I've always been curious about this. One of the interesting things about soccer is that there seems to be little correlation about a country's economic ranking and how good its soccer team is. But is this actually the case? On one hand, soccer popularity is motivated by cultural factors that have little to do with a country's financial standings, and soccer does not have the financial equipment/facility barriers of sports like American football, hockey, or horse polo. On the other hand, a country has to have at least some money and population if it's going to put together much of a team: The Isle of Man isn't exactly boasting a powerhouse squad this year.
I decided to investigate the issue with this handy chart, comparing the remaining 16 World Cup teams' soccer power rankings (ESPN, before the tournament) with their countries' Gross National Product ranking (World Bank's rankings - a seemingly decent metric of a economic power). And yes, that's a U.S. Quarter behind the GNP numbers, because that's how I roll. USA! USA!
Then, I busted out the old Excel and ran a correlation test. On a scale of -1 to 1, the correlation of a country's soccer ranking to its GNP ranking is a pretty weak .384. As in, a very slight correlation, but not much.
And yes, before the math nerds get all crazy on me, I know there are some problems with the sample size, outliers, variable selection, etc., of the test that make it less than mathematically pure. For reference, there are just over 200 total countries, and none of the bottom 100 GNP-wise had a soccer team that qualified for the World Cup (Honduras was the lowest, at #107 GNP).
Still. It's kind of cool to look at.