Does the solar wind ever affect the orbits of planets or other bodies? I know it has an effect on the magneto-spheres and atmospheres of planets resulting in the Auroras. But does the constant, slight pressure of the wind ever alter their trajectories in any way?
It’s not going to be a significant effect on anything much bigger than a grain of dust.
If Wikipedia is to be believed, the pressure exerted by the solar on an object at 1 AU (i.e., the same distance from the Sun as the Earth) is a few billionths of a pascal. This is about the weight of a (fine) grain of sand for every square meter of surface, and atmospheric pressure is about a hundred trillion times stronger. As another comparison, the light from the Sun exerts a pressure on you that’s about a thousand times stronger.
Even if you do have an object small and light enough for solar pressure to be significant, it falls off as 1/r^2, just like gravity, so the object would still be in a Keplerian orbit. It’d just be a Keplerian orbit with a slightly lower effective mass of the Sun.
Oh, and the light pressure from the Sun is actually considerably greater than the pressure from the wind.