When dogs wag their tails.....?

It is entirely voluntary. The amount of wag and the position of the tail communicate different things. Dogs use a lot of body language to communicate, employing not just their tails but ear positions, facial expressions, eyes, position of head and body postures in many differing combinations. You can find some good books to interpret these things at Dogwise [www.dogwise.com]. For example, most people tend to think a wagging tail means friendliness or happiness but it does not always mean that.