[jennyp]

This same trick works in every direction, and at every point within the sphere, so you--and everything else within the sphere--feel no net gravitational pull from it. All you feel is the pull of the Earth, just as before.

Hmmm... Then if I drill down 100 miles, then as far as the net gravitational pull on me goes, it would be like I was standing on a planet whose diameter was 200 miles smaller than Earth's? Because all the mass located farther out from the center than myself would be like that massive sphere in your example?

[VadeRetro]

If you get to the center, the pull on you is zero. (But you better wear your flame-proof undies!)

[Physicist]

Just so.

[RadioAstronomer]

Hmmm... Then if I drill down 100 miles, then as far as the net gravitational pull on me goes, it would be like I was standing on a planet whose diameter was 200 miles smaller than Earth's? Because all the mass located farther out from the center than myself would be like that massive sphere in your example?

Think of it this way. G decreases at a linear rate as you approach the center of the Earth if it was a uniform density. (as the radius "r" decreases from the center)

Geek alert: Since the density is not uniform and much of the mass is contained near the center, G would initially increase.