When studying composition, there are many "rules" or guidelines to consider to strengthen an image. Concepts include the rule of thirds, symmetry, leading lines, etc. The S-curve can also introduce a strong element of composition in a frame. I read one reference that described the S-curve as "compositional gold". Some say that the S-curve is one of the only geometrical shapes that can stand alone as a main subject.
You never know when you'll come across a S-curve while shooting. I happened to notice two of them in State Capitol buildings--the first in Kansas and the second in my home state of Illinois. I think the S-curve significantly strengthened the composition of these photographs:

Grand staircaseGrand staircase in the Illinois State Capitol building at 401 S 2nd Street in Springfield, Illinois on August 11, 2014. This photograph consists of five exposures blended together to create a high dynamic range (HDR) image.