Quick disclaimer: these aren't meant to be the absolute most plausible scenario that could have happened. These are just possible scenarios created over a weekend by someone with a lot of imagination and very little research. If you have your own ideas, please share them in the comments.
#1: The War-in-Sight Crisis (1875)
Cooler heads do not prevail during the War-in-Sight Crisis and Britain, France and Russia decide they can't have peace with a united Germany. They are joined by Austria-Hungary, who want to get back at Germany for their defeat in the Austro-Prussian War. The Germans hold their own for several years, but eventually surrender against the combined forces of Europe. Germany is dismembered, although Prussia still maintains large parts of northern Germany. Prussia will try a couple more times in the future to unite Germany, but will always fail and always lose more territory in the process.
Today German nationalism is only really popular in the rump Prussia, with the other German states preferring their local identity over Pan-Germanism. This is important to their survival since the monarchist-clerical alliance led by the Kingdom France and the Imperial Federation of Austria don't want any trouble from that corner of the globe. They have enough trouble opposing the Anglo-American-Russian republican coalition, especially after their last attempt to reinstall the House of Saxe-Coburg and Gotha to throne of Britain failed miserably.
#2: The Fashoda Incident (1898)
An argument between the British and French commanders at Fashoda leads to the British commander being taken prisoner and shots being fired after British forces came to his rescue. Coupled with the heated rhetoric from both sides, war erupts between the two traditional rivals. Russia comes to the side of France, who signed a secret alliance with them earlier, as does Italy, who found this a good of chance as any to grab as much colonial territory as they could from Britain. Surprisingly, Germany and Austria-Hungary join on the side of Britain, who see France and Russia as greater threats to their sovereignty. Japan also joins the Anglo-German side, but just so they can swallow up as much French and Russian territory as they can. After years of war, the Anglo-Germans and their allies defeat the Franco-Russians and their allies. France and Italy lose much of their colonial empires, while Russia is forced to cede territory to its neighbors as well.
Decades later, right-wing governments come to power in France, Russia and Italy and try again for revenge in a Second World War. They actually managed to overrun Germany and Austria-Hungary, before a combined force of Britain, Japan and the United States breaks their hold over Europe, but not without copious amounts of nuclear weapons. Today Europe is still recovering from the nuclear onslaught it faced while the Anglo-American alliance fights for influence with the Empire of Japan. Thankfully, both sides in the struggle have seen the dangers of nuclear warfare and have agreed to limit their atomic arsenals...but not get rid of them entirely.
#3: The Russo-Japanese War (1904-05)
More British fisherman die during the Dogger Bank incident and it incites the British public to war. After the Royal Navy drives the Russian fleet back to the Baltic. France sides with Russia, but Germany and Austria-Hungary join on the side of Britain (Japan, meanwhile, couldn't be happier that Russia now has a war back east to deal with). The Anglo-Germans are eventually victorious, but leftist revolutions in Russia and France lead to the creation of Marxist governments in both countries. As soon as they secured their rule, both government began working together to undermine the power of imperialists who defeated them.
Eventually the Anglo-German alliance become fed up with all of the social unrest in their nations and colonies caused by the Franco-Russians and decide another war is in order to end their threat. Neither is prepared, however, for the amount of preparation France and Russia made for this moment and that, coupled with rebellions and general strikes behind Anglo-German lines, leads to a victory for the Reds. Marxism spreads across Eurasia and Africa, only contained by the American-Japanese alliance. That alliance is starting to fray at the edges, especially as the Reds use Japan's harsh treatment of its subject peoples as propaganda. Some American politicians and generals are beginning to think that it would be in their nation's best interest to incite a war between Japan and the Reds, but one where they sit out and rebuild the world afterwards.
#4: The First Moroccan Crisis (1905-1906)
In a surprising turn of events at the Algerciras Conference, German diplomats actually manage to come to an understanding with France and Russia, keeping Morocco independent, but open to all nations, while forming a new military alliance: the Quadruple Entente (Austria-Hungary was allowed in as well). Britain, finding itself suddenly isolated, rejects the decision at the Conference and, after a period of increased tensions, finds itself at war with all of Europe. With the Royal Navy bottled up at the Home Islands by Entente forces, the British watch in horror as their Empire is overrun. At the end of the war, all of British territory is divided among the Entente powers and their allies, except for Ireland, Canada, South Africa, Australia and New Zealand The United States also invoked the Monroe Doctrine and occupied British territory in the New World to keep it from falling into Entente hands.
The defeat in the Great War led to a total collapse of British society. A long civil war ended in the rise of a totalitarian government that sought to isolate Britain even further from the world and control every aspect of its citizens lives. A cult of personality formed around the position of Grand Minister that was passed from father to son, while the British poured vast amounts of money into weapons programs, even if it meant their people starved. At first the rest of the world tried to ignore what was happening on Britain, but after evidence was uncovered that the British were selling weapons of mass destruction to other rogue nations, the world decided they couldn't ignore them any longer. In 1984, the Entente, along with America and Japan, invaded Britain and overthrew the government. The leaders were tried for humans rights abuses and international aid poured in to alleviate the suffering of the British people, but the indoctrination program of the government was so prevalent that many British citizens still backed their former rulers, leading to a long occupation by the international force that is still ongoing.
#5: The Casablanca Incident (1908)
Three German deserters from the French Foreign Legion are arrested by the French, but in the process one of them dies. The event leads to war between Germany and France, with Austrian-Hungary and Russia, joining their respective allies. Britain, however, decides to sit this one out and the war drags to a status-quo peace. Both Russia and Austria-Hungary collapse and shaky democracies arise in their successor states. Germany also becomes a constitutional monarchy, while France came under the control of a socialist government that seeks to disentangle themselves from world affairs. Deciding they couldn't handle the strain of maintaining their colonial empires, the exhausted powers give their colonies independence. The British aren't happy with decolonization, but nevertheless decide they don't want to fight long-drawn out colonial wars and free their colonies as well. Europe turns into a sleepy backwater where not much happens and, to be honest, the people like it that way.
The same can't be said about the rest of the world, Other powers tried to fill the power vacuum left by the Europeans and the increasingly isolationist Americans. Japan and India, which was never partitioned, fought several bloody wars over China, dividing that region between several tiny states. Africa also had several regional conflicts as the Brazilians and the united Arab state battled for influence. There is a growing fear that an Indian/Arabic alliance and a Japanese/Brazilian alliance could lead to another global war if something is not done soon.
#6: The Bosnian Crisis (1909)
Russia refuses to back down over the Bosnian annexation leading to war breaking out between the Entente and the Central Powers (Germany, Austria-Hungary and Italy). In a surprising turn of events, the Ottomans find themselves on the Entente side, although they don't profit much in the short-term from the victory over the Central Powers, but it begins a new era of peace and understanding between Russia and the Ottoman Empire. Meanwhile, both nations reform themselves from the inside. Russia becomes a constitutional monarchy and works to unify the Slavic people into a union that becomes Pan-Slavia. The Ottomans do the same, except they seek peace and unity among all sects of Islam. After making a deal with the secular Arabs, the Ottoman Empire is transformed into the Islamic Federation.
Although there was a few close war scares, the Russo-Islamic bloc has managed to stay at peace with the Western powers, even after decolonization set in and many Muslim majority nations joined the Islamic Federation. Even without major ideological differences, things aren't always peachy between the great powers, but they are more friendly rivals than outright enemies. A new age of imperialism, however, is beginning now that the crescent moon has been raised over the actual Moon.
#7: The Agadir Crisis (1911)
When the German warship Panther mysteriously blows up off the coast of Morocco, the French are blamed and war begins between the Triple Entente and Triple Alliance. The war in the west breaks down into bloody trench warfare, but on Christmas, a truce happens on one stretch of the front that soon spreads from the English Channel to Switzerland. The high commands are puzzled and then horrified as the truce continues to last in the days to come. Attempts to get the troops fighting again, ranging from officers shouting at subordinates to firing on their own men, incites all the soldiers to turn on their generals and politicians. A unified, international army spreads across the continent. Forces on the Eastern Front join in and even Britain falls when the Royal Navy mutinies in support of the rebels. A new democratic European Federation is established to ensure universal liberty, rights, and equality, and to share knowledge and resources in peaceful cooperation.
Although not all of the Federation's Utopian ideas stood the test of time, it still managed to prove their detractors wrong by surviving and thriving in the years to come. The question of what to do with their colonial empire led to the next evolution of the Federation. At first the colonies were administered as whole to benefit all Europeans, but when that seemed to go against the guiding principals of the Federation, the colonies were given the option to become full members in the Federation, transforming it into the United Federation of Earth. Although some former colonies did choose independence, many other joined and even some nations that were independent at the time requested membership.
Today the UFE is the world's largest, most populous and richest nation on the planet. They have led the world in space exploration as well, establishing bases as far out as the Asteroid Belt and nuclear powered ships are already venturing into the Outer System. There are few states that remain outside of the Federation, the largest being the paranoid and xenophobic United States, which has been the UFE's largest rival. Although increasingly isolated, they refuse to surrender to foreign scum and tell their people to trust the leadership and to ignore rumors that there 105 year old President actually died ten years ago. That is only just another lie from the evil one world government.
* * *
Matt Mitrovich is the founder and editor of Alternate History Weekly Update, a blogger on Amazing Stories and a Sidewise Awards for Alternate History judge. When not writing he works as an attorney, enjoys life with his beautiful wife Alana and prepares for the day when travel between parallel universes becomes a reality. You can follow him on Facebook, Twitter and YouTube. Learn how you can support his alternate history projects on Patreon.