The Mayans are probably the most-quoted of the 2012 doom prophecies, and can perhaps be credited with getting the whole fad started.
Back when they were an advanced civilization living in Mexico's Yucatan Peninsula about 3,000 years ago, they developed around 15 to 20 calendars, all with a slightly different purpose: the Tzolk'in was used to calculate crop cultivation, the Haab followed the cycles of the sun and the Long Count ticked off the harrowing last days until face-bursting ultimate destruction.
It's all fairly self-explanatory.
The Long Count calculates a period of time known as the Great Cycle, which is a count of about 5,125.36 years. Scholars paired up the dates of the Long Count with Gregorian calendars and found that the current Great Cycle began August 13, 3114 B.C, and ends on December 21st, 2012. Dum dum DUUUUUMMM!!!
Bolstering their theory is that the date coincides with a winter solstice during which the Sun will align with the center of the Milky Way galaxy. When that happens, some say the Earth's poles will shift and every horrible natural disaster imaginable will come together to form a Megazord of planet crushing assbeat.
What Predictions (Supposedly) Came True?
Uh... It's a calendar. It accurately predicts the rise of the sun every day. Otherwise nothing.
Why it Might be Bullshit:
First of all, the end of the Long Count holds no more significance than Dick Clark's Rockin' New Year's Eve: the Maya just had a celebration and then started a new calendar. Even they didn't think it was going to be the end of the world, and even if they had, why the fuck would they be expected to know?
As for the winter solstice thing, that's just when the Sun is at its greatest distance from Earth. Our poles shifting because the Sun is aligned with the center of the Milky Way makes about as much scientific sense as saying you shouldn't drive at sunset because your car might crash into the sun.
Besides, the solstice occurs in June in the southern hemisphere, so if the world looks like it's going to end we can all just move to Australia.
A less popular but equally convoluted source is the I-Ching. In the pre-800-number era of human existence, the people of China received their psychic advice from one of their oldest texts, the I-Ching. You asked the I-Ching a question and a certified physic flipped three coins in to the air, drawing a hexagram based on the results. This told your fortune, somehow.
The I-Ching had nothing to do with the end of the world until a man by the name of Terence McKenna came along and made a pattern out of every possible result. After applying this pattern to a line graph accompanied by a timeline of recorded history, he discovered that the high and low points of the graph coincided with several significant events.