The people on the alternate history boards have speculated on what the rest of the world looks like. I haven't spent too much time on that, because as White wrote
"In most of the world, the New Middle Ages were merely a rerun of the Old Middle Ages. In England and Japan, the constitutional monarchies dumped their constitutions. Europeans turned again to the Roman Catholic Church for guidance. Camels plodded along the caravan routes of the Middle East, bringing silk from China and pilgrims to Mecca, just as they did a thousand years ago"
So except for a few specific border or language changes, there would probably not be major upheavals. Society as a whole would pretty much resemble its Middle Ages counterpart. England might stick to its Anglican Church (Island nations can do that), and China may or may not be an empire, or so isolationist in this period. Some things, like pizza or Fried Chicken or Lord of the Rings or Baseball can probably never be unlearned, but given a few centuries, the old world cultures will appropriate it as we see fit. But Asia, Africa and Europe would probably be pretty similar. (Africa was actually pretty advanced until its population was raided for the slave industry) Russia is the only "old world" region which would have a hard time resembling its Middle Ages equivalent. America is so fascinating for medieval case studies because it was so radically changed by colonialism.
Australia is another continent that was colonized by Europe, although not to a great extent, as the country only has 20 million people. This would mean 4 million in medieval terms at best. The wildlife is also very dangerous, and the soil not great. I guess I would expect something similar to the Arabian peninsula--a few port cities around the coast, but a largely nomadic desert population. The proximity to the much more populated Indonesia could radically change it. New Zealand, for its part though, might more closely resemble England with an upside-down calender.
But then there's Latin America. Consisting of almost twice as many people as in the US, Central and South America have ties we're vaguely familiar with, but may not know as much as we should. In some ways, it's easier to gauge its medieval life, because 1) Its Pre-Columbian civilization was more advanced than North America's, 2) It has been colonized for longer. Still, systems in the feudal ages take hundreds of years to develop, so I do think we would see differences. One interesting thing to point out that "Middle Ages" is a term that mostly to Europe--many other civilizations of the Western World were doing alright. Even thriving. But considering most of the planet had to start over, it's possible both North and South America are working at the same place.
But Latin America does have the benefit of much more resources than Anglo-America. White even references cocoa, rubber, balsa and coffee, in addition to many precious metals. Spices are possible as well. Important trading ports also possibly exist around Central America, with the Panama Canal being the crucial gateway from East to West.
Mexico is already touching some regions of the US, however White did not generally include it like he intended to with Canada. This is because the majority of Mexico's population is actually separated from the U.S. by large desert, which only pockets of nomads inhabit in the new Middle Ages. Today Mexico contains 100 million people, with a large percentage centered around Mexico City. It possesses one of the most diverse landscapes for a country of its size, with deserts, alpine mountains, grassland and rainforest. As a result, it's hard to really find a great counterpart, but if I were to choose one, it would be the Anatolian Peninsula, which Turkey is located on. Unlike much of the U.S., Mexico always had a relationship with its pre-Columbian past, and was the site of a thriving civillization. Of course, it would be ridiculous for Middle Ages Mexico to be a copy of its Maya or Aztec past just as one would expect the Middle East to copy the Persian Empire. But because there was a level of advancement for Mexico, one could see the occasional trappings of art and even social structure combined with Christianization and additions like carts, horses and grain. There's a lot of speculation to how big the Mexican nation-state would be. Before Spanish colonization, the empire did claim a large part of Central America.
Brazil is the largest nation in Latin America, both in size and population. Also, like America, it's a nation that was more radically influenced by its colonization than its native roots. As such it definitely bears the most inspection. As a nation of rainforests, savannah and scrubland Brazil, from a biome standpoint, bears a strong resemblance to India. It probably also shares aspects like being the source of natural resources. Its distance from the rest of the New World definitely allows it to go its own path. But South Asia would probably be the model for Medieval Brazil. During the Middle Ages, almost half the of the world's largest cities were in the Indian subcontinent and its sphere of influence. India was also the largest economy at the time. Not hard to imagine for a city of its resources. Sadly, in some ways, Brazil resembles modern India in its less positives aspects--the large divide of rich and poor. A rigid caste system would most likely plant itself.
Of course, as a large nation, Brazil is not going to be one homogenous entity, (Neither are most South Asian nations, contrary to popular belief) although I'm sure people from around the world will sometimes consider it one. But the country is divided into five sections, with very distinct identities. The North and Central parts would probably not have much of a population at all...just various tribal villages. The Northeast is definitely has an Afro-Caribbean sensibility. They may even resemble the Secretarial states, provided a South American empire doesn't claim it. Conversely, the southernmost points of Brazil start to draw more on its European heritage (As well as slightly more European temperatures). Not only that, but the grasslands also start to resemble neighboring nations like Argentina and Uruguay. There's much grassland here, but I don't see them quite going Nomadic, due to their proximity to the coast. What we'll probably have is a feudal structure like in the Neo-Medieval Midwest. All in all, aspects of Southern South America might resemble Europe in some ways, but due to Brazil's sphere of influence, the calender of the Southern Hemisphere and isolation from everything else, there could be some radical differences.
Finally, there are the more Andean nations. On this side of the continent, including nations like Peru, Paraguay and Chile, we finally see a strong native ethnicity amongst the populace. In fact, some of the more mountainous areas even have the old Native languages still intact. What's also interesting is, that like the West Coast of North America, there's chapparel, and desert hugging a large mountain range. In a lot of ways, it's the mirror image of its American counterpart, and I wonder if there could be an entire seafaring culture with strong Native/Hispanic roots being a common denominator in the entire Western sliver of the Americas. This probably wouldn't be dissimilar to the long but narrow Muslim world of the Middle Ages.