Okay, so the world didn't end today, just a cycle in the Mayan calendar. But from a gaming perspective what if you actually built a specified date for the end of the world into your campaign world? And what if this fact was known, either to everyone in the world or only by a learned few? Obviously if that final date is a long way off, on the order of several centuries or more, then it doesn't affect people's daily lives much--except for creatures with a very long life span such as dragons, vampires, or liches. A very close date, perhaps 30 days or less, means your campaign will be a rather short one.
Another major factor is whether there are any signs that the end is nearing. Jack Vance's Dying Earth stories are set on Earth far in the future where the sun is going red and often flares or dims without warning. Everyone is afraid that the end may come at any time: the warning signs are there, but nobody knows the actual date. Naturally, there is a lot of speculation. Religious cults appear trying to explain it and prescribe methods to ward it off, philosophers offer explanations, and frauds peddle various schemes to exploit the fearful. If people already have been told that the end is coming, these portents will add to the mixture of dread and apathy in the populace. If most people do not know, then the signs are more likely to cause panic and confusion.
So, if you wanted this End of Days to affect plot and story lines in your game you'd probably have to set the date no more than 20 years away. Assuming that this end of the world is an event which no mortal (the PCs) can affect, then you have to plan your story arc accordingly. But then, if the world is ending in less than a couple years who really cares about anything? Sure, most people will have a will to survive day-to-day and so in the short term they will keep plodding on. But why save money? Why go to school? Why have children? Why take care of your long-term health? Why not just turn to a life of wanton crime?
Really, I suspect that a game set in the actual end days would probably have to be a storytelling type game where people enjoy building the story and exploring character motivations. The typical group probably wouldn't go for it.
But what if the "end" is really a new beginning? Take the story of the ark in the Bible, for instance. It was the "end" for everyone not on the ark but there was a new beginning. Or in a more modern vein the ark ships at the end of the movie "2012". You could arrange for the player characters to be the only survivors or among the few survivors who start the new world. This could be a "cleansed" or devastated world now to be rebuilt or the survivors might migrate to a completely new place.
For my campaign world I have an "occulted" chaotic primordial god secretly working behind the scenes to destroy the world built by the other three lawful primordials. Maybe I should give that occulted primordial some sort of timeline for his plan--now there's a good major plot line!