What Does A Dog's Tail Wag Mean?
As more scientists study dog behavior, the more they find that a wagging tail means more to a dog than "I'm happy". The dog's tail can provide a lot of insight into the dog's emotional state, both positive and negative.
Dogs in general are more sensitive to movement than they are to colors or shapes, so they communicate with each other mainly with body movement. Many dogs have distinct tails - whether bushy, white-tipped, or very long - and this may be for the purpose of having their tails more visible to other dogs. Research shows most dogs don't wag their tails when alone because there's no need.
Of course, there are different dog "dialects" based on tail shape, natural tail height, and breed, but here are some general tail meanings:
What Does The Tail's Position Mean?
Straight & Horizontal: Attentive & Alert
Angled Upwards: Dominant & Threatening
Lowered: Submissive, Worried, or Sick
Tucked Under Body: Scared
What Does The Wagging Type Mean?
Speed: The faster the tail wags, the more excited the dog is
Width of Wag/Sweep: The wider the wag, the more positive the dog is
Wag With A Right*-Bias: Relaxed
Wag With A Left*-Bias: Anxious
*Right & Left from the dog's perspective
Narrow, Slow Wag: Tentative, Curious
Broad Wag: Friendly, Pleased
Medium-Height, Slow Wag: Insecure
Quick "Vibrating" Wag: Ready To Act/Attack/Run
Circular Wag: Extremely Excited
Of course, there are many more combinations, but hopefully this has shed some light on your dog's behavior. If you see a dog moving its tail and are still unsure of whether s/he is excited by you or threatened by you, look for other body clues, such as a tense torso or relaxed ears to get a clue into what the dog may be feeling.
[Sources: Psychology Today, QuickandDirtyTips.com, Animal Planet]