Remember this thought experiment?

Imagine a perfectly straight hole drilled through the Earth, passing directly through the center.  Now imaging falling into this hole.  What would happen?

With this program you can also model another interesting thought experiment:

Imagine a train which goes on a perfectly straight track between two cities.  Perfectly straight, as in, through a tunnel drilled into the earth (to compensate for the Earth's curvature between the two cities).  What would happen?

The surprising answer is - the train would be powered by gravity down into the tunnel, reaching maximum speed halfway between the two cities, and would then slow down just as it reached the other side.  Neglecting air resistance and friction, the train would not need any other source of power to travel between the two cities.

As far as I know, this phenomenon has never been exploited for actual travel.