Not really - or at least nothing so dramatic.

In his Works and Days, Hesiod (borrowing generously, if probably unconsciously, from Near Eastern myth) describes a succession of the five ages or generations of men who have populated the earth: the golden age, the silver age, the bronze age, the age of heroes, and the age of iron. Hesiod's own age/generation, the age of iron, is no picnic:

"[now] men never rest from labor and sorrow by day, and from perishing by night; and the gods shall [continue to] lay grievous trouble upon them." (176-7)

In the future, according to Hesiod, mankind will decay morally:

"The father will not agree with his children, nor the children with their father....Men will dishonor their parents as they grow quickly old...There will be no favor for the man who keeps his oath or for the just or for the good; but rather men will praise the evil-doer and his violent dealing. Strength will be right and reverence will cease to be; and the wicked will hurt the worthy man..." (182-94)

This degeneration will be physical as well as moral; eventually babies will be born prematurely aged. At that point, Zeus will wipe out the human race from disgust. (179-80)

This theme does not reappear often in later authors. Ovid references it in the first book of the Metamorphoses, but without explicitly identifying humanity with the decaying men of iron.

Another more or less apocalyptic thread in Greek myth centers on the prophesied overthrow of Zeus and the Olympians. The most famous passage is in Aeschylus' Prometheus Bound. Prometheus, chained to a rock in the Caucasus, foresees the downfall of Zeus:

"Yes, truly, the day will come when Zeus, although stubborn of soul, shall be humbled, seeing that he plans a marriage that shall hurl him into oblivion from his sovereignty and throne; and then immediately the curse his father Cronus invoked as he fell from his ancient throne, shall be fulfilled to the uttermost." (907-12)

Prometheus, as the later mythographer Apollodorus explains, is referring to Zeus' plans to have an affair with Thetis, the minor sea goddess who would later give birth to Achilles. If Zeus had conceived a son with Thetis, that child would have overthrown Zeus, and so destroyed the order of things that makes human life possible. (On becoming aware of the prophecy, Zeus married Thetis off to a mortal, Peleus, to preclude the birth of any future usurper).

There are various moments in Greek myth - most notably Zeus' tangle with Typhoeus, and the gods' battle with the savage giants - in which the divine order, and thus the human order, is threatened. But with the exception of Hesiod's pessimistic view of human destiny, there seems to have been little sense that it was all fated to end.