Spiral stairs are a specialized solution to accessing another story or level. Theaters and equipment mezzanines are the main uses for a spiral stair. A residence in need of a little drama is another use. 
Benefits
Besides being aesthetically cool, spiral stairs have some key benefits. They have a very small footprint, rivaling a ship's ladder. Spiral stairs are extremely functional. None of their structure is excess, everything works together. For the architect there is no detailing to do, just a layout and selection of parts from the manufacturer's standards. Finally, spiral stairs are fun to use - at least for a while.