World War II happened largely because two countries were unhappy with the status quo in the world. These countries were Germany and Japan. They did the most to start WWII.
Germany was unhappy with the status quo after World War I. Germany had lost that war and the victorious allies had treated Germany very harshly in the peace treaty that ended the war. This led to a great deal of anger among Germans and a desire for revenge.
Japan did not lose WWI, but it was unhappy with the status quo as well. It wanted to be a major imperial power. However, the major European powers (and the United States) already had control of most of the areas that Japan wanted to colonize. These powers were not comfortable with the idea of Japanese expansion.
Thus, WWII began because these countries tried to upset the status quo. Countries like Great Britain and the US, who were happy with the status quo, fought back to prevent major changes from happening.
If one had to name a particular cause of World War II; it would be the Treaty of Versailles that ended World War I. Germany was treated most unfairly by the terms of the treaty. Germany was forced to accept full responsibility for the cause of the war, and full financial responsibility for its costs. This caused so much bitterness and resentment among the German people that it provided a ready platform for Adolf Hitler. Hitler railed about the unfairness of the Treaty, and also the need of the German people for Liebensraum, or "breathing space." This was the basis for his marching into the Rhineland, and his taking of all of Czechoslovakia when he had been promised the Sudetenland. This should have been sufficient warning to those who opposed him that he would not keep his word, but they were more inclined to appease him. Finally, on September 1, 1939, he invaded Poland, and the war in Europe began.
Strangely enough, the war in Asia with Japan was also largely the result of the Treaty. Japan had entered World War I on the side of the Allies hoping to gain large amounts of German held territory in Asia, but walked away empty handed. This played into the hands of the militant war party in Japan who started a campaign to take Manchuria and large areas of Indochina. When the United States stopped shipments of oil and scrap metal to Japan, the Japanese high command saw war with the United States as inevitable. Adm. Isokuru Yamamoto, who commanded the fleet that attacked Pearl Harbor, had reasoned that the United States did not have a "warrior heritage," and did not have the stomach for a long war. He believed that if the Pacific Fleet could be eliminated, the United States would make peace before the Atlantic Fleet could be repositioned. It was for this reason that Japan attacked Pearl Harbor on December 7, 1941.
Japan had previously signed the Tripartite Pact with Italy and Germany as a result of which, when the United States declared war on Japan, Italy and Germany declared war on the United States within 72 hours. And the full war was on.
The invasion of Poland in 1939 in usually given as the beginning of World War II, although there were three other wars often seen as the beginning of what is often referred to as the "era of Hitlerian wars." The Spanish Civil War was one, as was the Italian invasion of Ethiopia, both in 1936. The following year fighting broke out between Japanese and Chinese troops the night of July 7 at an ancient stone bridge outside Beijing called the Marco Polo Bridge, probably incited by agents of Mao Zedong in his struggle with Chinese Nationalists. The fighting was seized upon by the Japanese Army in China as an excuse to start a full scale war (the Second Sino-Japanese War), in defiance of the Japanese government. There had been fighting between the Japanese and Chinese off and on since the 1931 incident in Mukden.
The real root cause of WW II, however, was the outcome of World War I. The collapse of German morale (due largely to the British blockade) and the military reverses in France due largely to the massive influx of American troops led the German high command to ask for an Armistice. This was not an actual surrender by the Germans, and their troops were never pushed back to German territory. The humiliating terms of the Armistice, the political collapse of Germany's government(s), and the economic disaster following the war left the German nation feeling they were undefeated but treated unfairly. The feeling that the Army did not lose the war but was "stabbed in the back" by socialists (and "Jewish bankers and businesses") at home led to a belief shared by many that the German nation essentially deserved a sort of rematch. This and the armed rebellions by socialists, put down by the Freikorps, led to the rise of ultranationalist groups such as the Stahlhelm and the National Socialist Worker's Party. All these groups espoused a rebuilding of industry and the military, and an eventual new war with France and her allies.
Ironically, this was very much the same reaction of France following the Franco-Prussian War of 1870. The humiliation of the French Army and the seizure of Alsace and Lorraine were actually the true cause of the First World War, as the humiliating terms of the Armistice led to the Second.
The treaty of Versailles ended World War I and placed the blame of the first World War directly on Germany. This left the German population very bitter. Many German citizens felt betrayed by the government for being weak and signing the treaty. The Treaty of Versailles limited the German military and forced the Germans to pay for war damages. When Hitler rose to power in the 1930's he began invading other countries which eventually started WWII.
The culmination of events that led to World War II are generally understood to be the 1939 invasion of Poland by Nazi Germany and the 1937 invasion of the Republic of China by the Empire of Japan. These military aggressions were the decisions made by authoritarian ruling elites in Germany and Japan. World War II started after these aggressive actions were met with an official declaration of war and/or armed resistance