Why is the centre of Earth's axial precession perfectly perpendicular to the ecliptic? (is it?) It is my understanding that the Earth's axial precession is such that the line of the North pole pointing away from the planet traces out a circle on the celestial sphere with a period of roughly 26,000 years. My first question on reading this was, 'where is the centre of that circle?' In other words, what axis is the Earth's rotation precessing about? I had assumed this would be somewhat arbitrary but have since learned that it points towards the north ecliptic pole. Why is this? Am I correct to assume that planets naturally tend to rotate in the same plane as their orbits, but the effects of precession caused by other massive bodies cause the axis of rotation to oscillate around the north ecliptic instead?
(bonus) If so, then what is going on with Uranus and it's unusually high axial tilt? Is this another phenomenon or does Uranus' rotation axis also precess about it's own ecliptic north pole? Albeit with a much larger amplitude.
 A: The answer lies in the cause of the precession. Spinning objects don't simply precess of their own accord, it is the effect of other bodies acting on the rotation object to induce a torque.
In the case of the precession of the equinoxes, the precession is caused by the other bodies in the solar system, most significantly, the sun and the moon. Because the Earth is slightly oblique (the equatorial radius is greater than the polar radius), there is an equatorial bulge. Further, because of the tilt of the Earth's axis, this bulge is tilted with respect to the ecliptic. The gravitational pull of the sun acts more strongly on the side of the bulge closer to it and creates a small torque. Similar effects take place due to the presence of the moon, the combined effect is known as lunisolar precession. Other near by massive bodies also play a role. 
A complete understanding of how/why this torque produces the effects of precession requires an understanding of angular momentum in general and is relatively trivial given that.
To answer the question explicitly, the centre of axial precession points roughly along the ecliptic pole because the effect is caused by the sun (which is always on the ecliptic) and the moon (which is very close to the ecliptic).
A: The way I read this question it is really asking about the orientation of the axis of rotation of a perfect axisymmetric planet (which would not have any precession). 
I think this comes down to how the original planetary accretion disk formed, and how planets condensated out of it. I am not an expert in astrophysics, but my understanding is that the material in the accretion disk has angular momentum that is uniform to a good approximation (although not exactly), and normal to the ecliptic plane. Without external disturbances, we therefore expect the planets to rotate around axes normal to the ecliptic plane. However, if you have collisions with objects outside of the solar system, the axis of rotation of a planet subject to such a collision may be different.
Such collisions probably occur to some degree for all planets. Neptune is a significant outlier, with an axis of rotation tilted by about 30 degrees. Pluto is even worse (well, poor Pluto is not counted as a member of the club anymore), with an axis that's almost exactly in the ecliptic plane. Per Bill's comment, Earth's axis of rotation precesses around an axis that is tilted a bit more than 23 degrees relative to the normal on the ecliptic plane.
