Kane's dominant character trait is his curiosity and willingness to boldly go where no one has gone before. Unfortunately for Kane, it turns out he's more Redshirt than Captain Kirk's crew.
Curiosity + Cat =
When the Nostromo lands on the unknown and inhospitable planetoid, Ash learns the mysterious signal they have been tracking is within walking distance. Before Dallas can even put an away team together, Kane's hand shoots up: "I'll volunteer to be in the first group to go out," to which Dallas replies, "Yeah, that figures" (Alien).
As the away mission into the heart of darkness progresses, Kane's curiosity keeps getting the better of him. When Lambert suggests they turn back from the brutal atmosphere of the planetoid, Kane says, "We've come this far. We must go on. We have to go on" (Alien). He's the one who climbs the wall to discover the dead alien in the derelict ship. He's the one to venture into the cave-ish room to find the alien eggs, and we're guessing it's not because he lost the round of rock-paper-scissors.
The downside (oh yeah, there's a downside) is that Kane doesn't know when to not mess with an alien egg that contains an unknown organism that looks foreboding and dangerous.
Seriously, did he not hear his mother's voice in the back of his head screaming, "Kane, drop that filthy thing!"?
As payback for his curiosity, Kane suffers one of the most literally gut-wrenching deaths in cinematic history. The facehugger inseminates him with another alien, and Kane gestates it before the creature pops out of his chest during dinner in a horrific scene of bloody, violent birth.
Wrong Movie, Buddy
Kane helps us see how Alien plays against our expectations by blending the horror and science fiction genres. In science fiction, curiosity is often rewarded. Think characters like Luke Skywalker and Captain Kirk. Luke Skywalker is intrigued by a mysterious message; he learns to be a Jedi and master the universe. Captain Kirk explores strange new places and civilizations; he gets to have high flying adventures and seduce green-skinned alien vixens. It's pretty much win-win for these guys.
In horror, though curiosity is a punishable offense. Exploring an ancient tomb is likely to awaken an evil spirit or to get one possessed by some nefarious demon. Exploring your sexuality is going to make the nearest axe murderer feel all stabby. Even exploring your family tree is likely to rustle up something unpleasant.
And that leads us to Kane. On the one hand, Kane is the perfect science fiction hero; on the other hand, he's horror movie fodder. Going in, we might expect Kane to be the hero of the film if we are expecting the movie to play towards its science fiction roots. But once Kane dies, we know which conventions we'll be following.
Kane Is the New Abel
Kane—as in Cain—is a name you might remember from your Sunday (or Saturday) School class. If not, here's a refresher: Cain is a Biblical character and one part of the not-so-dynamic duo Cain and Abel from Genesis. Abel garners more of God's favor because his sacrifices are more pleasing to the Lord. Jealous, Cain kills his brother by way of a big old rock. Congrats, Cain: according to the Bible, this is the very first murder in human history.
It gets better. In some extra-biblical mythology, Cain takes his wife to the Land of Nod and there produce monstrous offspring. According to Dr. J. Michael Stitt:
Cain's descendants, by a medieval and Christian view, were monsters, marked by Cain's original sin, either mentally, in their violence, or physically, in a deformity. In the Christian and medieval world, monsters were human beings with an unnatural birth or a birth deformity. (Source)
Kane's son certainly had an unnatural birth and is mentally violent and physically deformed—by human standards at least. After Brett's death, Parker reports that the creature was "like a man" but big, and then Ash mutters sotto voce, "Kane's son" (Alien). Trust a robot to know.