Dave, you've got part of the picture. The centrifugal force of the earth's rotation does indeed cancel gravity to a minute extent, but it also causes the earth to bulge at the equator. Therefore the surface is closer to the centre of mass at the poles, and as Newton sez gravity increases as the two objects get closer together (the old inverse square rule). And for the rest of you, forget the notion that gravity will increase as you descend a mineshaft- it actually decreases (there is more mass above you and less below) and is zero at the centre of the earth.