Yes, they do, either long or exceptionally short. All Yorkies are born with tails that appear thin, long, feathery, and a little curled at the onset. However, the tail needs docking if the owners or breeders intend to get the Yorkies registered. In fact, as per the American Kennel Club, a purebred Yorkshire terrier should have a moderately docked tail, raised above its back. The United Kennel Club, Continental Kennel Club, Australian National Kennel Club, and New Zealand Kennel Club have also set the same standards. Thus registered Yorkies wouldn’t have a full-grown tail. Instead, they would have a stub-like projection appearing a little elevated to the level of its back. If docked, their tail would measure between 1 and 4 inches.
Tail docking seems a controversial topic of discussion, and many veterinarians are against it. As for the Yorkie, tail docking could be for aesthetic reasons to give it an elegant appearance.
Though short or docked tail Yorkie is a norm, unless one is preparing to take their Yorkies to shows or for competitions, there isn’t much need to dock their tails. In fact, for Yorkies kept as pets, docking the tail isn’t required.