The Hebrew Bible and The Epic of Gilgamesh are written in related languages—which isn't shocking, since both the Israelites of the Bible and Gilgamesh's Sumerians lived in the same region.
It should be no surprise, then, that the sneaky character who tricks Eve into eating the fruit that gets her and Adam bounced out of Eden, and that scoundrel that steals Gilgamesh's last hope of a semi-eternal life—that stay-youthful flower—both show up in a snake costume.
Coincidence? We think not.
Snakes are kinda creepy and all, but beyond that, snakes are just plain dangerous—especially in the Middle East where there are 22 species of vipers and six species of cobras. So, we understand that when these cultures start talking about seriously dangerous stuff that can mess you up, snakes naturally come to mind.