Possible to happen? Yes. Likely to? No. Our doom can happen at any time...though we'd probably foresee it by a small margin - like seeing a meteor through a telescope, seeing a virus mutate or simply another country's nukes heading your way (though very unlikely, to fire nukes is suicidal)
If scientists are arguing about this, then they're not very good scientists.

This is entirely based on the Mayan calender ending and it being interpreted as being the end of the world. If you were to look at it rationally you'd think differently: if they were predicting the end of the world, what evidence do we have to suppose that people have a means of looking into the future? Given there is no "theory of divination" and such things are often considered to be superstition, it seems daft to take 2012 seriously.
An alternative explanation is that the Mayan calender had to end somewhere? It could depend entirely on effort on their behalf. Or could they have been predicting their own end? (which seems to have a margin of error...but if we suppose that they can't foresee into the future, but possibly believed they could, then it's a possible reason) Maybe they decided that 2012 was far enough into the future.
With talk of global warming and rising sea levels, you might wish to calculate the Norse and of the world, Ragnarök, but we don't. Add that every so often we have a prediction for the end of the world, but it would seem it never happens either. With the film 2012, I think Hollywood have just decided to play off of it.
People you have nothing to worry about.