I will preface my post by saying that I am an Aztec and Mayan history student. I have read numerous texts and studied as much as I could ever get my hand on in college or after I graduated. They are an intruiging society to say the least.
For years Mayans were looked at by some as being more "civilized" than others like the Aztecs because initially during the 1960s archealogists believed they didnt follow the practice of human sacrifice like the Aztecs did. In the last 50 years though they have come to discover that the two civilizations had marked differences BUT were very similar in their beliefs of what their gods stood for (ie the Sun, the Moon, the harvest, the rain, etc..)
Ok, now to how the 2012 prediction is not relevant. Aztecs and Mayans followed the same basic calendar. The followed the solstices and the equinoxes, evidenced by their pyramids being on those axis. Their calendars were very cyclical following like some have said blocks of 12 year or something of the like. Their larger calendar was based on 52 years, at the end of this calendar cycle they would say it was the end of the world. At that time they would extinguish all fires throughout the empire and after 1-3 days the priests would sacrifice victims using their hearts to start a new fire for a "New" world and a new set of 52 years. The idea of the end of the world was a very common idea within Mayan and Aztec beliefs. Years within the calendar had certain meanings, not too disimilar to what the Chinese calendar is today.
All we have to do is look at 1519 when the Spanish came to the new world and made contact with the Aztecs. It was not their appearance that threw off Moctezuma as much as their was a prophesy of the return of the god Quetzacoatl during the year One Reed, 1519 was the year One Reed. It had been prophesied that the gods return would also signal the end of their world and a beginning of a new one, for the Aztecs that was true to a great degree.
Their is alot we do not know about their calendars but the belief that it signals some cataclysmic event to change our world, I just dont believe it. I believe their calendar was based upon their animistic religious beliefs in the cycles of life and they didnt bother to make one to last for eternity.
Ok there is my rant about ancient civilizations haha.
Just an FYI, early christians also believed the world was going to end very soon after the death of christ because of circumstances in their world and the ideas of salvation and the end that were taught to them by the early disciples.
Not trying to preach, just trying to pass on some information that might help others understand.