The Greymarch

With every era comes the Greymarch, where Jyggalag walks the lands of the Shivering Isles (Sheogorath's realm) to bestow order through the realm and try to destroy madness.

The event is a massive battle between the minions of Jyggalag and Sheo. By the end of it all, it is Sheo's champion (whomever is wielding the Wabbajack, a powerful staff) tries to defeat Jyggalag's chosen champion.

Should Jyggalag win, he will destroy the Shivering Isles completely and leave it formless, covered in silver and gold, conforming and without individuality.

Should Sheo win, Jyggalag goes back into his dormacy and waits for the next Era to try again. Upon the defeat of Jyggalag, Sheo has to rebuild the Shivering Isles from the destructive manner of the Prince of Order.

As of yet, Jyggalag has remained unsuccessful in taking over the Shivering Isles. However, it doesn't stop him from trying.
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References:
http://elderscrolls.wikia.com/wiki/Greymarch_(Lore)

Bloodmoon Prophecy

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The Hunt of Hircine is an event that occurs every era when the Prince enters a realm releases his Hounds upon the land. The Hunt is proceeded by four signs.

1. The coming of the "Hounds", when an abundance of werewolves appear on the land.
2. The "Fire from the Eye of Glass", a pillar of fire which appears on the surface a frozen lake.
3. The "Tide of Woe" where there is a massacre of coastal creatures that is by far out of ordinary, and noticable.
4. The last is the namesake of the prophecy: the "Bloodmoon" when the moon turns crimson from the blood of the Hunter's Prey.

After the four signs is something called the "Hunter's Game", which varies from era to era. It could be a massive hunt, or it could be the hunting of one man.

Regardless, he chooses a Champion from the Hunt.
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References:
Bloodmoon Prophecy