There doesn’t seem to be a legend to explain how the stones got here – Jordan in her ‘Folklore of Ancient Wiltshire’ suggests that perhaps that’s because of the village: familiarity breeds contempt?
Various stones have special names; there’s the Swindon stone mentioned below, the Devil’s Chair at the southern entrance (young women reputedly sat in it to make a wish on May Day Eve), and the cove of the N inner circle were called the ‘Devil’s Brand Irons’.
There is a rumour (mentioned by Stukeley?) that snakes cannot live within the circle. But in christian mythology the snake often represents the devil. So really you’d expect the circle to be knee-deep in snakes! However, on the church font at Avebury there is a carving of a bishop crushing a dragon/serpent with his crozier (nasty man) – so perhaps the ‘no snakes’ thing is actually a memory of the christian church insisting that Paganism Is Over Around Here. On the other hand, you will notice that the church isn’t actually within the stone circle: perhaps they didn’t dare put it in there??