I have come across three possible equivalences: Assuming one of the first two equivalences, the Long Count will again reach 18.104.22.168.0 on 21 or 23 December AD 2012 - a not too distant future.
A typical Mayan date looks like this: .2.6, 3 Cimi 4 Zotz.
The Long Count is really a mixed base-20/base-18 representation of a number, representing the number of days since the start of the Mayan era. The basic unit is the kin (day), which is the last component of the Long Count.
If a day is, for example, "4 Ahau 8 Cumku," the next day falling on "4 Ahau 8 Cumku" would be 18,980 days or about 52 years later.
Among the Aztec, the end of a Calendar Round was a time of public panic as it was thought the world might be coming to an end.
Since the numbered and the named week were both "weeks," each of their name/number change daily; therefore, the day after 3 Cimi is not 4 Cimi, but 4 Manik, and the day after that, 5 Lamat.