Final answer:
The Minoans and Mycenaeans were the civilizations that had the most influence on Greek and later Roman societies, spreading their seafaring trade and cultural practices throughout the Mediterranean, which would be adopted by the Greeks and Romans, profoundly affecting Western civilization.
Step-by-step explanation:
The civilization that had the biggest influence on Greek and Roman societies was that of the Minoans, whose emergence on the island of Crete set the stage for the later flourishing of Greek civilization. The Minoans, along with the Mycenaeans, were significant due to their strategic location near the Mediterranean Sea, which facilitated maritime trade and cultural diffusion. These early civilizations used their advanced seafaring capabilities to interact with and influence various peoples around the Mediterranean, including the Egyptians, Hittites, and others. While both civilizations were primarily traders, the Mycenaeans were also known for raiding, and together their legacy was absorbed into classical Greek culture, which instilled its own pervasive influence on Roman society.
By the Archaic period, Greeks had established colonies across the Mediterranean, spreading their culture, language, and political ideas such as democracy and republicanism. These colonies created a common Greek civilization by culture, not by a central government, which would later be adopted and adapted by the Romans. Indeed, the Roman empire heavily incorporated Greek culture, deities, and learning, fundamentally shaping Western civilization. Greek commerce, artisanship, and script like the Greek alphabet were disseminated through trade networks as far as the Celts in western Europe, showcasing the breadth of Greek influence before Roman times.
Romance languages derive from Latin, which transformed under the immense influence of Greek culture. Roman culture during and after the formation of the republic reflected strong Greek influences, including in the concepts of citizen participation in governance, mythology, and cultural practices.