Flying into Manila I am always reminded how densely populated the city is (Metro Manila has a population of about 11.5 million packed into an area of 636 sq km, giving it a population density of over 18,000 people per sq km). That makes it the fourth most densely populated city in the world after Mumbai, Kolkata and Karachi, and on about a par with Lagos. Some sources list Shenzhen, Seoul and Taipei as more densely populated than Manila, but from my own experience in those cities, I don't think that is right. I guess it depends on how the boundaries are defined.
Shenzhen, Seoul and Taipei all have more high rise apartments than Manila, but once you have spent some time on the streets of these cities, I don't think there is any doubt that Manila is the more densely populated.