He calls them subway maps, but of course that term suggests that the service is all underground, which few "subway" systems are. What matters is that they're rapid transit. In this case, they're specifically rail rapid transit, which is why Staten Island's rail line in the lower left appears disconnected from the rest. In reality, it's just connected by rapid transit of a different mode: the Staten Island Ferry.
(By "rapid transit" this blog always means transit services that run frequently all day in an exclusive right of way with widely spaced stations -- linking centers to each other, for example, rather than providing coverage to every point on the line as local-stop services do.)
The opposite extreme is the Paris Métro, where a thick network of interconnected subway lines really does cover the dense part of the city, to the point that most of the population can easily walk to a station.
Neil's Paris map is a little misleading, because it doesn't show the outer-suburban RER network -- much of which does achieve rapid-transit levels of frequency. Yet it's helpful to look at the Paris Métro in isolation, compared to these other maps, just to see how small Paris proper is, and how densely it's covered with service.
Every line in this system has a long suburban tail, but they've been overlaid at the center in a way that creates a bit of an inner-city network.
Of course, it helps that among the American rail transit systems created entirely in the late 20th century, Washington's is the most extensive in terms of total miles of lines. Could this have something to do with the fact that Federal funding is administered by people who live there? No, couldn't be ...