I've been fishing around my mind for some time of a good premise for an alternate history novel, and I finally have one! We'll see what I can do with it. I may or may not get something written, and this thread may or may not come to anything.
There are two branching-off points. (Generally speaking, the fewer branch-offs you do, the better off you are, lest you end up with
a total mess, but the first branch-off is totally irrelevant until after the second branch-off, and evolves with almost no influence going one way or the other, so I think it's probably excusable.)
a) Firstly, the Norse colony of Vinland on Newfoundland, which in real life was abandoned within two decades of its founding, survives and grows, albeit slowly. By the mid-fourteenth century there are 50,000-100,000 Norse and Norse/Indian creoles living on Newfoundland and Nova Scotia, with regular excursions as far as Montréal and Cape Cod. The only contact with the Old World remains a lone tribute ship from Denmark that arrives every couple years and taxes the Vinlanders for their furs. Greenland, which is about to kick the bucket anyways (in reality the Greenlandic Norse were all gone by 1420), is in Vinland's sphere of influence for as long as it sticks around.
b) HIV jumps from monkeys to humans sometime in the late 13th or early 14th centuries instead of the early 20th century, and is carried to the Middle East with Mansa Musa's hajj party in the 1320s. HIV has a very high mortality rate but an equally long incubation period, which means it does exactly what I wanted my Black Death replacement to do. By the time anybody notices there's a plague starting in the Middle East in the 1330s, HIV has already spread to Europe, India and China, and anybody who knows that there's even a plague is probably in an already-infected area. As Mamluke Egypt and the Persian Ilkhanate start falling apart and disorder starts to spread along trade routes, they're replaced by a slowly-expanding power vacuum. In the 1340s, a band of Mongol wannabes from Central Asia take advantage of the power vacuum in the Middle East, China and Europe to conquer a vast, unstable and decivilizing empire stretching from the Rhine to Shanghai. Their troops, of course, only exacerbate the issue by spreading the disease through their rape and pillage. (The "eat, drink and be merry" attitude of hedonism that tends to emerge in the wake of plagues doesn't help matters, either.) The steppe empire falls as quickly as it emerges (since population collapses make for poor tax bases).
By 1360, there are no truly stable large state societies anywhere in India, China, Europe or the Middle East, Eurasia's population is 20-25% what it was in 1320, and subsistence farming is just about all there is left. A few hotheaded warlords emerge every few years to conquer themselves a fief, but these inevitably collapse, too. The silver lining is that HIV is so virulent that it virtually disappears and never bothers humanity again.
Only two areas remain unaffected, or nearly so: Japan is too xenophobic to be infected on a wide scale, and Iceland is too isolated. It's worth noting that neither Japan nor Iceland were subject to the Black Death in the real world. The mercy shown Iceland applies to Vinland and Greenland by proxy; sometime in the mid-1360s, a small band of curious Vinlanders makes a journey across the Atlantic to find out what happened to the tribute ships from Denmark that have not arrived in more than a decade. They land in Copenhagen's deserted harbor and the novel (save for whatever exposition I'd like to write, which might be a lot) begins...
I'm not really sure where to go from that point. Vinland can't exactly reconquer Europe, despite the fact that it's now become the political center of the Norse sphere (which isn't saying much, since that sphere is now reduced to Vinland, Iceland and Greenland, the last of which is already living on borrowed time and will be gone in a century). It's tiny, poor, backwards and cannot sustain a military expedition; it only survives in the Americas because its neighbors are all hunter-gatherers. Japan is more populated and has a better chance of carving out some territory in China or Korea; but Japan wasn't truly unified in real life until the 16th century, and then only with the help of Portuguese firearms. The Aztecs certainly aren't going to be making a trip across the Atlantic for a while, the Polynesians can make contact with the Americas but are too fragmented and sparsely populated to create states, and Africa is nearly as decimated as Eurasia by HIV. States will re-emerge in mainland Eurasia after things settle down, but the population clock has been set back to early antiquity or thereabouts.* It's hard to say how much technology can be re-imported from Japan and Vinland, or relearned from books, too.
Thoughts?
*It's hard to get a good number on this- I can only find Wiki's population stats at the moment- but we can make an estimate. Almost everyone in 1350 lived in Eurasia or Africa; the total world population was about 400 million, and in 1750 20 million people lived in the Americas or Oceania. We'll cut that down to about 15 million for 1350 (since there was a big dip around European "discovery", and a subsequent slow rise), leaving us 385 million people. 20-25% surviving gives us 77-96 million people in Eurasia, plus 15 million outside it, to give a total world population of 92-111 million people. This is about equal to the world population in 500 BC.