Kepler tells us that all orbits are ellipses. However, if one were to consider only a two body system (Sun and Earth) the elliptical orbit would be quite a bit different than is displayed in reality. A three body system consisting of the Sun, Earth and our Moon actually predicts an orbit of the Earth nearly exactly that which it is.
Many references will state that only the Sun's gravitational force affects the Earth's orbit. However Newton's inverse square law tells us that any and all bodies with mass exert gravitational forces on each other, including our Earth. We know that the Moon contributes to the wobble of our Earth's rotation, for example. Calculations indicate that all of the planetary bodies gravitational forces (especially the gas giant Jupiter) combined produce only an additional 1/10,000th gravitational force as that of the Sun (since the added forces tend to cancel each other out). But, intuitivelyat least, this must contribute to the ellipse.
Additionally, it's unclear if the center of mass of our Sun is actually equivalent to the center of gravity. It's proposed that the center of gravity (due to a number of reasons) is more near the surface on one side of the Sun. This too, (if found to be accurate) could contribute to our slight off center circular orbit...
The final, definitive answer, I suspect will be derived from Kepler, Newton and especially Einstein's demonstration of gravity being a curvature of the space/time fabric.
But that's another discussion, no?