Stone is durable and impressive stuff, but it's also challenging to quarry, and heavy to move, and it has tension and stress limitations. Where there are resources available to excavate and cut it precisely, stone can be an extremely strong and useful natural material. Unlike brick, it can be stacked without mortar and support heavy vertical loads. Stone resists deforming, weathers the elements well, withstands fire and helps maintain stable interior environments. There are so many extraordinary stone structures that it seems a shame that modern construction uses stone more as decoration than anything else.
Today, there are cheaper and more efficient building materials that have usurped the position of stone in modern building construction, not the least of which are decorative stone veneers. It seems humbling, but steel, wood and concrete construction with a thin layer of decorative stone on the outside is more in keeping with modern budgets and standards of construction than the impressive, towering stone edifices of historical buildings. Newer synthetic materials are even mimicking the look of stone in much lighter weight, inexpensive incarnations, eliminating the need even for veneers.
Stone is still popular for its esthetic value, and it's unlikely that it will ever be completely eliminated. Stone has probably been around since the first Stone Age settlers reached for a few rocks to hold down their tent flaps, and as a decorative element in human design, it's bound to be a part of our structures for a long time.