After World War 2 most of the world's super powers developed nuclear weapons. Said weapons were so powerful that nobody really dared to use them because if somebody used one they'd receive another one in return. There is no winner since everybody basically dies. A nuclear war is enough to send the entire planet into chaos, a.k.a. nuclear winter.
Of course, this theme is popular in some modern day shooters. For example almost all Tom Clancy games have a nuclear war that's inches away from happening. Another popular idea is to show what happened after the nuclear war, making the player explore a desolate wasteland. Nuclear war is a recurring theme in the Fallout series.