The change in the mean distance (from year to year) follows a cycle that is roughly 100,000 years long. The main culprit is Jupiter, with the rest of the planets having much smaller effects.
However, the change is not regular. For the last few years we have been moving away from the Sun, now we are getting closer.
In 2009, our mean orbital distance is diminishing. We are talking of small values here (1.000016 au to 0.999998 au from January to June 2009, a difference of 2,700 km ( 1/5 of Earth's diameter ).
This is completely separate from the eccentricity of the orbit, which takes us (in 2009) from a perihelion of 147,095,260 km to an aphelion of 152,091,221 km. The eccentricity itself changes, following a (roughly) 400,000 year cycle. However, eccentricity -- or even a changing eccentricity -- does not, by itself, change the mean distance. It only changes the distances of perihelion and aphelion.
There is also another expected effect (but not really measurable): as the Sun produces energy, it loses mass. Four million tonnes per second. As it loses mass, our orbit should move outward. But that is not much (a few metres per million years?).
Because Earth and Sun orbit a common barycentre, they form a quadropole. As such, they should emit gravitational waves (according to Relativity). This energy being lost to the system should cause the Earth to get closer to the Sun. However, the rate of "gravitational luminosity" is around 300 watts. This effect would not be measurable, even over billions of years.