking causes pain. This is not just my opinion but the opinion of the American Veterinary Medical Assocation (AVMA), based upon scientific research ().
I have made the decision to no longer dock the tails of my Norwich terriers. So Shaksper kennel Norwich terriers have "European" tails.
As a breeder I think that the issue of Norwich health is much more important than tail docking. I expect that with the passage of time, the Norwich Terrier Club of America will change the Norwich standard to allow European tails in the show ring.
 Canine Tail Docking FAQ
Specifically, the scientific article cited is
Noonan G, Rand J, Blackshaw J, et al. Behavioural observations of puppies undergoing tail docking. Appl Anim Behav Sci 1996;4: 335-342.
Last updated 20160825