Greek influence on Western Culture
Ancient Greece has had an enormous amount of impact on culture in the western world. Some of the first works of literature in the west of which we have record come from Greece, and although they were created at a time after older works from Mesopotamia or China, such epic poems as the Iliad and Odyssey have exerted wide influence over generation after generation of western thinkers.
Greece was home to many other "firsts" in the humanities, such as the first history and historian (Herodotus), the whole of the initial development of dramatic and comedic plays, the first practitioners of mathematics, many developments in political science including the creation of democracy and republics (albeit in oligarchic form), and virtually the whole of the fundamentals of classical western philosophy, as found in the works of Plato and Aristotle. Much of architecture has its roots in Greece, as well.
It is difficult to fairly ascribe to Greece the roots of science, since science as a recognizable discipline only became distinguishable rather recently, but for most of history what we consider science has been entwined with philosophy and politics, and in that form the Greeks (particularly Archimedes) were once more the progenitors. To this end, they created the first siege engines, the first alarm clock, and many other inventions.