Its common enough to where I've seen it multiple times. If the snake is handled respectfully and very carefully, there's nothing wrong with it - but incorporating the snake with one's dance needs to be well done (like everything else), otherwise it ends up looking silly. We had a local dancer years back who had a number of snakes - unfortunately, one of them eventually grew entirely too large to dance with, she was too busy trying to manage this huge snake to do much dancing.
As for type of snake, usually a smaller constrictor of one sort or another. Texas Rat Snakes seem to be popular.
With all that said, I generally don't care for it for the same reason I generally don't care for sword dancing. Too cliche', and rarely done well. There are exceptions.