The Taliban had strictly forbidden the game of chess in Afghanistan, but there was recently a tournament in Kabul. And in Iraq, it looks like the Shia leader Grand Ayatollah Ali al-Sistani - "the most powerful man in Iraq" - will win the election and so chess in Iraq will also be forbidden. It used to be forbidden in Iran, but now it is "blossoming." Supposedly it was banned because the Ayatollah Khomeini said "it hurts memory and may cause brain damage."
The USSR banned blindfold chess in the 1930's because "it was too taxing and led to mental sickness or even death."
Here is more history of chess bannings and condemnations:

Chess was condemned and forbidden by the Eastern Orthodox Church in 1093. Rabbi Maimonides included chess among forbidden games. Bishop of Paris Odo Sully banned chess from the clergy in 1195. King Louis IX forbid chess as a useless and boring game in 1254. King Charles V prohibited chess in France in 1375. Ivan IV of Russia banned chess and labeled it a pastime of Hellenic deviltry in 1551.