That's a good question. Here are some of my thoughts on this subjects...
First of all, it seems that the idea of The End of Times has been with mankind since the earliest civilizations and cultures. Virtually every major religion has room for this particular belief - that the world will end, judgment will be made, and eternal life will follow. Astrological cosmologies place very high significance on cosmic cycles, the nearest of which will occur in December 2012. Most versions of the Mayan calendar end on December 2012. Even Time Wave Zero, a mathematical theory of time formulated by Terence McKenna, forecasts that an event of unknown proportions will take place in December 2012. And the list goes on and on...
Here's my first point. I suspect that what the ancients meant by the End of Days was the end of life as we know it. That doesn't mean that life itself will end; it could very simply - and much more likely - mean that we're about to witness such a mind-boggling transformation after which our life as human beings will never be the same again. That may be a very bad thing -- but then again, it may well be an incredibly amazing, wondrous, and positive thing!
As for why this belief has always been so persistent in the collective human psyche, this is a long discussion. I happen to adopt a rather striking theory that will take a bit of time to explain. But here's the crux...
The general belief is that life in the universe has been pushed from behind ever since the Big Bang, the formation of the Earth, the emergence of life, the evolution of hominid forms of animals, the plunge into history, and so forth and so on. Now, I happen to believe in a rather esoteric mathematical model, which is that life is being pulled forward by some kind of attractor that lies ahead in the future. An attractor is a mathematical construct that became known with the advent of Chaos Mathematics, and explaining it in detail would take too long, especially since I'm not very good at explaining things. But if you're interested, you could look it up and learn more about.
Now, back to our conversation. The reason the belief in the End of the World is so common and prevalent is because this attractor is, metaphorically speaking, casting a shadow over its past - which is our own past, present, and near future. Many people have experienced this shadow over the course of history. Prophets, artists, visionaries, etc. The problem is that, since this attractor is infinitely unlike anything we know, the people who caught a glimpse of it couldn't understand, let alone explain to others, what it was. Some said it was God Almighty herding us to His Eternal Kingdom. Others saw it differently. But the end result is that the masses, which are always prone to hysteria, were much more inclined to believe that it meant an apocalyptic end to existence. And of course, the media - thriving on sensationalism and hype - found a treasure trove in making movies and documentaries about the apocalypse, the Second Coming of the Messiah, and so forth and so on.
I fully realize that my answer, short and incomplete as it is, poses even more questions. But then again, that's what discussion forums are for, right? :-)