As to the Maya, it wasn't until 20 years ago or so that we had begun to read their inscriptions, let alone understand their calendar system well. There were larger cities in Mexico and central America than there were in Europe at the time not long before Columbus arrived. And, things weren't all sweetness and harmony -- there were wars, rumors of wars, human sacrifices, slavery and all the rest 1000 years ago, or 500 years before Columbus.
Don't misunderstand the idea of "translating" a calendar. Did our calendar tell us the world was going to end at the end of the year 2000? No, it was the end of a year, a decade, a century and a millennium, but not the end of the world. December 31, 2000 was the end of all those cycles, and January 1, 2001 was the beginning of a new year, decade, century and millennium.
The same thing was the case with the Maya calendar, which was based on a cycle, in turn based on a count of 20 (I guess the Maya didn't wear closed toe shoes, because they did their math "base-20" where we do ours "base-10").
Anyway, December 21 is the end of a Tun (a Maya year-like interval made of 20 "months" of 18 days, plus some 5 or 6 extra days like our leap day, to keep the calendar in sync with the astronomy. It is also the end of a Katun (a 20 year cycle) and a Baktun (a 400 year cycle of 20 Katun). This whole Baktun cycle lasts 144000 days. So it is the end of a Tun, Katun, and Baktun (the 13th Baktun). The next day starts a new Tun, Katun and Baktun (the 14th Baktun starts) and a new 144000 day cycle starts counting again, just as they had calculated 13 times in the past.
The Maya did not predict the end of the world -- any more than Pope Gregory did when he developed our current calendar. The Maya "year" is called a "tun", and 20 of these is called a "katun". 20 katun is called a "baktun", about 4000 years, and on December 21, 2012, the 13th baktun will end, and on December 22, the 14th baktun will begin. This is just like December 31, 2000, the end of the 20th century and second millenium, and January 1, 2001, the beginning of the 21st century and third millenium. (I guess the Maya didn't wear closed-toe shoes, as they counted by 20s instead of 10s.)