Is Dhaka, the capital of Bangladesh which has 100,000 residents per square mile. In practice that means having a city with approximately the same area as Bradford and packing it with the population of LA or Moscow.
Population density is generally a good thing. It boosts economic productivity by bringing consumers and producers closer together reducing transport costs and more importantly in the present day allows for more rapid dissemination of ideas as one comes into contact with more people. For similar reasons it also boost cultural creativity. Cities are also able to support a greater range of amenities than smaller settlements.
However, my instinct is that Dhaka probably has too much of a good thing. When I visited the second most dense urban area, Mumbai, I was very struck by the way that the congestion effectively inflated distances, making traveling even short distances into a lengthy ordeal. The city would effectively seize up during rush hour as the cities mediocre transport system buckled trying to move the population of a modest sized country around. The cliche cached image of Indian trains so busy they have passengers clinging to their roofs is basically unknown in most of the country but is commonplace in Mumbai. Dhaka’s terrible scores in measures of quality of life do perhaps bear out this suspicion.