This article is from the Calendars FAQ, by Claus Tondering firstname.lastname@example.org with numerous contributions by others.
Logically, the first date in the Long Count should be 0.0.0.0.0, but
as the baktun (the first component) are numbered from 1 to 13 rather
than 0 to 12, this first date is actually written 18.104.22.168.0.
The authorities disagree on what 22.214.171.124.0 corresponds to in our
calendar. I have come across three possible equivalences:
126.96.36.199.0 = 8 Sep 3114 BC (Julian) = 13 Aug 3114 BC (Gregorian)
188.8.131.52.0 = 6 Sep 3114 BC (Julian) = 11 Aug 3114 BC (Gregorian)
184.108.40.206.0 = 11 Nov 3374 BC (Julian) = 15 Oct 3374 BC (Gregorian)
Assuming one of the first two equivalences, the Long Count will again
reach 220.127.116.11.0 on 21 or 23 December AD 2012 - a not too distant future.
The date 18.104.22.168.0 may have been the Mayas' idea of the date of the
creation of the world.