This is my first post, but this question interested me.
Think of it this way, it's like taking a ball that's perfectly sphere like. Put that ball in a "pool" or "half-pipe" like substance and or "shape" if you will. (Some will argue that gravity isn't straight, it's a force dependant on... well we all know that.) Anyway, assuming the friction and outside force(s) is slim to none (wind, obscurities, random objects.) you would go down one side, then out the other, this is assuming you drilled the hole on the right side side, some say that the earth is more like a sphere that's squished on the top, and bottom, kind of like a football. Assuming all that's true, you would eventually just end up floating in the center of the earth.
When you know how to drill a hole through the middle of the earth let me know, i'll jump with you.