The star Polaris is commonly known as the Northern Star because it always points North. This being said is there a South star that always points south?
There is a "South Star" called Sigma Octanis located in the constellation Octans, but it is so dim that virtually nobody calls it the south star.
Just another side note: Polaris doesn't always point North. The reason is that our Earth has a precession effect which make the North pole circulate around the sky. This picture illustrates my point.
EDIT: Just to clarify, the picture is showing the circulation of the south celestial pole around the south ecliptic pole.