Given how often one comes across the phrase "Mayan Prophecy" (including the titles of books and documentaries) you'd expect to discover that the Mayans predicted the end of the world in 2012.
Although most of the ancient Mayan literature has been lost forever (the Spaniards burnt all except 3 or 4 of their books), there are still many monuments and murals that have been deciphered, and only one has been discovered, so far, that makes a prediction for 2012. It reads:
…(long ago) it happened, the day Eight Chuwen, the ninth of Mak
when the Becoming-Ripe-House was constructed(?).
It was the ‘underground house’ (shrine) of (the god) Ahkal K’uk’.
It was two and nine-score days, three years, eight-score years and 3 x 400 years
(before) the Thirteenth Bak’tun will end
on Four Ajaw, the third of Uniiw,
when ..?.. it will occur,
the descent..?.. of B’olon Yookte’ at ..?..
The few translations of this inscription from Tortuguero Monument 6 are all very similar. Where it says "it will occur" is translated from the Mayan verb utom, which can also be translated as "it will happen" - and is a strong indicator of a prophecy being spoken of. The god B’olon Yookte’ has various meanings. Unfortunately half of the inscription is missing, so we might never know the full story. I came across this inscription years after deciding that most pyramids are bunkers, and therefore I conclude the above is discussing the building of a bunker (underground house) to be occupied in 2012 (the descent) by the god (Mysterous Elder - not a Mayan).
However, in many places we have found the Mayan "myths" of what took place at the end of the previous ages, and each involved humans being totally wiped out, so the gods could recreate us from scratch.
Otherwise, Mayan prophecies tended to be rather mundane, such as "137 years hence, it will be a Tuesday, the 200th anniversary of our king's birthday."