I found this intriguing article in Construction Weekly - a lot of speculative proposals for high-rise buildings exceeding 828 meters (the height of the Burj). Included are not one, but two, building proposals for Houston that top out in excess of a mile in height. I think one of them goes all the way back to 1981, but I'm not sure about the other. Judging by the list, if built, they would have been the tallest buildings in the US for quite some time.
http://http://www.constructionweekon...urj-khalifa/1/