How dense are dense cities?

I am often talking about densification of cities as a way to avoid urban sprawl, achieve both economic and environmental goals and at the same time get a more attractive city for the inhabitants and visitors. But how dense are actually dense cities?
Few large cities have a higher density than 10,000 persons per square km as long as we talk about the whole urban area. This is for example the case for Asian cities like Mumbai, Delhi and Seoul. Seoul with 12 million persons on an area of 605 square km, and a population density of 17,000 persons per square km, is really a very dense city. Paris is a European city of very high density, at least in the central parts. The density in the city of Paris, an area of just 87 square km, is actually as high as 25,000 persons per square km. For the metropolitan area of Paris, the density is only 3,500 persons per square km however.
Cities with a population density of 2,000 persons per square km for the urban area could hardly be regarded as dense, but those cities usually have a higher density in the core area. A number of these cities have densities of approximately 6,000 persons per square km. Stockholm has a population density of 4,200 persons per square km in the administrative city and 3,300 persons per square km in the urban area. The density in the inner city however is 8,200 persons per square km, and in the densest parish, Maria (where I happen to live), density is as high as 24,000 persons per square km, same as in Paris. But this is a very small parish with a population of only 20,000 persons compared to Paris with more than 2 million. Hundred times as big, but with the same density.
Central parts of Stockholm.
American cities are well known for urban sprawl and low density. But New York City is actually quite dense. New York City has a population of more than 8 million and a density of 6,800 persons per square km. The maps of Central part of Stockholm (above) and Manhattan in New York (below) are in the same scale for comparison (maps from Google Earth).
Central parts of Manhattan, New York City
Pune is an Indian city in the state of Maharashtra south east of Mumbai. Pune has a population 2007 of approximately 3.2 million persons within the administrative area and a population exceeding 5 million in the metropolitan area. The central parts of Pune are shown on the map (below) at the same scale as Stockholm and New York City.
Central parts of Pune, Maharashtra, India
The average population density in Pune in 2007 is estimated to approximately 12,000 persons per square km. The density will most likely exceed 20,000 persons per square km., in 20 years from now.
One conclusion is that dense cities is not only a question of density, but also a question of size.