The war itself is partly to blame, because it incited intense nationalist feelings. The Treaty of Versailles, however, contributed the most to the stigmas that caused WW II. It not only shamed Germany by forcing the country to accept full responsibility for the first war, but also required that the Germans pay reparations to the Allies with money they didn't have, dropping their nation into a deep depression.
The nature of WWI was such that it obligated all nations to choose sides, so to speak. With so many different regions involved, nationalism was heightened nearly everywhere. This allowed for the rise of various fascistic regimes. In Italy, Benito Mussolini rose to power when he founded the Italian Fascist party and instated him self as dictator. In Russia, Stalin took command of his country and ran it as he saw fit. Perhaps most critical, however, was Adolph Hitler's meteoric rise to power during the late 1930's, being named chancellor of Germany in 1933. In all three cases, the citizens of these countries were so blinded by their pride, and hatred resulting from unresolved issues, that they did not question the motives of these leaders, and did not challenge their authority.
As far as Germany was concerned, they had been disgraced by Britain, France, and Italy in the Treaty of Versailles. It was designed to punish Germany, and said that all of the blame for WWI fell squarely on the shoulders of that country, despite President Wilson's vigorous warning against doing so. This meant that when Hitler extolled the virtues of the Fatherland and spoke of a newly strengthened Germany, which would earn back all of its previous glory, people stood behind his ends, even if they disagreed with his means.
Finally, there was the question of finances. Demilitarization and reconversion after World War I left many nations in deep depression, particularly Germany. Hitler promised the people of his country many things, including a prosperous economy, which he did in fact make good on. Given this extra assurance, even more people began to support the National Socialist, or Nazi, party. When he did in fact bring Germany back into opulence, he converted many people to his cause, but they were not aware of his methods. He reinflated the economy and cut unemployment significantly by expanding his country's industries. With the help of Hjalmar Schacht, Hitler used MEFO bills to manipulate the national economy and make things seem better than they really were. In this way, he garnered much support from citizens who would otherwise have been indifferent. Hitler rose to power more quickly, and was able to launch the attacks that began World War II.
All of these factors contributed to the beginning of WWII. If nationalist feelings had not been so strong, no one would have stood behind the leaders of the Axis and Allied nations. Had the Treaty of Versailles not been so harsh on Germany, the Germans would not have been so eager to prove their wrath to the world. And, finally, had it not been for depression, fascistic leaders would not have gained the support they needed. Clearly, the roots of World War II can be traced back to World War I.