A dog's wagging tail doesn't always mean that it is happy or excited. Popular researches and studies over the years, suggest that the tail position and wagging direction represent different feelings or moods of dogs.
When the tail is hung down in its natural position, it means that the dog is calm, and is not worried. If the tail is curled in between its legs, it indicates that the dog is scared or anxious. When the tail is straight up, it indicates that the dog is curious or wants to show other smaller dogs that it is bigger and dominant.
Moreover, if the tail wags towards right, the dog is expressing positive emotions such as joy, excitement, etc. However, if it wags towards left, it conveys negative emotions such as anxiety, stress, etc.
