Is it possible to dig straight down and come out in China?
The opposite point of the earth, from where you are, is called the Antipode. I have created a map that will show you the two opposite ends (antipodes) of anywhere on the planet. You can drag the map around, and zoom in and out, and the other side will move around and show you the antipode.
What are Antipodes?
In geography, the antipode of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal to each other are situated such that a straight line connecting the two would pass through Earth's center. Antipodal points are as far away from each other as possible.
Resources
Mental Floss has also done a great article on the idea of digging to china.