A square has four sides, a triangle has three, and a circle has one. What is the name of the shape that has two sides?

It is called a diagon. Personally I could not picture it in my head.

http://wiki.answers.com/Q/What_is_a_two_sided_shape_called

The wikianswers response http://wiki.answers.com/Q/What_is_a_two_sided_shape_called apparently added an "a" in the middle of the actual term, digon. The digon is described at http://encyclopedia.thefreedictionary.com/Digon, and it and many other shapes are listed at https://en.wikipedia.org/wiki/Polygon.

In spherical geometry, a digon looks like a coloured panel of a typical beach ball. [my own observation: If one of these panels were flattened out on a plane, it would be two intersecting curved arcs, which would form two sides, if one accepts the curved side of a circle as a one-sided figure.]

Since a circle was mentioned in the question, we're not restricted to polygons, so a crescent or semicircle also have two sides. You could also have a shape with two different curves in opposite directions, but I don't know what that would be called.

http://labs.bio.unc.edu/harris/Courses/biol166/curvature.html

The question was inspired by wondering what the two-dimensional shape of a Zulu shield is called (angled on the ends with curved sides -- like an American football or an eye or an almond).