The date is the apparent end of the "long count" calendar of the ancient Mayan civilisation.
Believers have gathered in Mexico near Mayan ruins, and in other supposedly spiritual places around the world.
Chinese police have arrested hundreds of members of a Christian group who apparently believe the prophecy.
Last year, experts said a new reading of the calendar revealed that it did not in fact predict the apocalypse.
Many believe the date in fact marks the start of a new era in the calendar.
However, among some the date is still being taken as heralding the end of the world.
Magical sites
Hundreds of spiritualists gathered in the city of Merida in Mexico, about an hour and a half from the Mayan ruins of Chichen Itza.
One spot thought by some to destined to escape the end of the world is the mountain of Bugarach in southern France.
However, those preparing for the end of the world were reported to be far outnumbered by journalists.
The Turkish town of Sirince, another site reputed to be safe from the end of the world, saw similar scenes on Thursday.
Hundreds of reporters were wandering aimlessly around the beautiful town of 570 inhabitants, the AFP news agency reported.
However, hotels around the Rtanj mountain in Serbia, a site rumoured to have magical powers, were booked out for the big date.
"I do not really believe that the end of the world is coming, but it is nice to be here in case something unusual happens," Darko, a 28-year-old designer visiting from Belgrade, told AFP.
'Evil cult'
In China, police have arrested almost 1,000 members of a Christian group which has predicted that Friday will usher in three days of darkness.
The group, called Almighty God, apparently urged its members to overthrow communism.
State media terms Almighty God an "evil cult", the same description it applies to the banned Falun Gong group.
The belief has gained considerable popularity in China, where the film 2012 was a box office hit.
A farmer in Hebei province, Liu Qiyuan - not a follower of Almighty God - has built seven survival pods which can contain 14 people each.
The pods, made of fibreglass, float on water and can survive storms.
Mr Liu told the AFP news agency: "If there really is some kind of apocalypse then you could say I've made a contribution to the survival of humanity."
To calm anxieties, police in Beijing have posted an online notice telling people that "the so-called end of the world is a rumour".
source: BBC
