Well dry could denote many things such as hot and cold dry. When it comes to hot dry I would say Mongolia, India, Afghanistan, Iran. On the other hand, countries like Russia can also be seen as dry in the sense that it is so cold the vegetation does not grow, regions in northern Russia especially fit this criteria.
The driest are probably Saudi Arabia and Mongolia.
The Gobi desert in north western China and Mongolia, if you include the Middle east, the Rub al Khali (the empty quarter) in Saudia Arabia.
Qatar and Bahrain get only about 75mms per year of rain; that is the least in Asia. They are surrounded by the Persian Gulf so there's lots of coastline but little rain.
