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Do Earth's rotation/revolution is regulated by other planets (and vice versa) in any way? How?

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Yes they do, and this is a great way to introduce perturbation theory. Exact solutions to n-body problems where n is greater than 2 are hard to find. It has been accomplished in the case of 3 and 4 bodies, and a general solution where bodies do not collide has also been found, but these problems are extremely complex. One way to get around this complexity is to start with a two body problem (like mercury orbiting the sun) and then perturb the solution to reflect the effects of other celestial bodies. This is possible especially since the mass of the sun is so much greater than the mass of all the other planets in orbit.

UPDATE: To modify to reflect Ron's comments, a good way to understand how other planets effect each others orbits is to look at the anomalous precession of mercury which can be visualized here. Each planet causes a perturbation on the orbit of the planet, which can be understood as a slight lateral acceleration from the intended path if there were only two bodies. The anomalous precession of mercury was found after the effects of all the other planets were subtracted. One of the successes of General Relativity is that it can explain the anomalous precession, which appears to be non-conservative until one accounts for the full stress-energy-momentum pseudotensor.

As far as the rotation of the Earth, the Moon, Sun, Jupiter and other planets do have small calculable effects on the tides on earth. Tidal forces arise because objects like Earth have spatial dimension, and the gravitational force from another body has greater influence on the side of the planet closer to the force. Differentiating the gravitational force allows one to determine the tidal force.

The ocean tides caused by tidal forces do effect the rotation of the planet, so although the effect of other planets beyond the Moon, Sun and Jupiter is negligible, it is calculable, and does have some non-zero effect on the rotation of the planet.

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The effect on the rotation is negligible, and the effect on the revolution is the precession of the orbit to leading order, and not much else. You should say this to make it a complete answer. –  Ron Maimon Sep 21 '12 at 6:49
Thanks Ron! I will modify here shortly. –  Hal Swyers Sep 21 '12 at 11:54

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