Changing a straight line to a curve (and vice versa)

Select the point handles at both ends of a line segment. For several line segments select all bordering point handles.
Click the Make curve or Make line button on the InfoBar, or press "L" or "C" (these shortcuts only work in the Shape Tool).

After changing the line type, you may need to move the curve handles for a smooth transition between curved and straight line segments.

You can select several line segments and convert them all. The point handles at both ends of the segment must be selected.