There are a lot of doomsday predictions in the XX century. Each of the predictions indicates its own date, but nothing have happened yet. You can find the List of doomsday predictions on Wikipedia. From the astronomers points of view the December 21 is interesting as the day of winter solstice. It is going to be the shortest day of the year. All scary predictions disasters for this day has no scientific basis. It is only a plot of imagination of fantasy writers. The most popular predictions are Nibiru's coming, geomagnetic reversal and planetary conjunction.

Here you can find short description of each of these versions:

Nibiru - a mythical planet in the Solar system. There is no scientific evidence of its existence. More details you can find here or on Wikipedia. If such big body had been directed to the Earth, we would have noticed it several months before the approach even in a daylight. Nothing like this has been happened. So there is no reason to afraid of a mythical Nibiru.

A geomagnetic reversal is a change in the Earth's magnetic field such that the positions of magnetic north and magnetic south are interchanged. The Earth's field has alternated between periods of normal polarity, in which the direction of the field was the same as the present direction, and reverse polarity, in which the field was the opposite. These periods are called chrons. The time spans of chrons are randomly distributed with most being between 0.1 and 1 million years with an average of 450,000 years. Most reversals are estimated to take between 1,000 and 10,000 years. The latest one, the Brunhes–Matuyama reversal, occurred 780,000 years ago. Brief disruptions that do not result in reversal are called geomagnetic excursions. More information you can find here

Planetary conjunction  occurs when two astronomical objects have either the same right ascension or the same ecliptical longitude, normally when observed from the Earth. In the case of two objects that always appear close to the ecliptic – such as two planets, or the Moon and a planet, or the Sun and a planet – this implies an apparent close approach between the objects as seen on the sky. In contrast, the term appulse is defined as the minimum apparent separation on the sky of two astronomical bodies. Conjunctions therefore involve two Solar System bodies, or one Solar System body and one more distant object such as a star. A conjunction is an apparent phenomenon caused by perspective only: there is no close physical approach in space between the two objects involved. Conjunctions between two bright objects close to the ecliptic, such as two bright planets, can be easily seen with the naked eye and can attract some public interest.

You can find a lot of different models and planetarium of Solar system in the Internet. For example, on this website. You can set the date, for example, December 21, 2012, and you will see how the world will be located. There is nothing unique in their location. If the conjunction could had lead to negative phenomena during the existence of mankind, it would have already been known. All the conjunction can be calculated and compared with historical events of those times, but this work is not for astronomers.

To summarize, I would like to recall, the end of the world in 2000, stories, theories, predictions, assumptions... The end of the world did not happen, as it will not happen in 2012. We can only gues how is it possible in our enlightened age be so naive and believe in such nonsense.