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Buddhism generally utilizes the Hindu Cosmology, [http://en.wikipedia.org/wiki/Religious_cosmology#Buddhism], except where it doesn't. Buddhist and Hindu Cosmologies posit an infinite number of universes (and infinite beings).
It also has in its list of the 1000 Buddhas[http://www.rigpawiki.org/index.php?title=1002_buddhas_of_this_Fortunate_Aeon] that will rise in this Age, of which 3 have already lived and died prior to Buddha Shakyami. Maitreya (See Matthew's links.) would be the #5 Universal Buddha. Mahayana Buddhist Sutras also has further legends of "future" Buddhas, such as Chinrezig, Padmasambhava, Lama Tsonghapa, etc., that would be born in India, Tibet, etc., in the 2 centuries after the Buddha's death. (I don't find all of these cosmologies useful, but each to his or her own.) Hope that helps.
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Another Buddha -- Metteyya (Maitreya) -- will gain Awakening, his monastic Sangha numbering in the thousands Digha Nikaya 26 ref- http://www.basicbuddhism.org/index.cfm?GPID=29
I had to look up apocalypse, "the complete destruction of the world." That doesn't seem to be a theme in the Buddhist cosmologies where the universes have no beginnings and no ends.
(EDIT: Hmm, looks like I'm wrong-- the universe periodically falls to pieces and then rebuilds itself. But it isn't immanent-- a Mahakalpa is a long time from now, and a new universe rebuilds itself every time.)
Mappo, the time when the Dharma is forgotten and no longer taught is a Buddhist catastrophe, but more of a moral one.
Digha Nikaya 26 ag
Monks, a time will come when the children of these people will have a life-span of ten years. And with them, girls will be marriageable at the five years old. And with them, these flavours will disappear: ghee, butter, sesame-oil, molasses and salt. Among them, kudrusa-grain will be the chief food, just as rice and curry are today.
And with them, the ten courses of moral conduct will completely disappear, and the ten courses of evil will prevail exceedingly: for those of a ten-year life-span there will be no word for "moral", so how can there be anyone who acts in a moral way?
Those people who have no respect for the mother and father, for ascetics and Brahmins, for the head of the clan, will be the ones who will enjoy honour and prestige.
Just as it is now the people who show respect for mother and father, for ascetics and Brahmins, for the head of the clan, who are praised and honoured, so it will be with those who do the opposite.
Mappo also leads to interesting consequences for current times, such as questions on if traditional forms of practice are effective anymore if we don't have a Buddha in the world. This is a big theme in Nichiren Buddhism.
When the Maitreya Buddha returns he is a like the historical Buddha, but in some accounts, much better. For people who care about the future Buddha, it is sort of like Pure Land Buddhism, where you wait to be reborn in a universe with an active, living, teaching Buddha. In Maitreya's case, that happens to be the same universe as our own. By the logic of Pure Land Buddhism, it seems like it would be more expedient to be reborn in the next life in the Amitabha's Pure Land.
Also interestingly, Maitreya played a big role in the White Lotus Rebellions, a political-religious movement in ancient China that lasted several hundred years that predicted Maitreya was returning right now. http://en.wikipedia.org/wiki/White_Lotus
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In Buddhism the universe goes through a cycle of expansion and collapse. The collapse is not the end of everything but part of a cycle like the waves in the ocean. So this might not fit into the traditional sense of an apocalypse.
See Wikipedia Entry on Buddhist Cosmology for further details on the cycles.
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Read the Saptha Suriyuggamana Sutta and the Agganna Sutta. Unlike other beings, humans life span is said to be variable. It's said to be on the decline now. One day, it is going to fall down to 10 years. Then the apocalypse will happen by one of three ways. If hatred is prominent in the societies, weapons will bring about the apocalypse and most of those who die will be born in Niraya. If craving is more prominent in the societies, famine will cause the apocalypse and most of those who die will be born in the Peta(hungry ghost) realm. If ignorance is more prominent, epidemics will cause the apocalypse and most of those who die will be born in heavens due to the compassion towards the sick.
After a while, those who had left civilisations and hid in the forests and caves come back to see the destruction caused. They realize hatred, craving and ignorance caused the near extinction of humans. So they start to become virtuous, start to keep to the five precepts. Then the life span slowly increases again. It will increase up to an Asankya(10^140). Having such a long life span is also not a good thing. People start to think that they are eternal as they don't see death. Then the defilements start entering the minds again. As a result, the life span starts to go down over time. When it drops down to 80,000 years, Maitreya Buddha will appear in the world.
Saptha Suriyuggamana Sutta goes on the explain in detail, how the world ends when the Seven Suns appear in the sky. This happens after a long time, even much long after the Maithree Buddha Sasana ends.