In reverse chronological order:
-- The Allies, despite their misgivings regarding a new war, react adequately to Hitler's aggression. His bullshit regarding Chzechoslovakia isn't tolerated. The instant he tries to annex land in the east, be it from the Czechs or from the Poles, the western powers land on him like a giant hammer. Teach this jerk a lesson before he gets a chance to murder a vast amount of people. And since it's the west doing it, in co-operation with Poland, Czechoslovakia etc., the new german government is going to be a democratic and somewhat anti-Soviet one, installed by the west. Result: no more Hitler, Europe doesn't get raped by the nazis, and basically all of Europe is united in an alliance that won't tolerate Soviet aggression, either.
Side effects: slightly better-organised decolonisation, since no long WW II to mess everything up.
-- World War II is prevented altogether. The Central Powers win the first round by adopting a defensive strategy in the west, and going on the offensive in the east. No Germans in Belgium. No British involvement. No American involvement. In the west, France will get stuck in the trenches. At the very best, they reach the Rhine, but don't manage to cross it. In the east, after initial brutal fighting, the Central Powers gain the clear upper hand just as in OTL, but earlier. Russia collapses by mid-1916. A Brest-Litovsk style peace is signed, whereby German monarchs are installed in the Baltics, Poland, Belarus and Ukraine. Finland also gets a Hohenzollern monarch, as briefly planned in OTL. Lenin never gets sent to Russia. There is no USSR. Following this, Italy throws in the towel, and France is forced to sue for peace at the end of 1916. Having gained massively in the east, Germany makes no further territorial demands against France, but permanently removes the French from Elzass-Lothringen. Pretty much all of Europe gets absorbed into a Germany-led customs union. There will be no second world war, Russia is too unstable, with its Tsarist government relying on German backing to prevent unrest. France alone is too weak. Britain and the USA are not getting involved. All in all, Europe is in good shape. Austria-Hungary will need to reform or eventually split apart, but Germany will manage the situation either way. The Ottomans struggle on, but even without the war, Turkish reformers and Arab rebels will soon begin to play major roles. I imagine a territorially reduced, much more Turkish empire eventually emerging, which on the flip side is reformed/modernised to a considerable extent.
Side effects: Irish Home Rule goes through on schedule without WW I to mess things up. With Britain out of the war, the collapse of the Empire is avoided. It still ends, but it's far more gradual and far less messy. Expect a Commonwealth on steroids. Expect decolonisation in general to take that shape. Former colonies of the various European powers will generally be in much better shape due to this peaceful transition, and due to the absence of the horrid (often Soviet-backed) communist regimes that cropped up in several former colonies in OTL.
-- As the South secedes from the Union, the Union actually respects the tenth amendment of its own damn constitution and thus recognises the secession as perfectly legal. This prevents any border state from seceding in the first place. The CSA is just the Deep South. The Union then aggressively pursues a policy of ending slavery in its own domain. Right after that, it works with Britain and other leading world powers to completely embargo the CSA until slavery ends. With no customers for their raw materials, and no-one willing to sell them anything, the Confederates are left with no choice but to obey. [I know this is ASB, but this is how I wish it had gone.]
Side effects: international co-operation for humanitarian purposes becomes a thing earlier, and secession is more widely recognised as a legal right.
-- The more radical French Enlightenment thinkers, who for the most part knew each other personally in OTL, hold a large ATL meeting in a salon early on in their careers. The building burns down and they all die. Their works are entirely forgotten. Names such as Rousseau and Diderot are largely lost to history. Following the French involvement in the ARW, France is still in trouble. But without the radical influence of the aformentioned thinkers, the more radical revolutionary streaks are butterflied away entirely. If there is a French revolution, it is more like the American one, with the ideas of thinkers like Turgot, Quesnay and Condorcet forming the intellectual cadre. The resulting state may be a constitutional monarchy or a republic, but it isn't going to be lopping off heads on a large scale. The royal family, even if the monarchy is abolished, will be treated well. Frace is going to be a sane and stable country. No Robespierre. No Terror. And in the end, no space for a man like Napoleon to put a crown on his own head. The French Revolutionary Wars and the Napoleonic Wars simply don't occur.
Side effects: Europe isn't messed up by bloody wars. Pre-revolutionary crowns remain in power, but an evolution towards constitutionalism is inevitable. There is no hardline 'Concert of Europe'-reaction to radical republicanism, either, so we get a far more peaceful and gradual political evolution. Without the French revolution, the later OTL revolutions get butterflied. Socialism and communism as we know them don't even arise. Nor does anything like Nazism. the whole basis for modern Western collectivist totalitarianism has been removed at the root. All in all, there is much less (totalitarian) radicalism in the world.
-- Charlemagne marries Irene Sarantapechaina of the ERE. They produce an heir. Their other respective children later die mysteriously in freak accidents. Yielding to Byzantine custom, Charlemagne adbandons the Franks' succesion laws, and from that moment on, the empire is given over, undivided, to one heir. The union of east and west restores the Roman Empire, more or less. The Great Schism is avoided as a result of the resulting unity. By and large, Europe is politically and religiously united from the dawn of the ninth century. Eventually, this empire comes to include all of Christendom. There is no Reformation. In this world, despite some sects, Christianity is mostly undivided, and also largely contained within the borders of what we may call a universal empire. No wars of religion, or other wars between European peoples.
-- Hadrian gets a sudden brainwave. Instead of abandoning Mesopotamia and keeping Britain, he abandons Britain and puts a lot of energy into keeping Mesopotamia. He understands that denying it to Persia will weaken Persia to a massive degree. Seeing as he also keeps Armenia, this denies two vital areas to Persia. A Persian attempt to take back these regions fails, although the fight is bloody. In the aftermath, Persia collapses into civil war. Rome makes Media and Susiana into client states, to serve as a buffer in the east. Persia never recovers from the losses, while the wealthy eastern lands grant immense wealth to Rome. Which Rome uses to expand its northern border, eventually establishing a border that follows the Elbe, then the northern Czech and Slovak mountains, then the Dniester to the Black Sea. That kind of set-up should allow Rome to survive basically any threat. The eastern conquests should initially provide great extra wealth. Once the heavy plough and three-field rotation get discovered, the northern conquests will prove to be a new breadbasket, just as gradual climate change is making the old one (North Africa) less fertile.
Side effects: this undivided Roman Empire lasts for a good long time, too strong to be threatened, and the great wealth of the conquered areas largely contains OTL economic troubles. Peace reigns within the borders of the empire.
-- Hephaistion doesn't die in 324 BC. Alexander the Great's self-destructive spiral of grief is thus avoided. Alexander conquers Arabia and the western Med during his lifetime (plus some other modest bits here and there) and carries out his infrastructural plans. By the time of his death, two decades later than in OTL, there's a half-Macedonian half-Persian elite emerging, examplified by Alexander's son and heir. The Great Oikoumene lasts for a long time, and brings extensive east-west contact. Science, philosophy and art flourish greatly. The great works of not only Hellenic culture, but also of Persian culture and many others, are fully preserved to the current day. The world is infinitely richer for it.