From a developed world perspective and a North American one, my understanding is that the best time to develop a subway network in a relatively cheap way was the early 1900's. That's when many networks like NYC, Chicago, Boston, Philly were built, same with Paris, London. Currently I believe we're in the ballpark of Chicago & Boston in terms of population, but back then we were a much smaller city than those. Things like cost of labour, safety regulations, accessibility requirements, and property prices now make building transit more expensive in the developed world.
Population of cities in 1900:
Old City of Toronto: 208,000
What is now the City of Toronto, the “416″: 238,000
Island of Manhattan: 1.8 million
New York City: 3.4 million
Paris: Over 3 million
Greater London: Over 6 million
In North America, most of the cities listed above haven't built many new lines in the later quarter of the 20th century. In the west coast, many of the new transit lines are LRTs. I believe that LA's new LRT lines are often along hydro corridors or rail corridors, so they don't involve expensive tunnelling. Portland has been building LRTs, Vancouver uses Skytrain.
Chinese cities and other developing countries are probably at a similar stage as say NYC back in the early 1900's, except possibly even more so with bigger populations, no regulations or restrictions and cheap labour. Their city's populations are 5x-10x Toronto, so it's not even comparable.
Interesting post on this:
http://stevemunro.ca/?p=9275