I've got two good ones:
No Quebec Act means Canada goes with America in the revolution. Rupert's Land is purchased and Newfoundland declares independence and petitions for statehood in the late 1800s after considerable Yankee immigration takes over the government. The US, being more Catholic from the start and needing more southern states to balance out the Senate, annexes Mexico down to Hidalgo, Veracruz, and Michoacán. The civil war is sparked partially by increased Catholic immigration in the South and the banning of Catholic immigrants. An amendment is passed by Congress during the civil war banning regulation of immigrants by nationality or religion. This causes the Chinese Exclusion Act and other laws like it from being passed, or they are passed and deemed unconstitutional. The population of the US explodes with millions of Russians, Indians, Chinese, and Japanese flooding into the country and with the new immigrants becoming citizens and voting, they prevent a majority large enough to pass an amendment revoking the immigration amendment. By 2018, the USA has a population of 600 million and is the undisputed hyperpower of the world, stretching from Greenland to Puerto Vallarta.
Russia in the 1800s is a dangerous place, full of nihilists, self-interested bureaucrats, nationalist agitators, and even worse... liberals. With the Tsar's first son killed in childhood by disease and second son Nicholas is killed in Japan by a rogue assassin, when Alexander the Third dies in 1894, his milquetoast, sickly son George takes the throne. He dies in 2 short years thanks to the stress of the position. His successor, the young Michael is assassinated by an anarchist before he is even coronated. This has left Alexander's militarily-inclined brother Vladimir as Tsar. And he is in no mood to be assassinated like his father and two separate nephews. He integrates the Imperial Guard with the Okhrana and expands the power of the Okhrana drastically, making it the primary mechanism of the Emperor's power and the head answering directly to the Emperor.
He conducts a great purge to try to rid Russia of all its subversive elements and it appears he is successful, dismantling the Social Democratic Party and executing its members, such as a man by the name of Vladimir Ilyich Ulyanov. It also completely disorganizes the Polish nationalist movement and purges the military and bureaucracy of corruption. Hailed as a great reformer, Vladimir moves Russia into the 20th century as a prosperous and growing, if autocratic, country.
When the war between Italy and Austria-Hungary breaks out in 1910, Vladimir, the military man, is chomping at the bit. He has prepared his whole life for this. His purges and reforms to the military pay off amazingly, with the Russian army crushing the Austro-Hungarian army and even holding its own on the defensive against Germany. Although it was a long three years, and almost bankrupted the country, Russia made it through the war as a victor, even claiming the provinces of East Prussia and Galicia-Lodomeria as its own. In 1913, Russia was the master of the continent, eclipsing even the power of France and Germany.
But Vladimir made a lot of promises to a lot of people during the war and he would have to pay up. He made sure to form a Duma and write a constitution, he even gave universal male suffrage. But when the election results come in, he is shocked! The Social Democrats, who he had long ago dismantled, had 20% of the seats in the Duma! In the position to play kingmaker between the liberals and conservatives, these socialist traitors have vowed to do horrible things, like take land from aristocrats and even... God forbid, the Crown! Obviously, Vladimir had to shut it down. He dissolved the Duma and arrested the Social Democrat delegates, hanging them one by one in Petrograd for everyone to see the wages of socialism.
The reaction isn't pleasant. Vladimir has overplayed his hand, not realizing that when you give millions of men rifles and combat training, betraying your promises to those men isn't smart. These men have been forming soviets to organize local government, and when the soviets sent their delegates, they were slaughtered. The Okhrana is in every town, but it seems more and more towns have Okhrana agents hanging from the trees in the middle of town and even the Okhrana are scared of attempting to dissolve soviets that express sedition. Eventually Vladimir calls for the dissolution of the soviets and the formation of military governments in every province. To restore order to these places where tax receipts have suddenly turned to zero and the Okhrana has stopped sending monthly reports from.
When the order is sent out, the Petrograd Soviet somehow hears about it before it even leaves the palace grounds. When the Imperial Guard arrives at their headquarters, the streets are already barricaded. When the Guard settles in for a seige, they hear news that the Guard's armory has been overrun by an angry mob. They turn around in panic, to march to the armory, but a deafening buzz rings out as the Soviet headquarters opens fire with a machine gun on the Guard. The rest, as they say, is history.
The Soviet revolution succeeds fairly quickly, with both Petrograd and Moscow taken within a few days. The army, wracked with mutinies, is unable to take control of anything outside of areas within walking distance of a railroad, and even then only in the west. The Emperor disappeared in the first week, said to have drowned when trying to escape Petrograd by ship, and his family taken captive by the Soviet government. But government is a strong word. When the Petrograd Soviet and Moscow Soviets proclaimed the Republic of Soviets and asked each soviet in Russia to send a delegate to Moscow for their Assembly of Soviets, they drastically underestimated the number of soviets in the country. Over ten thousand delegates swarmed Moscow in 1915, ready to negotiate their Constitution.
The Constitution took over two years to negotiate, as the war against the White Army and Tsarist Pretenders often took precedence, and delegates could not often afford to stay long, but it was negotiated. The Republic of Soviets was established as a series of exactly one thousand(1000) soviets with varying territorial and demographic jurisdiction. The Russian Orthodox Church and Catholic Church even had soviets, non-territorial, but representing the power of the church, that clergy and church employees voted on. The central government was weak, but still had the power of calling up the militias that every soviet was supposed to support and also the responsibility of supplying the militias with arms. It also was the mediator of disputes between soviets and between the Republic and foreign powers. Each soviet had its own criminal code(though most shared a common code agreed upon at The Assembly) and managed its own economic affairs. The Bureau of Economic Planning was the most powerful central government organ, and largely just negotiated agreements between soviets, with little authority to enforce a central plan. In a way, these soviets implemented Tolstoy's dream and to this day, the Christian Socialist Party that usually maintains majority in the Assembly explicitly cites him as their ideological founder.
The Republic of Soviets largely avoided the Second World War, giving back most of East Prussia to Germany in the interwar period and maintaining trade relations with both the Arbeiter Republik and the French State. It declared war on Japan near the end, invading Mongolia and Sinkiang and annexing them into the Republic before the Republic of China could get to them and ethnically cleanse them like they were doing to Tibet.
In 2018, the Republic is still largely an agrarian and rural society, partially industrialized but lacking the property rights protections to invite foreign investment and the central government to implement planned industrialization. The population growth of Russia has not slowed down significantly since its founding, and chugging along at a solid 1.5% annual growth for a century has left the population of the Republic of Soviets at 842,000,000 and making it the third most populous country, after Hindustan and China. People have called the Soviet Republic the next great superpower since its founding, but a lack of economic growth and an inability to project power beyond its borders have left it a regional player, albeit an intractable one.