It really depends on what you would consider 'World' and how you interpret the question
If by 'World' you mean 'The Earth with its inhabitants.' - then IF some disaster happens ('Naturally' - e.g. an Asteroid hitting the planet, or 'Manmade' - e.g. Nuclear War) during 2012, which kills all life on the planet then the answer is 'Yes - the World would end'
However, if by your definition of 'World' is 'A celestial body such as a planet', then even if all life is destroyed - the actually planet would most probably exist (even in a mangled wreck) so technically the 'World' will still exist so the answer would be 'No....unless the disaster is the Sun going Supernova & disintegrates the planet to dust'
If however you are asking that 'something' will happen in 2012 that will achieve any of the above scenario's is very slim, so MY opinion on that is a '99.9% No'.
But since no-one can predict the future (even 'Nostradamus' predictions are vague anyway) & that the phase 'Anything can happen' IMHO is very appropriate in this situation - there may be that very slim chance, even at 0.000000001%, that 'something' does happen that will affect the whole world - maybe not necessarily 'end it' but will certainly 'change it'