This has become quite a long post so I'm going to start with the conclusion first so you don't have to read through the whole thing.
1. Only a handful of people live in Mega Cities (5.3% of all people living in cities) or cities over 10 million people (14.3% of all people living in cities). Most people live in the hundreds of medium sized cities. (I'm still wondering why we're focused on Mega Cities)
2. Most of the world's largest (by area) cities are in developed nations. New York is largest city in the world followed by Tokyo.
3. On the other hand, the most densely populated cities are in developing nations, most notably India.
4. The densest populated cities in the world are not Mega Cities or large cities. 53 of the top 58 densest cities of the world have less than 5 million people.
5. There is a clear negative correlation between population density of urban areas and wealth (GDP). The richer countries have cities that are much larger, most likely due to developed transportation infrastructure.
6. Cities in developing nations are growing much faster than cities in developed nations.
Sources
There seems to be two comprehensive sources of population data online:
http://www.citypopulation.de/
Website lists all the "Principle Agglomerations of the World" over 1 million people (471 of them) which they define as: "Agglomerations include a central city and neighboring communities linked to it (e.g.) by continuous built-up areas or commuters. Some agglomerations have more than one central city (e.g. 'The Ruhr')." The list of references show the usual web sources (CIA Factbook) along with other national statistics offices, but the table does not show which data comes from which site. Furthermore, apparently the data is estimated for a given date since not all the offices publish the data simultaneously. The website also offers a clunky map and graph interface using Java.
http://www.demographia.com/
An extremely cluttered website by Wendell Cox, a public policy consultant. The website has an amazing amount of data and studies, but most of them hidden in .pdfs. The list of world urban area populations (warning .pdf link) has reliability and source type listed for each data, and is sorted in couple different ways. They also have city size listed and data on population density.
Defining Cities, Urban Areas, etc.
From Demographia
"An urban area (urbanized area agglomeration or urban centre) is a continuously built up landmass of urban development. National census authorities in Australia, Canada, France, the United Kingdom and the United States designate urban areas. Except in Australia, the authorities use a minimum urban density definition of 400 persons per square kilometer (or the nearly identical 1,000 per square mile in the United States)."
"An urban area is different from a metropolitan area. A metropolitan area is a labor market and includes substantial rural (non-urban) territory or area of discontinuous urban development (beyond the developed urban fringe)."
"An urban area is different from a municipality (also often called a city). Municipalities have political boundaries that usually include only a part of the urban area. For example, the city of Seoul represents barely one-half of the population of the Seoul urban area, which extends well beyond the municipality."
Urban area/agglomerations seem to be most popular statistic since it's closest to what we imagine the word "city" to be. Municipality is rather arbitrary and metropolitan area can include farm lands if the transportation is there.
City Population Curve
Below is the bar graph of all cities larger than 2 million people from citypopulation.de. The red section shows city population larger than 20 million, the orange section shows city population larger than 10 million (I did the coloring in photoshop, not from the website).

I have the full graph with cities over a million people, but blogger is not letting me upload it, so here it is on my website.
As you can see, it's like many other popularity curve, a power law. Going with BMW's definition of over 20 million people (which LA and Shanghai aren't), there are 7 Mega-city with a population total of 160 million people. If we drop the bar to 10 million people, there are 26 cities with a total population of 430.2 million people. If we assume half the world lives in cities, and the world population is 6 billion people,
160/3,000 = 5.3% of people living in cities live in the 7 Mega Cities
430.2/3,000 = 14.3% of people living in cities live in cities larger than 10 million people
While the Tokyos, New Yorks, and Londons of the world are iconic and eye-catching,
they are hardly the dominant paradigm. Much more people live in the Seattles, Sevilles, and Hiroshimas of the world.
So why the focus on Mega Cities?
City Area and Population Density
From Demographia (.pdf link)
Urban Areas sorted by Land Area

Since the data is in a .pdf file, I copied and pasted the first page (top 58) into a gif. Observations:
1. While you may imagine New York and Tokyo to be these densely populated areas covered by high rises, they are also the largest cities in the world by area too.
2. A significant portion of the top 58 are cities in the US and cities in developed nations. The first city from a developed nation that makes the list is Jakarta, Indonesia at 14 followed by Beijing, China at 15. The first Indian city to make the list is Delhi, India at 58. I mention India because...
Urban Areas sorted Population Density

Again, the top 58 (unlike most rankings, they don't skip numbers when two things are tied). Observations:
1. The list is filled with India and other cities from developing countries. The first city from a developed nation that makes the list is Busan (or Pusan) from South Korea at 61
(not listed above) with a population of 3.6 million and 36,000 people per sq mi. The first US city to make the list is Los Angeles at 592 with 13.9 million people and 6,200 people per sq mile. The second most dense US urban area is the San Francisco - San Jose Bay area at 5.3 million people and 5,500 people.
2. Besides Mumbai, there are no cities with 10+ million people on the top 58 list. In fact, 53 of the 58 cities are under 5 million people, and 31 of the 58 cities are under 1 million people. The most densely populated cities in the world are not Mega cities. (I just realized Mumbai is not a Mega City in this data, possibly because they use statistics from 2001, while I'm guessing citypopulation.de extrapolated that data to get those figures).
Just to get a sense of 76,200 people per square mile (Hong Kong), imagine if 73.5 million people (about twice California) lived in the San Francisco Bay Area (and imagine how much worse real estate prices could get). Also 76,200 people per square mile means 366 sq ft of land per person.
In the final pages of this population report from Demographia, the following plot was presented:
(Note, this isn't GDP versus Population density, but rather GDP versus Population density of urban areas) The richer countries in the world have much less densely populated cities. Combining this from the earlier Gapminder post, you get the conclusion "Richer countries are more urban, yet those urban areas are much less densely populated."My instinct is that as cities develop and transportation develops, the cities expand faster than the population growth and people move to the suburbs for more space / cheaper cost of living.
Population Projections 2020
Demographia also has projections for urban area populations in 2020, based on what seems like previous trends. While I'm wary of such simple extrapolation (most likely exponential in this case) techniques, I think this gives an interesting look into what cities are growing fastest.

Again, this is only the first page (56 data points) out of a 3.5 page list (roughly 200 some data points). It's ordered by projected population ranking in 2020, and I added the red (lost spots), blue (stayed the same), and green (gained spots) dots to more clearly indicate changes. The yellow dots are cities in developed nations as defined by CIA World Handbook (and I don't agree with some designations).
Observations:
1. Cities in developing countries are growing much faster than developed countries, and some of the least developed countries are growing the fastest (i.e. Lagos, Karachi, Kinshasa). The only developed cities on the list to gain spots, Johannesburg, Toronto, Dallas, and Atlanta are all near the bottom of the list.
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