Looking at the world's biggest structures (well, I just got curious, and Naaman is refuelling close by on the way back to Oz), and found that Burj Khalifa in Dubai is heftily the biggest by quite a way. 828m, or over 2,700 feet. Astonishing structure, with all sorts of records - like how about an open air viewing platform at 1400 feet.
Plans are afoot (apparently) for a mile high building, so over twice the height of Burj Khalifa.