The Mayans "predicted" the end of the world with one of their calendars to be on 21st December 2012. On this date, doomsayers assert that Earth will be ravaged by a smorgasbord of cataclysmic astronomical events ensuring we have a very, very bad day. However the Mayan Calendar never predicted an apocalypse.
The Mayan civilization existed from 250-900 A.D. in the current geographical location of southern Mexico, Guatemala, Belize, El Salvador and some archaeologists who have been studying this fascinating culture have been able to decipher their many calendars but their longest calendar that is "The Long Count" is what had created a stir in the minds of some theorists.
The Long Count
The Long Count was used by the Maya to document past and future events unlike their other calendars which were too short to document any date beyond 52 years. This calendar being a departure from the other shorter calendars is a numerically predictable calendar and not based on archaic measures of time.
According to this calendar, it will last for about 5,126 years. This calendar was set to start in the year 3114 B.C. according to our modern Gregorian calendar. If the Long Count began in 3114 B.C. and it's calculated to continue for 5126 years, the "end date" will be 2012 A.D. Further refinement sets the date to Dec. 21 to be the date for winter solstice for the Northern Hemisphere.
The Mayans noticed the relative slippage of the positions of stars in the night sky over long periods of observation. By the Long Count, the Mayans fast-forwarded to anchor December 21, 2012 as the end of their Great Cycle and then counted backwards to decide where the calendar would begin. Thus the Great Cycle we are currently in began on August 11, 3114 B.C.
Also in the words of Joseph Robert Jochmans, "The Mayans recognize that we are approaching the end of a World Age... However, the Mayan elders do not prophesy that everything will come to an end. Rather, this is a time of transition from one World Age into another. The message they give concerns our making a choice of how we enter the future ahead."
It is however, interesting to note that there is only a difference of 12 years between the Hindu's beginning of the Kali Yuga and the Mayan's beginning of the Fifth Great Cycle which is the long count. If an average lunar year equals 354.36 days, then this would be about 5270 lunar years from the time when the Kali Yuga started until 21 Dec 2012.
This is the same year that the Mayans predict rebirth of our planet. It is amazing that both calendars began at about the same time over 5,000 years ago and both calendars predict a totally new world and/or golden age after about 5,000 years into their calendars.
The Mayan calendar does not really "end" in 2012, but rather, all the cycles turn over and start again, vibrating to a new era.