1910, the Year of Dead Monarchs, ushered in a sea change across Europe, first to die was the unlamented Leopold II of Belgium on New Year's Day. Next up was Kaiser Wilhelm II of Germany, who took a header off a gangplank after touring the SMS Nassau on January 10. Next came Franz Josef of Austria Hungary, dead of a blood infection after stubbing his toe on February 12th. Next up was Edward VII of the UK, who died on the 6th of May after smoking one too many cigars. But Death was far from done with his list, Nicholas 2's heir, Alexei, had perished from a bad bleed on January 18th and Nicholas had spent 3 hours eulogizing his son in the frigid Russian air, going the William Henry Harrison route of coming down with pneumonia, but actually dying from a heart attack on July 2. Japan's Meiji Emperor died of complications brought on by his diabetes on October 29th. Finally, the already short reign of Sultan Mehmed V, was cut off before it really started by an 'unknown' assassin's bullet on November 1st.
With the exception of Russia, which devolved into the bloody succession crisis, then the Soviet Revolution, then the Trudovik/Bolshevik civil war until Alexander 'the Great' Kerensky finally prevailed and finalized/legitimized the Union of Soviet Republics, the wave of new Monarchs were far more 'progressive' in outlook than their fathers (at least when it came to their European neighbors), in the formation of the League of Nations at Zurich on June 28, 1914, Emperor Franz Ferdinand declared, "The era of secret alliances and imperial aspirations on the European continent is over. To initiate a state of general warfare would throw all our nations into a chaos worse than that which the Russians are weathering." The League of course setting the stage for the economic and political conflicts between the Imperial powers and the USA/USR and the brush wars and other problems of both 'hard' and 'soft' Imperialism.
But if 1910 hadn't had Death cleaning house among Imperial heads of state its quite possible for a general war among European Imperial powers themselves, with Japan maybe joining in. The disconnect between Imperial and Republican posters is pretty stark though (which is why I'm using such non-biased language), and I'm not trying to ask the tired "Who would win?" question, actually I'm taking a poll. If we accept the words of Franz Ferdinand himself as proof that Europe was a tinderbox in the early 1900's (diehard deniers need not apply), which Monarch's death was most important in keeping Europe from going up in flames... either because he would have initiated the conflict or because his successor stopped things?
For me its clearly Wilhelm's death, by plunging off that gangplank, the Kaiser removed his ultra nationalistic, jingoist self from the heart of Europe and allowed his far more mellow son William on the throne to defuse a whole metric ton of diplomatic crises brewing externally and internally in allowing the Alsace-Lorraine and, later, Polish plebiscites to mollify France as well as dealing with recalcitrant and restless minorities.