I think that the fundamental notion of struggle and how suffering looks in the Hebrew tradition has been a part of Western Civilization and world history, in general. The template of enduring despair in the hope of external redemption has been something replicated by many groups throughout history and many have come back to the struggle of the Hebrews to articulate their own condition in the world.
The biggest impact on Western Civilization has been the advent of Christianity. The Hebrews believed themselves to be God's chosen people; that they were in a covenant relationship with him. This effect on Western Society is minimal, as Judaism is not a missionary religion; rather it discourages converts. There was some economic and intellectual influence by the disapora of Jews to Europe; but its effect is largely overshadowed by Christianity.
Christians also consider themselves in a covenant relationship with God; however they believe that theirs is a "New" covenant; the old one was fulfilled by the crucifixion of Jesus which satisfied its terms. The first Christians were Jews, as was Jesus himself, so there is a direct, inexplicable link between God and the Hebrews and Christianity. Christians accept the Holy Scriptures of Judaism as their Old Testament.
Christianity's impact on Western Europe can hardly be overstated. After it was made legal by Constantine in the Edict of Milan and later the official religion of the Roman Catholic Church, it was the major influence in Western Europe; so much so that for many years, Europe was known as Christendom. The Christian church had a virtual stranglehold on European history; with Popes wielding tremendous temporal power and often conflicting with Kings and Emperors
So to directly answer your question, God's relationship with the Hebrews in the Old Testament is only one step removed from the major history of Western Europe through its Christianization.
Most modern cultures are affected by the covenant between God and the Hebrews. Western Civilzation resulted from it, and Muslim civilization is in opposition. Although it might seem like modern society has nothing to do with ancient culture, if you look closely you'll see that our society is heavily built on and influenced by thiers.
The covenant that was supposedly made between God and the Hebrews led to the creation of three of the world's largest religions. This covenant marked the creation of the Jewish faith. This faith, in turn, gave rise to Christianity and Islam. This is a huge impact.
One can argue that the covenant was a forerunner of things like the US Constitution. It was a written deal between a ruler (God) and a society in which both sides had defined responsibilities and rights. This is something that would be replicated in the Constitution.