Whereas I'd agree with /u/Khundes that the "Reformation" amounts to, essentially, a heresy tantamount to the controversy over Christology (specifically the status of miaphysitism) that split the Church after the Council of Chalcedon (451), I don't agree that the modern Orthodox Church is "founded on the ruins of the ancient Roman Church" (implying the Roman Church was demolished or destroyed and hasn't continually existed since its inception in the 1st century), "that sprang up when Constantine made Christianity the official faith of the Empire" (he did not, Theodosius I did), nor do I agree that the Orthodox Church "reached a structure featuring 5 Patriarchs" (the Pentarchy was - and is - rejected by the Roman Patriarch, aka the pope), or that the Patriarch of Rome "became" the pope after the Roman Empire fell, et cetera.

/u/Akuran has a more compelling point concerning "reformations" within the modern Orthodox Churches extant following the 11th century schism, which are the Churches I believe you're referring to. Major "reformations" or growths of heretical movements are stunted by modern Orthodoxy's fractured nature as a series of largely nationalist Churches; their compartmentalized nature acts as a sort of bulwark against the wide spread of things such as what happened to the Western Churches in the 16th century.

However, this same compartmentalization can also be seen as a split (or leading to splits) tantamount to the 16th century schisms in the West - for example, the fierce nationalism of many Orthodox Churches has led to charges of phyletism, the independence of the Russian Orthodox Church (with its size and prestige) and its rivalry to the Greek Orthodox Church has led to a host of issues in Orthodoxy (such as the inability to hold an Ecumenical Council, though I'm sure some Orthodox Christians would debate this), and the division of some of national Churches has led to jurisdictional issues that have caused schisms yet to be resolved (as with the Ukranian Orthodox Church and its independence from Moscow).

While not necessarily a bad question, this is a historically flawed question. And since it's come up a few times, I'm going to explain why.

Essentially this is analagous to asking why Japan didn't experience the Renaissance, or Australia the Enlightenment. These are not historical events or periods that just happen.

In the case of the Reformation, you have a very particular version of Western European history, the development of late medieval Catholicism, the impact of Humanism, the political situation in (modern) Germany, and the individual impact of individual actors such as Luther and so on.

The history of the Orthodox church is very different. Its theological emphases and development are different, its socio-cultural setting and embedding in eastern europe, its relationship to secular authority, and so on.

So what would an Orthodox Reformation be?

If all we mean by the question is a reform movement, then there are all sorts of legitimate questions we could study about comparing reform movements in general. If we mean a reform movement that led to a schism, similarly there are some historical questions worthy of research.

But if we mean something like,"Why didn't a western style Reformation occur in Orthodoxy?", then we are problematically close to thinking of the Reformation as a monolithic 'event' that occurs without regard for historical context.

In the end the answer to why Orthodxy didn't experience its own Reformation, is simply that the Reformation is a conceptualised schema of an event in western european church history which is illegitimately applied elsewhere.

Better questions would ask about reform movements within Orthodoxy, their origins, beliefs, relation to social history, and eventual outcomes.