Per Emporis as of today. Note that we are approaching 1000 skyscrapers.
Also add high-rises + skyscrapers to get a count over 7000+ as they are differentiated based on height. I believe skyscraper over 300 + per thier definition. Either 300/400 ft, but I'm inclined to believe they classify it over 300 ft.
Current U/C list as per CTBUH. Note that the Emporis list includes high rises as well or structures 8-12 floors depending on height.
This is not everything, nowhere near the u/c activity, but just some of the biggies rising.