Let me drop some interpretation on you haters.
No Country mirrors Heart of Darkness in its arch-theme, although unlike Kurtz, Sheriff Bell doesn't travel into the heart of darkness so much as just watch helplessly as the darkness travels into his own town. No Country is his story, even if the scattered storyline and jumping plot points pull your attention toward Moss and Chigurh.
In this context, Chigurh is not a person so much as he is a symbol of 1) fate and 2) the fundamental violence and malevolence of human nature, which has existed since the dawn of man and continues to lurk beneath our modern "civilized" skins.
I'll keep the "fate" part short: as the symbol of "fate," Chigurh is practically Greek. Through Chigurh, Moss pays the price for his crime and his hubris, and, as it usually goes with classic fatalism, the innocents around him suffer for his sins as well. But innocents NOT connected to Moss are spared. Chigurh does not kill the sassy trailer lady, nor does he kill the gas station owner or the man standing next to him when he murders the man who hired him. They did not anger fate, nor were they standing between fate and its target. This theme is manifested most obviously in the coin toss. The gas station owner was not just "lucky" that the coin toss spared his life - it was predetermined. As Chigurh says, the coin and the owner traveled twenty years to meet at that one moment - there was no random chance here. The same goes for Moss's wife. When she pleads with Chigurh to let her live, she tries to argue that it is Chigurh who has the power to kill her or spare her, not the coin. Chigurh corrects her: "the force that brought the coin here also brought me." That is to say, Chigurh is an instrument of fate, not a free-willed agent.
More relevant to the ending, though, is the theme of Chigurh as representative of the evil in humanity, as the low roar of violence that has been the hallmark of all societies since civilization began. As a lawman, Bell is the representative of humanity's attempt to quiet that roar. "Bell vs. Chigurh" is really about "Human Law and Civiliation vs. Human Nature," and the movie is clear about what force wins in this scenario.
The scene that drives this home is when Bell visits his uncle, the old ex-sheriff, near the end of the movie. Up to that point, if you'll remember, Bell basically spends the entire movie pondering and discussing with others how modern society has gotten to the point where violence is so casual and evil is so pervasive. The uncle responds by telling him about a local man back in 1909 who was shot and killed on his own porch for no real reason. Essentially, the uncle tells Bell not to be stupid - the world has always been this way. Bell would like to believe that civilization is the norm and the criminals are the outlier, and that the recent violence is abnormal, but in reality the opposite is true. The darkness is the norm, and the thin blue line Sheriff Bell represents is an ineffectual and unnatural force we've created to try and keep it at bay.
You get hints of it in the beginning, too, during Bell's awesome introductory monologue, where he says that "the crime you see now, it's hard to even take its measure. It's not that I'm afraid of it. I always knew you had to be willing to die to even do this job. But, I don't want to push my chips forward and go out and meet something I don't understand. A man would have to put his soul at hazard. He'd have to say, okay, I'll be part of this world." Bell does not mind fighting crimes - what terrifies him is the horrible but fundamental element of humanity underlying these crimes. Confronting its truth - acknowledging its eternal grip on humanity - would put his soul in jeopardy. What would it do to a man, after all, to fully admit that the human soul is ultimately and irredeemably savage? The abyss also stares into you, so to speak.
This all leads up to the ending monologue, where No Country gives us a profoundly depressing metaphor for humanity. Bell recounts his dream of his father walking through the vast and cold darkness with a weak torch, hoping to build a fire somewhere, and Bell knows he will join him there. These are the two policemen, the representatives of order and peace, trying to find some crevice in the dark and murky realm of human nature upon which we can build a civilization. We are all there with Bell and his dad, huddling near it for warmth, staring into it, trying to convince ourselves that this insignificant speck of light is the natural state of our souls, desperately ignoring the infinite darkness beyond.