The following is courtesy of my brother, Kebes:

Most sources seem to rank countries by gold medal count, or total medal count. I prefer to scale the results by the population of the country. After all, if Olympic aptitude (raw talent/motivation) is spread uniformly throughout the gene-pool/geography, then having 10-times the population means that you have 10-times the chance of a citizen within your arbitrary borders being born with the requisite talent/motivation. (Yes, this assumption has its flaws.) Differences beyond this population-scaled value can then be attributed to funding, opportunity, national spirit, etc.  (and in the case of China, the government forcing kids to train/compete, sometimes against their wishes). 

So, presented below are the current Olympic standings, after scaling for population. (The list of participating countries comes from Wikipedia, the medal standings come from the CBC, and the population and GDP statistics are from the CIA World Factbook.)

The shape of the above data might suggest my technique is unfair. After all, the big-population countries seem to have a difficult time ‘overcoming’ the size of their population (whereas a small country can anomalously grab one medal and be rocketed to the top). Then again, there are many small-population countries without any medals, so the peak in performance is actually somewhere in the middle of the population distribution.

Here is a table listing with all participating countries:

The countries without medals are sorted by population (so the last entry on that list is the one with the highest population that didn’t win a medal).

Another thing I was curious about was which country was the most “efficient” in terms of “medals per dollar of Olympic funding” or something like that. Unfortunately funding stats are hard to find. Instead I estimated the economic power of a country using published numbers for gross domestic product (GDP). Here is the trend based on GDP and GDP per capita:

(The log plot obviously cuts off all those countries without any medals at all.)

Lastly, it isn’t surprising to see that more money means more athletes sent to the Olympics:

Point being, there are many ways to interpret the Olympic rankings. A straight medal count isn’t necessarily the most fair.

Addendum: The BBC also put together some similarly-themed lists.

Conclusion by Nique:  In the end we can see that the U.S. and China don’t rock as hard as one might first assume.  They are in fact, rather average.  As is Canada.  And there ain’t nothing wrong with being average.  Go team!