Since 2012, a team at New York University has been working on something called the Atlas of Urban Expansion. What they are doing is collecting and analyzing data related to the quantity and quality of urban growth around the world. Everything from population densities to how well the streets were laid out during each geographic expansion.
The Atlas defines a city as having at least 100,000 people, which is a commonly used benchmark. According to this definition, there were 4,245 cities on the planet as of 2010. Included in their study is a representative sample of 200 of them, all of which can be found here.
They are also, rightly, looking at each city in terms of its extrema tectorum — the limits of its built-up area. This is as opposed to using administrative boundaries, which wouldn’t be as relevant in a study like this.
I really like the animations that they created depicting urban growth from 1800 to 2014, because they show: (1) where each city started (the dark nucleus); (2) how different urban shapes emerge as a result of geography, transport, and other factors; and (3) how land consumptive many of our cities have become in recent years.
Image: Atlas of Urban Expansion