Because your other questions are about World War I's aftermath, I'm going to assume you mean the early twentieth century. I would argue for three major influences on twentieth century thinkers.
The first is Charles Darwin. Darwin's theory of evolution was influential in two ways. The first is that it contributed to a rising spirit of secularism among European intellectuals, because it seemed to be inconsistent with a Biblical version of creation. The second was that it was quickly co-opted by social theorists who sought to use it to justify war, imperialism, racism, and unregulated capitalism, among other things. It would remain an influential idea among some until after World War II.
The second is Sigmund Freud. Freud's psychoanalytic theories emphasized not the rational man (though that was part of his understanding of the psyche) but the irrational id. Ultimately, people were driven by their animalistic urges, and in some ways their mental health depended on their ability to resolve internal conflicts. The point is that this idea dovetailed nicely with the thought of many European intellectuals who were beginning to question some of the rationalist assumptions about human nature that had existed since the Enlightenment.
Finally, there is Karl Marx. Marx's influence in the early twentieth century can be seen most explicitly in the formation of the Soviet Union, though he had hardly thought such a revolution possible in Russia. Marx, however, was very influential among the many radical socialist, communist, and anarchist groups that existed in Europe, and even moderate reformist socialists agreed with his assessment of the effects of capitalism. Almost every European nation before World War I, and certainly after, had a large Communist Party. Just as Marx had seen the Revolutions of 1848 as the cataclysm that would spark revolution in some countries, many radicals thought and hoped that World War I would usher in a proletarian uprising.