This is not really a yes/no question as it's written. I think that many of the skyscrapers are structurally sound and have to be re-examined over the years to make sure they stay that way. There's always a possibility that natural disasters, acts of war etc. can lead to destruction and danger for residents of Manhattan.
Modern skyscrapers are safe because they are built to withstand most issues. Tall buildings are built using the latest technology and they have all of the latest safety features. There is no reason not to trust safety in tall buildings. Of course nothing is 100% safe, but Manhattan's skyscrapers are about as safe as you can get.
The skyscrapers were built by engineers who understands the science behind building a building. Most of the skyscrapers have been around for a long time and can withstand a great deal of stress. Skyscrapers are well built and they can stand up to almost anything with the possible exception of earthquakes.
The simple truth is that just how much functional life we derive from a property is, at the same time, dependent upon our maintenance. The fact is, there are construction strategies that are going to put a stop to devastating failures similar to the tragedy that happened at the World Trade Center.