I'm doing an essay on Epic of Gilgamesh and it's historic input, and, while I'm not asking any of you to write it for me, I'd like to know to which civilizations Mesopotamia was connected to so I can research further influence of the Epic. I've read somewhere that ancient civilizations weren't familiar with Mesopotamia since not even historians like Heredotus mention it (?), while on other places I've seen referenced "Epic's influence on Homer's work". Turning me onto some sites would be of great help too, in which case I'll have more material for "References" section.
Mesopotamia was in close contact with several other regions, including the eastern Mediterranean and Iran. I've written previously about Egyptian-Babylonian interactions and Hittite-Babylonian interactions.
For more information about Mesopotamian interactions with other regions, take a look at the two excellent free Met Museum catalogues.
Art of the First Cities: The Third Millennium B.C. from the Mediterranean to the Indus
Beyond Babylon: Art, Trade, and Diplomacy in the Second Millennium B.C.
Also take a look at the chapters on Mesopotamian interactions with neighboring regions in Crawford's The Sumerian World (chapters 23-28) and Leick's The Babylonian World (chapters 34-39).
A lot has been written about the impact of Mesopotamian literature on Greek literature. M.L. West's The East Face of Helicon: West Asiatic Elements in Greek Poetry and Myth is absolutely the best place to begin. Recent works on the topic include Johannes Haubold's Greece and Mesopotamia: Dialogues in Literature and Mary Bachvarova's From Hittite to Homer: The Anatolian Background of Ancient Greek Epic. The various books by Walter Burkert (especially Babylon, Memphis, Persepolis: Eastern Contexts of Greek Culture and The Orientalizing Revolution: Near Eastern Influence on Greek Culture in the Early Archaic Age) are worth a look too.