As you scan the Olympic medal tally, one thing stands out: larger countries tend to win more medals. There are a few notable exceptions, though, including New Zealand, which wins many more medals than you'd expect of a country its size.
So who leads the world in medals when you correct for population? That is, which country wins the most medals per capita? This site, which is updated daily during the Olympics, provides the answer.
In addition, it calculates the leaders in gold medals per capita, as well as a weighted medal count where gold is worth four points, silver two and bronze one (weighting as suggested by the New York Times.) Finally, it's a little unfair to ignore the relative wealth of countries, so the site counts medals relative to GDP (provided by the World Bank.)
My bias? I'm originally from New Zealand, which has consistently been in the top half-dozen or so countries for total medals and gold medals per capita, and in 1984 won the most golds per capita.
Others have thought about this, of course. Here are some links to other discussions: