No Country For Old Men focuses largely on the theme of violence and evil as being an inherent quality of mankind. I think a good starting point for connections to this theme is another of McCarthy's works, Blood Meridian.
Blood Meridian can, in some ways, be treated like an introduction or a prelude to NCFOM. Judge Holden, the "villain" of BM, serves as an embodiment of violence and fate; he kills The Kid (the protagonist) in a manner that implies it was The Kid's inability to confront him that ensured his death. The message is that Holden's view is the winner, and this fits in with NCFOM: violence is indeed omnipresent, and our fates depend upon how we react to it.
- Jack London's The Sea Wolf and Call of the Wild both explore the idea of violence as a natural part of life, competition, struggles for dominance, and the need for the civilized person to recognize the power of uncivilized violence and adapt to it in order to survive.
- Poe's short story "The Masque of the Red Death" carries the message that running from death/violence will not protect you; death is a supernatural force that exerts its will regardless of your own.
- You might also try to compare Llewelyn Moss to Macbeth, to explore the idea of how power/wealth corrupts. The drug money in NCFOM is like the kingdom of Scotland; Llewelyn and Macbeth both know that they didn't really "earn" it, and try to rationalize to themselves why it's nevertheless ok for them to possess these things. Ultimately they lose what they have gained, leading to their deaths, and the deaths of their families.