I imagine a world several years after a nuclear war. The outside world is a barren wasteland. Many live on the outside, free to do whatever they want, but struggling to find clean food and water. Some, though, live in underground vaults; they're confined within the small living quarters, but don't have to worry nearly as much about finding purified water and food.
The radiation has brought dangers to the world other than making food and water dangerous to consume, though. Many of the people affected by the radiation mutated. Though the mutations offer some benefits, such as prolonged life or immense strength, it has side effects. Rotting flesh makes many mutants outcasts; degeneration of the brain drives other crazy.
Thankfully, there are still weapons left from the war to fend of vicious mutants. Many people make a living trading guns. Unfortunately, with most of the old money lost or destroyed, they only have bottle caps to use as currency...

(I just beat Fallout 3 a few hours ago. That's exactly what I'm going to think about from now on when somebody mentions a post-apocalyptic world.)