Something reminded me of this remarkable building recently.

http://farm2.static.flickr.com/1053/1488454529_cc202cbd73.jpg

 

It must have an aspect ratio of a million to 1, with weight reasonably distributed along it, including at the top, and yet it stands.

Pretty impressive, but the cable stays are doing all the work, it's too slender to get much stiffness out of the cylindrical tower.

I should imagine that a building could be constructed like this to be extremely tall. Although given the angles of the cables they would have to be extremely long.

 

Given that the diameter of the earth is 12756.2km and the angles and heights of the cables proportional to the height of the building, one could work out the tallest possible building of this design.