Where do I end up if I dig straight down?

Alex Harford posted a message on the piclist (electronics enthusiasts, mainly PICmicro microcontrollers) debunking the common belief that if a person in the USA digs straight through the center of the earth, they'll end up in China.

I determined to resolve the question and explore where the end of the tunnel occurs given any spot on earth. I spent an hour making an antipodal geography tool using Google Maps to answer the question: