The point in time where people started to dance is very hazy, in fact it is more like a cloud than a point. Indeed, there are people who believe that man has danced since before sapiens was a species.
This is true in the fact that before he had the power of speech ancient man conveyed thoughts, wishes, and emotions through actions, just as we do in modern day ballets. However, for our purposes we will consider man to have started dancing when he danced for entertainment or spiritual reasons.
The first recorded dancing, by our definition, is among the ancient civilizations of the middle east and India and among the aboriginal people of the Americas, Australia, and Africa. The Hindu god Shiva, known as Nataraja, Lord of the Dance, is portrayed as a many-armed being balanced on one leg. Actual dance forms appear to have been in place in India around 6000 B.C.1 In studying the First Dynasty of Egypt, (around 3000 B.C.), archaeologists have found relief's showing a kind of dance or body language2, and as culture in Egypt advanced, paintings were made showing musicians and dancers.3
In the Americas, Australia, and Africa the aboriginal people danced both for spiritual reasons and for entertainment. They would dance for almost everything from the potlatch to the funeral. I think they were one of the "danciest" groups of people of all time. Their dances still influence dance today. For example, there have been many ballets performed in North America based on the dance and legends of the First Nations people, the All Blacks rugby team performs a cheer based on the dance of the Aborigines of Australia, and Afro-Jazz is a recognized form of dance around the world.