A dog that sees another dog's tail wagging asymmetrically to the left or right elicits a different response in the dog that sees it. In a recent study, researchers found if a dog sees another's tail wagging to the right, the dog responded calmly. If it saw it wagging to the left, its heart rate increases and got anxious. If it saw it chasing its own tail, it felt sorry for the dog the same way you would a stupid younger brother.
Earlier, the same research team discovered that dogs wag to the right when they're happy, like seeing their owners, and to the left when they're feeling stressed or anxious (like seeing a dog they're hesitant about). Their prior study showed that left-brain activation produced a wag to the right, while right-brain activation produced a wag to the left -- a consequence of left/right asymmetric functionality in the brain.
Honestly, I'm just surprised dogs are smart enough to notice what side another dog's tail is wagging towards. Hell, I'm human and I can barely tell my left from my right half the time. "Lift your left arm." *lifts* "That was a leg." Dammit, let me try again.
Hit the jump for a video showing the two different wags, then go home and dog-whisper.
Thanks to Carolyn, who's concluded cat tail wagging mean absolutely nothing whatsoever.