Corona688

I'm not sure if this is quite the same as the Yarkovsky effect, but scientists HAVE measured the extremely small deviation from orbit of one GPS satellite, due to light pressure.

Worldtraveller

The good news is, all of the answers here are right to some extent or another.
To answer your direct question, the earth's, and all planets/moons/asteroids have elliptical orbits that are nearly circular. Most of the planets in our own Solar System have quite circular orbits (e less than 0.1), with the exception of Mercury and Pluto which have quite non-circular (e=0.21 and 0.25 respectively) orbits. (ref.http://www.aao.gov.au/local/www/cgt/planets/pressing/) Pluto's orbit is so eccentric that it actually crosses Neptune's path! And all of the planets lie within the same plane, to within a fraction of a degree, except pluto, as well.
(I'm trying to remember stuff from my orbital mechanics & astronomy classes, that was far too long ago, and I don't have my reference books here with me.)
There are several inconsequential (for short term orbits) like solar wind, other planets influence etc., that become significant in the long term. (and, obviously, when calculating trajectory to other planets)
The comment about planets in prograde motion actually spiralling outward is true. While some of the other effects act to slow the orbit, if I remember correctly, the prograde/tidal locking action is dominant. Yet even that is on the order of billions of years for a measurable effect.
Hope this helps.
Lane

Lobstrosity

Ok, I think there are several effects that could be responsible for perturbations from the ideal elliptical orbits predicted by Newtonian physics. Most of these have already been mentioned, however I think the main one you were getting at with your OP has been left out. I believe there's a subtle effect due to GR that causes orbits to decay, though I'm no master of GR, so perhaps someone with more knowledge in this area can correct me. I believe GR predicts that accelerating masses will produce gravity waves. These waves have not been detected yet because of the intrinsic weakness of gravity, but massive detectors are currently being built that should have the sensitivity to see such waves should they exist (and given how successful a theory GR is, I fully expect this phenomenon to exist). I believe the notion of gravity waves is very similar to the notion of EM waves. Any accelerating charge will radiate energy away in the form of EM waves (photons). What makes this significant is that the EM waves propagate to infinity, thereby carrying energy away from the charge. This is why the classical notion of atoms (you know, a nucleus with electrons executing circular orbits) cannot work--the electrons would quickly radiate energy away and spiral into the nucleus. So, if gravity waves are possible, this means that massive objects are radiating energy away in the form of gravitons. The energy for this radiation comes from the object's kinetic energy, which causes the orbit to decay, however the energy lost per orbit is exceedingly tiny. I think this effect would only be significant in binary star systems where two incredibly massive objects are experiencing large centripital acceleration. This, I believe, is in part why debris spirals into a black hole (although collisions within the accretion disc are probably a large factor as well), though I could be mistaken (as I said, I'm no GR expert and I'm probably misrepresenting the subtleties of the metrics and geodesics and whatnot).

Shadowy Man

Check out the Nobel Prize for Physics in 1993 .

Lobstrosity

Well, it seems my assessment of the theory was at least superficially correct.

Addendum: Isn't your "sic" a bit gratuitous, Shadowy Man? I realize that perhaps the term used most often by theorists is "gravitational" wave, but I don't think "gravity" wave counts as an error, any more than the term "water wave" counts as an error. Look, dictionary.com supports me, and I don't think anyone would question their physics prowess:

http://dictionary.reference.com/search?q=gravity%20wave