This New York Times article describes a new study that found that dogs tails wag more to the right when they are happy and more to the left when they are scared:
Thus when dogs were attracted to something, including a benign,
approachable cat, their tails wagged right, and when they were fearful,
their tails went left, Dr. Vallortigara said. It suggests that the
muscles in the right side of the tail reflect positive emotions while
the muscles in the left side express negative ones.
Our dog’s tail wags so hard, it’s hard to see which way it’s wagging!