Which planet has an orbit shaped most like a circle?

Venus and Neptune Has circular orbits.

Explanation:

The special case of an ellipse is said to be a circle. When the eccentricity of an ellipse is equal to zero it is said to be special case of ellipse. There are two planes that follow circular orbits in solar system. They are Venus and Neptune. Venus has eccentricities of 0.007. The eccentricity of Neptune is said to be 0.009.

Conic section is a term used to define the special cases of circles and ellipses It is said to be circular orbit when the ellipticity is zero. When it is in between zero and one it is known as a standard ellipse. It is said to be parabolic and hyperbolic when the ellipticity equal to 1 and greater than one respectively.