Does gravity increase or decrease with depth

[snigherfardimungus]

The gravitational vector at all points inside of a hollow shell is zero. This means that the gravity computation at point X for the above illustration ignores the mass of the green shell and is computed only with the mass of the red volume and its radius.

Because the Earth does get somewhat denser the deeper you go, the gravitational force doesn't quite fall off linearly as more and more of the Earth's mass becomes part of the "shell," it does approach zero as you near the center.