While home today with a nasty cold, I thought I'd pull out some trusty mapping software and have a go. The map below shows the earth in a Mercator projection, with points where there is land on exactly opposite sides shown in red. The amount of overlap is surprisingly small - even the largest continents have almost no representation on the other side.
At first I thought there might be a mechanical reason for this apparent lopsidedness, something to do with balancing a spinning globe. However, thinking back in the history of the earth, Pangaea was one large supercontinent that plate tectonics broke up into the continents we know today. With the continents still shifting around, there would seem to be no particular reason why they might not line up across the globe from one another sometime in the future.
We can also examine this result statistically. The oceans occupy about 70% of the earth's surface, while land occupies about 30%. That means we should see about 9% (0.3 × 0.3 = 0.09) of the land cover having land on the other side. The actual number is about 8.4%, so really it's not too far from the expected value.