The ultimate alternate history variation,but I know it's been done a lot. I've actually talked with some of the people I know,yes..we can give some reasons as to how the Roman Empire could have survived..but how would the rest of the world be? That..is where we tend to argue..
I've heard some say that if Rome survives,then Egypt would have to also..to provide balance. Unless Rome is just going to rule all of Europe to the Ural part of Russia and all of Africa if Egypt is not there to stop them.
Well, we've heard about Egypt from other posters. But why would it expand so much? OTL it remained pretty territorially stable from the reign of Augustus to the disasters of the 5th century: further expansion simply would be too much trouble, and would require the constant churning out of new armies and opportunities for ambitious generals that had brought so much strife to the Republic. As for Africa, again little to gain, plus a horrendous disease regime.
Of course, _something_ will have to be done about the Germans eventually, but expansion onto the Steppes or the boggy Russian woodlands seems unlikely before the invention of heavy plows and the development of the area enough for it to actually raise more in taxes than it takes to occupy. And then there's 800 years of horse-nomad invasions to deal with. And the Empire was so large it was hard to handle OTL: how much harder if it doubles in size?
No doubt a Chinese or Mongol or Manchu empire would rule most or all of Asia...
The Chinese empire lasted until 1911 in _our_ timeline, and they did no such thing. Why does the existence of Rome change this? Can't settle peasants in the desert or Siberia, south-east is jungles and Vietnamese, south-west is mountains followed by numerous and pugnacious Indians. West into central Asia is a possibility, if there aren't even more pugnacious Persians or Arabs or a Turkish Empire or the east end of the Roman empire. Until and unless it modernizes, I suspect the Manchu empire is about as large as a long-lasting Chinese empire gets. Now, _naval_ expansion is another kettle of fish - there's no reason why an alt-Chinese empire shouldn't be more grabby than OTL, especially if there are multiple Chinese colonizers and merchants softening things up to begin with.
But..the most interesting thing may be how the New World comes about..would Rome colonize it like the British,Spanish,Portuguese and French did? Or would Rome,Egypt and China ignore it..focusing on their own issues..leaving the Aborginies of the New World to develop on their own? ..
If Chinese or Roman navigation develops to the point where they reach the Americas, the Romans probably would: the native American civilizations are prosperous and weak targets, and whatever religion Rome has, they probably won't like the human sacrifice bit (memories of the Carthaginians and such). The Chinese might be a bit likelier to trade instead. In either case, the MesoAmericans and the Andean civilizations will be devastated by plague.
A super Aztec Empire covering all of Central America,northern South America and the American west?
The Aztec Empire was too ethnically confined to expand much- they didn't make their subject peoples into Aztecs the way the Romans did their conquests, AFAIK. They might last a while, but sans modern tech, they'll collapse and be replaced by some other MesoAmerican Empire.
A Maya or Inca Empire over all of South America?
Maya were already has-beens when the Europeans OTL showed up: the Inca might last quite a while sans Old World intervention, but they didn't penetrate the Jungle areas very much: too different from their normal environment.
You might get some interesting cultural hibrids from Chinese-Inca cross-Pacific contacts, if the Chinese decide that conquering these distant barbarians in their unlivable mountains [1] is too much trouble: Buddhist sun-worshippers sipping tea with just a touch of coca-leaf and writing in a pictographic language derived from the shapes of Quipu-knots...
What about Australia and New Zealand? A Hawaiian or Maori Empire?..
Maori might be interesting, but I'd suspect the area eventually falls under Chinese or Indonesian/Malay influence, unless the Romans play the role of "grab the backwards parts of the globe and exterminate their natives" that Europe did OTL.
And of course we're forgetting India, which in a Muslim-free world would take a quite distinctive path of their own. Perhaps the upper-caste Hindus never develop the phobia for sea travel they did OTL, and Australia, Indonesia, East Africa, and points east get colonized and Hinduized by the states of the subcontinent. Perhaps they even discover America from the west, after island-hopping eastward...
Bruce
[1] Seriously. During the first few generations, women from Spain had a great deal of trouble suriving childbirth at the high altitudes.