*Hundred Years War, a sruggle between England and France, with either a historical ending (both being independent and England abandons continental matters), a planteget ending (a "dual monarchy" empire title with kingdom of France and Britain as de jure kingdoms, perhaps even a hybrid culture), a stalemate ending, France never regaining parts of France such as Normandy, Brittanty, and Aquitane, or even a fractured ending - both parties are devastated, the English continental holdings become independent, France fractures.
*The Black death, a worldwide struggle that is triggered by the mongol invasion, serverely devastating highly populated regions unless decisions such as the Ventian quarantine is taken. (a struggle is probably not the nest way to emulate the black death, but it is possible)
*Formation of the Swiss confederation - triggered by high tryanny of the emperor while having high crownland, leads to a historical "republican" Confederation, the emperor completely crushing the confederation, or an ending where the confederation becames too successful and weakens the empire.
*Authority of the Pope - whether the emperor and Norman conqerors would cede central Italian lands to the Pope or not, as promised by the donation of Pepin. The struggle would either end in the pope gaining the entirety of the de jure kingdom Romagna, the emperor stripping the Pope of temporal powers, or a stalemate where the Kingdom of Romagna loses de jure duchies to Italy and Sicily except for Latium.
*Almohad Caliphate - Whether or not the Magreb and Al-Andalus would fall under Islamic funamentalism, in addition to the struggle of Arabization of Berbers in Magreb.
*Struggle of Anatolia - previous posts has already suggested a Turkish invasion of Anatolia, this is the struggle after the invasion. Anatolia fractures as the Sultanate of Rum weakens, would one of the beyliks reclaim the title of Sultan, or would Anatolia remained fractured, or would Eastern Rome restore its authority over Anatolia?
Matter of Pannonia - would the Avars, the Magyars, the Bulgarians, the Slovaks, or the Romanians dominate Pannonia or would none of them?
There are many more historical situations which can be a struggle in game, I am just listing a few.