Curves, and particularly those that make an "S" shape, can create very dynamic compositions. They can generate calming, sensitive, even sensual feelings in the viewer. For myself, I prefer curves that form a diagonal through the frame. In the above photograph taken at Swallow Falls State Park, the rocks cut into the river to force the current into an S-curve. Imagine the change in feel of this photo if the current simply flowed straight through the frame.
Now the lines do not have to be continuous lines. They can be implied by patterns in your composition. In the photo to the left, these Scaup were kind enough form a curve. So instead of zooming in on one duck, I decided to place four of them into my composition.