Emily Anthes is against the practice of surgically shortening a dog’s tail for aesthetic reasons:

A fast, wagging tail can signal excitement and playfulness, whereas a tail tucked between the legs is a sign of submission. A dog that’s feeling aroused, confident, or aggressive may hold his tail up high, while a relaxed pooch lets his tail hang down lower and looser. These tail movements provide important clues about how a dog is feeling–especially to other canines that may be sharing the same sidewalk or dog park.

She summarizes a study that tested robotic dogs, pictured above, in dog parks:

Large dogs approached a short-tailed robot with a wagging tail just as often as one with a motionless tail (85.2% and 82.2% of the time, respectively). These findings suggest that the dogs were less able to discriminate between a tail that’s wagging playfully and one that’s standing still and erect when the tail itself is short.