Depends on the classification, but the CTBUH classifies high rise as 100 ft or greater. With that, NYC has over 6500+. Add the proxy cities, and we are over 7000. I believe 500 ft + or 150m is a skyscraper, and anything from 100ft to 499 is a high rise.
But the category might depend on who are you are asking. Some South American Countries use a different system vs Asian countries. On a municipality or city prefecture system.