Unless you lived under a rock, you were probably aware the world was supposed to end twice in 2011 (May 21, then October 21, per Harold Camping) and once in 2012 (December 21, per Mayan "scholars"). Exactly why they're so fond of the 21st remains one of those mysteries (I'm assuming because it's 1/2 of 42).
This is nothing new. Since the beginning of time, people have predicted the end of the world, thus far without success. The number of failed predictions is huge, and too long to list. People hoping for an apocalypse make Cubs fans look pessimistic.
William Miller (1782-1849) was another unsuccessful doomsday seer at 0-3. An American preacher, he initially predicted the world would end between March 21, 1843 and March 21, 1844 (again with the 21st!).
When the second date passed without incident he re-scheduled the apocalypse to April 18, 1844. Then, after nothing happened, postponed it to October 22, 1844. The last failed prediction so rocked his church that it became known as "The Great Disappointment" (why they were disappointed is beyond me).
Miller himself felt the errors were from incorrect translation of the Bible's chronology. He believed the end of the world was imminent, and continued to do so until it ended for him in December, 1849 at age 67.
There have been, and will continue to be, many others.
Now I, Dr. Grumpy, will tell you how, and roughly when, the world will end.
As the sun converts hydrogen to helium, it's luminosity will slowly increase over time. The rise in solar radiation will reach a critical point somewhere between 500 and 900 million years from now, reducing the carbon dioxide in Earth's atmosphere below the level at which plants can survive. As the plants die out, the amount of oxygen in the atmosphere will decrease, and all animals will be lost, too.
About 1 billion years after all life is gone, the surface temperature will increase to where liquid water can no longer exist, and the oceans will gradually vaporize into the atmosphere. Some will also collapse into the planet's mantle, due to venting of the mid-ocean geologic ridges.
What's left of the Earth, which will likely be similar to our neighbor Venus, will continue to orbit for another 3-4 billion years. At that point the Sun will reach the red giant stage of its life, and start to expand. Its increased size will take it beyond the orbits of Mercury and Venus, incinerating them.
The now widely-expanded solar atmosphere will gradually pull the Earth's orbit inward, until it too becomes ashes scattered through the outer layers of an aging star.
Eventually the Sun will throw off the outer layers, becoming a planetary nebula with a white dwarf star at the center.
The ejected layers will travel through space for another few billion years, eventually being taken up by a cloud of dust that's slowly condensing into a new solar system - just as ours formed 5 billion years ago - and again become part of a new star and its planets. Just as we're made of the base parts of a long dead solar system, so we will become another.
And that's how the world will end. And begin, again
My dogs couldn't care less about the end of the world. And I will take that cue from them.