Enlil is the king of the gods and the one who grants immortality to the Utanapishtims.
As you might expect for a king of the gods, Enlil is a little hard to figure out. In Tablet 2, when Gilgamesh tells Enkidu about his brilliant idea to go kill Humbaba, the guardian of the Cedar Forest, Enkidu tells him, "Uh-uh, big no-no: Enlil put Humbaba in the Cedar Forest on purpose to protect it."
Assuming Enkidu is right (and it looks like he is), it's reasonable to ask: Why did Enlil make Humbaba the defender of the Cedar Forest? As so often when it comes to the gods, the answer seems to be "just because." Perhaps it is to actually protect the trees from people who would like to chop them down for sport. (Ahem … Gilgamesh.)
Similarly hard to figure out is Enlil's role in Tablet 7, when he crops up in Enkidu's dream. In this dream, the gods are holding a conference on what to do about Gilgamesh and Enkidu, who have been seriously ruffling feathers with their behavior. When Anu suggests that one of them must die, Enlil speaks up, saying that Gilgamesh shouldn't die, but Enkidu should.
Why Enkidu and not Gilgamesh? Isn't Gilgamesh the one that strikes the death blow? Is it because Enkidu knew why Humbaba had been placed in the forest, and therefore is more morally responsible? We aren't told.
Later, in Tablet 11, Utanapishtim tells us that Enlil was one of the major voices arguing in favor of destroying humanity with the Flood. In fact, when the Flood is over, Aruru (going under the name Beletili) basically accuses Enlil of being behind the whole thing. Supposing Aruru is right, why would Enlil want to destroy humanity?
Once again, we aren't told. (Although in some translations, authors have provided possible explanations—so be on the lookout for what your specific text says about this.) We also aren't told why he suddenly decides to grant immortality to the two humans who have survived the Flood: Utanapishtim and his wife.
Our theory? Enlil is trying to maintain his "perfect human kill" rate. It isn't a great theory, but it's all we've got. Still, all in all, we get a general picture of him as a pretty nasty, small-minded guy. Er, god.