probably the same thing that happened on 1/1/00.
As a matter of fact, mayan artifacts also mention dates as far in the future as 4000 AD. The date of dec 21 2012 is not the end of the mayan calendar, just the 13th cycle of the mayan calendar. When a cycle ends, a new one begins. Maybe something will happen "supernatural" at the end of each cycle, just like something was supposd to happen when we entered the age of Aquarius. Maybe nothing.
But I doubt it will be the end of the world.