DUBAI -- As financial crisis roiled much of the world in October 2008, the head of Dubai's biggest state-owned developer unveiled his latest megaproject: a $38 billion development that would include a tower nearly two-thirds of a mile tall.

"I'm sure most of you are asking why we're launching this, and you'd be mad not to question it," said the executive, Chris O'Donnell, at a news conference. Though there would be economic ups and downs in the years needed to build the tower, he told listeners, demand would continue to outstrip...