I'm at 58* 21' N, 134* 35 W, so my antipodal point would be around 58 S, where there is essentially no land at all. It's South of Madegascar (WAY South), and around 10 or so degrees North of Enderby Land in Antarctica.
Since the earth's surface is roughly 3/4 water, I guess we shouldn't be surprised that any randomly chosen point on it is quite likely to be miles deep in H2O. That points out the importance of being prepared to survive adrift, so maybe this whole thread isn't totally off-topic after all!
Nels