A wagging tail is not necessarily a sign that all is well and that your dog is happy.
The tail is merely a flag that signals a variety of emotional mindsets. You can learn to read your dog's emotions and thoughts by studying his tail signals.
A tail that's hanging low (below the rump) and wagging signals submissiveness. This dog is non-challenging and willing to be dominated by another friendly dog or friendly individual. He's saying, "I'm sweet, I'm lowly, I like you, and I'm not looking for any trouble."
A tail that is held high and/or stiff signals a challenge. The dog is making himself look as large and strong as possible by extending his tail upward or out. You may see the hair go up on his rump as he approaches another dog. His tail may wave slightly--proudly--but it won't be relaxed. This dog will also walk with an erect head, stiffened neck, and ears that are forward toward the dog or person he is meeting. The dog is saying, "I'm big, I'm bold...don't mess with me." Interestingly enough, this dog may quickly back down to a challenger, but he wants to put up a good front just to stave off any problems before they develop. (Note: the dog in the picture above is demonstrating this type of tail set. He sees something of interest approaching, and he's assessing it. The tail is up and ready to make a presentation. Ears are forward. Body is stiff and ready to spring.)
A tail that's high and waving frantically is probably attached to a terrier or other prey-driven breed that's on the hunt. Is he happy? Like a pig in slop! But the tail is a visible extension of this dog's nervous system and it tells you that the dog is 100% intent on the job he was bred to do.
A tail that's in seemingly perpetual motion signals a dog who is high-strung, nervous, anxious, unable to relax, and always wanting, waiting, anticipating. He wants you to pick up the ball and throw it, get the shotgun out, turn the sheep out, or just do SOMETHING. It's hard to say that this dog is happy, even though his tail is constantly thumping or vibrating. On the other hand, he's doing what comes naturally for his breed, whether it's a border collie craving something to herd, or a pointer wanting to go find birds.
A tail that rapidly goes in all directions as you approach signals a dog who's a bit unsure, submissive, nervous, and intimidated. You might get this response if you're teasingly reprimanding your dog and he's just not quite sure you mean it or not. This is a warmup wag that usually morphs into an all-out body wiggle.
So what does a truly happy tail look like? What humans would interpret as "happiness" in dogs is a tail at neutral height (about the same height as the rump), wagging in a graceful, pendulous , smooth and relaxed way. It may wag so hard that the entire body wiggles back and forth with the movement. This, too, shows relaxation of the spine...a sign of "happiness." You'll see other signs of "happiness" on this dog. His ears will be slightly back, his eyes will be relaxed, his brow will be relaxed and free of wrinkles. His neck will appear relaxed, not stiff, and the hair on his back will lay flat. You may even see him "smile." His lips won't necessarily retract in a human-type smile, but his eyes will smile for him, just as a human being's eyes glimmer during a sincere smile.
Dogs with docked tails or no tails can be notoriously difficult for strangers to "read." The emotions still show through on other parts of the dog's body, but it takes a second look--and some practice--to assess a tailless dog's mindset.