Do planets rotate in circular or elliptical orbits around the Sun?

All known planets rotate in an elliptical orbit around the sun.

An ellipse is essentially an oval, although it is more specifically described through geometry. It can also be thought of as an "imperfect" circle. The essential point, with regard to planetary orbits, is that elliptical orbits are evidence of the complicated gravitational interactions between the planets and the sun. In past centuries, they were also evidence that the planets were not perfect, which cast doubt on the geocentric model of the solar system. 

One way we can tell planets have elliptical orbits without going into space is to look at how quickly planets travel in their orbits. As a planet—or any other orbiting object—approaches the main body it orbits around, it will speed up. In a circular orbit, there is no need, or even the possibility, for a planet to speed up while maintaining that circular orbit. Thus, any change in the speed of a planet would indicate it has an elliptical orbit.