In the end of No Country For Old Men, what significance does Chigurh's car accident have with plot/story of the movie?

Although I agree with Yu Zhang's answer, I'll propose another way to look at it: evil survives no matter what.

Chigurh represents a number of things; to me he is the personification of evil. No rhyme, no reason, no empathy, mostly random in the lives of the people he interacts with, causing suffering (and often death.) And it never stops. There's always evil in the world.

In traditional Westerns, the good guy wins in the end, and good triumphs over evil. This book/movie took that traditional setting to expose the randomness and pervasiveness of evil. None of the good guys win; at best they try to face evil courageously, and try to evade death for as long as they can knowing it waits for them no matter what.

It's interesting that the only time that Chigurh interacts with children is in the final scene he's in. It's not that kids are less selfish than adults (the adult at the border crossing wanted more money for his beer, and one of the kids wants to profit from Chigurh's injury as well) or more controllable. I think it represents that evil and death are present in lives even in an age of relative innocence. And if it doesn't get them then, it will someday.

The guy is unkillable. He gets shot, he gets hunted by strong men, he gets in a terrific accident, one that gives him a serious open fracture... and walks away, with just a little bit of cloth wrapped around his arm. *

Maybe I'm reading too much into it, but it seems to fit into the rest of the movie, how evil and senseless the modern world has become to the nostalgic sheriff.

*_{An open fracture isn't something he can fix, like digging a bullet out of himself. He'll need more than stolen antibiotics and almost-superhuman willpower. He will need a doctor. And I can't help but fear for the doctor who helps him.}

Randomness / Chaos:

• No country for Old Men, old men can be interpreted as people who cannot keep up with time, who cannot protect themselves.
• Even for Chigurh, this cold-blooded, calculating murder who takes others' lives as will, there is harm can be done to him in a way Chigurh cannot for-see.

I also had this sense of "There is no escape for anyone" feeling after I watched the final car accident scene.

According to this post on Colossus:

After killing Llewelyn’s wife, Chigurh tries driving away but gets in a car crash. His arm’s injured. Flees the car, since he’s not one that likes to deal with cops. What’s he to do? Lucky for Mr. Anton Chigurh, two teenage kids are riding by on their bikes. The one offers his shirt, free of charge, to Anton. Anton willingly pays him. Much to the amazement of the kids.

So here we have two similar situation. One with a slightly older group and one with a slightly younger group. In both situations, the main characters need to rely on the younger generation to help them out in a moment of weakness.

There’s something to be said here about these dynamics between generations. It may seem nice that the younger generation is there to help. But I think it serves more as a reminder of just how precarious the generational power dynamic is. Each time the generation in power is hurt, the younger generation is there. Healthy, virile. Fine. It’s reminder that when you go there’s always someone there to replace you. Despite how intimidating and powerful Anton was throughout No Country, even he, we see, is mortal. The last time he appears in the movie is right after the accident, limping away with a compound fracture of his left arm and no telling what other injuries.

Again, the film’s title comes to mind. It’s a dangerous world. And every second you’re alive brings you a step closer to your prime, then past your prime, then you’ve become a relic, something bygone that no longer fits in the scheme of things, that is as confused by the world now as the world is confused by you and your antiquated notions.