The following is an Order of Magnitude puzzle: Guess within an order of magnitude of the answer and you win! You win nothing!
If you were to start any spot on land on Earth and dig a hole through the center of the Earth, what percent of the time would you come out on another spot on land, as opposed to having water spray out, comically spinning the Earth out of orbit to its death? (To be precise, the question isn’t about water spraying or not spraying out of the hole. It’s about the percentage of times you’d hit land.)
The answer is in the comments. But, wait, to help you, this fabulous mashup using the Google Maps API will let you sink your own knitting needles through the Earth’s nougaty core!
(All of this came from a mailing list I’m not supposed to acknowledge. Answers authenticated by the good folks at Wikipedia.)