Note: This post is almost completely tongue-in-cheek. Obviously the chances of December 21, 2012 heralding in an apocalypse, definable maybe as an event causing billions of deaths and/or global catastrophic infrastructure damage, are slim to none.
But they aren't actually none.
Let's say there's a 5% chance of a superhuman General AI being developed in the next 10 years and ushering in the singularity. Let's say 4/5 of those scenarios would lead to a Bad End which could reasonably be called an apocalypse (or an "AI-pocalypse", perhaps). And let's say the distribution of probability isn't linear, but is exponentially skewed somehow so that given the emergence of AI in the next 120 months, the chances of it happening in this very month are 1 in 100,000. Then let's divide that by 30 so we can get our apocalypse rolling on the right day.
5/100 * 4/5 * 1/100000 * 1/30 = 1 in 75,000,000
Admittedly, low odds. This comports with the fact that there would have to be a lot of unknown development progress being made already on the problem for an intelligence explosion to be anywhere on the horizon.
But compared to some of the scenarios debunked by NASA (http://www.space.com/18678-2012-mayan-apocalypse-fears-nasa.html), such as a collision with the rogue planet Nibaru, or Earth being sucked into the supermassive black hole in the center of the Milky Way 30,000 light years away, the AI-doomsday scenario starts to seem relatively plausible.
I think the only other (relatively) plausible contenders would be the release of a pandemic-causing biological weapon, or the start of an international nuclear war. I haven't done any Fermi calculations on those, but I'm sure their probability exceeds that of solar flares scourging the surface of the Earth.