During the Tang Dynasty, China flourished culturally and economically, experiencing what I believe to have been its highest point, and possessed territory substantially larger than its present demarcations (Much of Central Asia including parts of Pakistan, Korea, Mongolia). However, whether it could have actually dominated the world (entailing the defeat of both European and Arabic civilisations) is uncertain.
Does the Yuan dynasty, ruled by Mongols, count in this?
Another thing I want to know is, would the world be a better place if smoking tobacco never existed? I hate smoking with a vengeance, and I would not hesitate to criminalize the consumption, transportation, and production of tobacco if I was given the right.
I would not be inclined to say it counts, since it is a division of the Mongol Empire. In any event, while the Mongols were capable of swiftly overrunning vast amounts of territory in a short amount of time, they leave much to be desired as civil administrators capable of ruling their conquests, which the fairly rapid collapse of their empire indicates.
If the smoking of tobacco never existed, the world would most certainly be a better place.
Well, there's the wonderful Hitler Scenario. If he was taken out before he made the stupid decisions he did (I believe there were some three hundred attempts on his life), I would probably be typing this in Deutsch. Because Germany was already pissed. He was just the one who happened to become the leader, and the person who finally managed to kill him died in the process.
If three Polish cryptology students had died, we would be in a bad scenario. Because they deciphered Enigma, leading to Ultra, leading to Allied knowledge of many German things, leading to Normandy and the capture of Paris and weakening of Germany.
If German military intel during WWII was not led by someone who obviously hated Hitler, then they would be able to tell that a certain body found off the coast of Spain with a briefcase handcuffed to his wrist was not the British airman who was shot down that they thought but actually a homeless man in a RAF uniform. (holy crap long sentence) And they would not have believed the "intelligence" that told of the Allied plan for the invasion of Greece. And then Italy would not have been won.
If the Greeks had been beaten up by the Italians instead of delaying the German invasion of Russia by a month or two, then Russia would have been fought for in fair weather instead of the wonderful winter.
Oh yeah, and we (the US) got lucky at Pearl Harbor, too. If we had all, or even half, of our carriers there, we would be off to a VERY bad start in the Pacific. And the fact that the Japanese diplomats delivered the declaration an hour or so late didn't help. And if Japan hadn't surrendered after Nagasaki, what would we have done? Dropped our third bomb? Oh, wait, that was used for testing. What about the fourth? Oh yeah, that's right. We only had three.
The French failed in the Interwar period, just because they built the Maginot Line along the border of France and Germany, choosing to skip Belgium, because why would Germany reuse a perfectly good route? And then while Hitler was mucking around in Poland, Britain and France should have counterattacked instead of twiddling their thumbs like good little countries that have declared war on another.
But enough about the Great(er) War. Battle of Tours and Charles Martel, anyone? What about if Mohammad had died as an infant? Not a Muslim, it's just that Islam created a military/cultural juggernaut that also managed to spread Eastern knowledge westward far more easily.
Big one: What if Egypt never recovered from the massive cost of the pyramids? What if Alexander's soldiers had not decided to mutiny in India? What if the USSR never invaded Afghanistan? What if the tank had been deployed en masse in 1913?
I concur with your speculations and would like to add that the Allied performance during the Battle of France was very disappointing for several reasons, allowing Luxembourg, the Netherlands, Belgium and France (traditionally considered to have the greatest army) to fall in six weeks.
1) Insufficiency of the Maginot Line - Essentially, the Line fails to address France's national security concerns because it ends at the Swiss border.
2) Allied failure to properly anticipate German intentions - The Allied commanders mainly believed that the coming war would simply be a repeat of the Great War, with the Germans invading Belgium, and the Allies counter-attacking and establishing a relatively stable Western Front.
3) Allied failure to properly assess the nature of the war - World War II with its lightning swift Blitzkrieg movements and use of massive air and armoured power differed drastically from the Great War's trenches. The Allies did not factor this into account until it was too late, having held a World War I mentality for too long.
4) Allied failures on the battlefield, strategic and tactical - Examples of what the Allies could have done but did not are quite plentiful. For instance, not attacking the massed German tanks in the Ardennes Forest with airpower, being far too passive in attempting to meet the German spearheads, not destroying the German bridge across the Meuse River, etc.
Where regards the Battle of Tours, it is clearly a very significant turning point. The Moors and the Berbers having already taken possession of much of Spain, had pushed into northern France, but there, were turned back. Had Charles Martel lost the battle, Christian Europe might very well have not existed.
We should also note that the Islamic world, during its Golden Age, lasting approximately from the 10th to the 14th Century, was actually the the centre of enlightenment and knowledge, having preserved Classical wisdom which would eventually be transferred to Europe during the Renaissance. If Mohammed had died early, this would never have been. On the other hand, we can also surmise that there would have been no Saracens, no Crusades, no Ottoman Empire, essentially nothing which possessed an affiliation to Islam as we know it in its present form.
Alexander the Great perished from sickness, which would have terminated his campaigns whether or not his sopldiers mutinied in India. However, had they not, his empire would have stretched even beyond the Indus River, most likely.
What if the Spanish Armada defeated England?
What if Napoleon had not lost the Battle of Trafalgar?
What if the Holy League (Spain, Venice, Papal forces, Genoa) had lost the Battle of Lepanto?
What if Vienna had fallen to the Ottomans (either during the first or the second attempt by the Ottomans to take it)?
Most importantly: What if the Greeks had lost the Battle of Salamis?