Nuclear war, zombie outbreaks, meteor strikes, economic collapse, alien invasion, no matter how it happens an apocalypse makes for a unique and engaging setting to run a campaign in, even for a jaded GM.
Here’s a few quick tips that can make a good zombie or other post apocalypse game a great one, and keep the group coming back (from the dead?) for more.
At regular intervals, a god takes control of your world's weather. Choose the gods at random each turn of the interval and begin applying their effects subtly. Their power will depend on the strength of those who worship them.
For civilised people, worship of a god actually wanes during that god's month in an effort to reduce their potential destructive effect.