The Mesoamerican Long Count calendar is a non-repeating, vigesimal (base-20) and base-18 calendar used by several pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is often known as the Maya (or Mayan) Long Count calendar.
A few years ago there was much hullabaloo about December 21, 2012 being the end of the world since it was the last day on the Mayan calendar.

Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since a mythical creation date that corresponds to August 11, 3114 BCE in the proleptic Gregorian calendar. The Long Count calendar was widely used on monuments.
Taken from Wikipedia.

East side of stela C, Quirigua with the mythical creation date of 13 baktuns, 0 katuns, 0 tuns, 0 uinals, 0 kins, 4 Ahau 8 Cumku – August 11, 3114 BCE in the proleptic Gregorian calendar.