Parallels Between the Epic of Gilgamesh and the Bible
The most well-known parallel between the Epic of Gilgamesh and the Bible is the story of the Flood, in Genesis 6-7. This is essentially equivalent to the story that Utnapishtim, the Sumerian Noah, tells to Gilgamesh on Tablet XI. Even the way the narrative is laid out is similar - the gods put a bug in Utnapishtim's ear; a description of how the ark is built ("daubed with bitumen," a common glue or mortaring agent in Mesopotamia); everyone piles in, and it starts to rain. When it's over, Utnapishtim releases a dove, then a swallow, and finally a crow.
However, the section of the Bible that really seems linked to Sumerian mythology is the book of Ecclesiastes. The writer of that book informs us, in Eccl. 12:9-10, that in the course of composing it he read widely, presumeably everything that he could get his hands on in those days. From internal evidence it's obvious that he read some version of the Epic of Gilgamesh. It's fascinating to see that the story, already very ancient by Biblical times, circulated so widely in the Middle East.
Ecclesiastes 4:9-10 (in the Revised Standard version) runs, "Two are better than one, because they have a good reward for their toil. For if they fall, one will lift up his fellow; but woe to him who is alone when he falls and has not another to lift him up." This appears in fragmented form in Tablet V column ii of the epic. (If you want to look at the tablets in English translation the best one is by John Gardner.) It was apparently a common proverb in the Middle East, and you can easily find equivalents all over the place in literature. It appears in King Lear and in Beowulf, "Bare is back without brother behind it." (Alliteration's artful aid, what?)
The Epic of Gilgamesh has two main parts. In the first, Gil has a number of the standard Conan-the-Barbarian style adventures, whomping monsters, humping maidens, defying the goddess Ishtar. And he's king of Uruk, one of mankind's first cities - all very picturesque, and would make a great cover for a genre paperback. Then, in the second half, Gil has a spiritual crisis and goes on a quest for eternal life. Well, when he's wandering around having angst, he meets a Wise Woman, a barmaid - it seems the Sumerians invented beer, too.