I have heard this before. Gravity would accelerate it toward the center. Then when it gets past the center it would decelerate until it reached the surface at the other end at speed 0. Unless you picked it up, it fall back to the other side. The interesting thing is that you could create other shorter holes that do not go through the center of the earth. However the time taken to go from surface to surface would be equal because the shorter hole would give less time to accelerate.
Heres an article. http://www.damninteresting.com/?p=696 Its called a gravity train and would always take about 45 minutes from surface to surface. Heres another interesting one about the deepest hole ever drilled. http://www.damninteresting.com/?p=567
If I learned anything from Hollywood that would cause Earth's magnetic field to stop and all of us to get microwaved into crispy critters.
The train idea sounds cool, but I would have to say it is impossible! I don't think it would be conventional or easy to drill a hole that long/deep.