I would say that there are several distinct parallels between Gilgamesh and other examples of Ancient literature. The theme of the journey as something that defines the protagonist is something that can be seen in Homer. Odysseus has to endure a journey in order to go back home. Gilgamesh and Enkidu have to endure a journey to face Humbaba, the personification of evil. In both cases, there can be no rejection of this responsibility, no way of negating this duty. The journey is something that defines the protagonist and their way of life. Both sets of text us this idea. Another idea present in both Gilgamesh and Ancient literature would be the reality of honor. It is honor and the prestige attached to one's name that causes both the rise and downfalls of individuals. Again, in Homer, honor is one of the main ideas behind the Trojan War in The Iliad. Honor is what drives many of the characters to do what they feel they must do. Honor is important to Gilgamesh, who commences both physical and spiritual journeys in the desire to establish his own sense of understanding and name in the world. It is honor that compels him to do so for not doing so would be something far worse.
The Epic of Gilamesh central theme is the myth of the deluge. This myth has been repeated troughout different literatures in variations, but it is most famous for being featured in the Genesis. The book of Genesis, however, was written after Gilamesh. The explanation is trifold a) Genesis took the idea from Gilamesh b) Gilamesh and Genesis are to be read together or one is an extention of the other, and c) both stories come from yet another protostory.
The deluge story, as said previously, has been told in several ancient texts, which puts into doubt the reliability of many books considered "sacred". An example of this is the story of Noah's Ark.
In the link I provided, you will be surprised to find that, in nearly every major country and continent there is a Flood story, told in different versions. Yet, universally, it is understood that the closest resemblance to Gilamesh is the story of Noah.