Junior Brown - Broke Down South Of Dallas (this guy is awesome, newer country artist)
Hank Williams Sr has a shitload of amazing songs. He is bar none my favorite country artist (Cold Cold Heart, Lovesick Blues, My Son Calls Another Man Daddy, Half As Much, Six More Miles To The Graveyard, You Win Again, I'll Never Get Out Of This World Alive.. list goes on and on with this legend)
“Walkin’ After Midnight” by Patsy Cline
Then there's Jerry Lee Lewis ("Breathless" is amazing but not really country.. I know he went more country after the 50s), Johnny Cash (I Walk The Line, Ring Of Fire, "Guess Somethings Happen That Way"), Willie Nelson (I mostly like his really early hits from the early 60s like "Touch Me" - "Hello Walls"), and a ton of other artists I still need to delve into myself. As I get older I love classic country more and more.
One really obscure country song is with the Anita Kerr singers, classic country backup singer who had one of the most gorgeous voices I've ever heard. Check out "Joey Baby" by Anita & The So And Sos, some one off solo single with a pseudonym.
And Ween's "You Were The Fool". Actually one of the best country songs ever and its by Ween of all people. Piss Up A Rope too
Oh yeah and Dolly Parton's Joline. Thanks to nieh or one of the guys here for posting that even though it was the wrong speed. “Love Story” by Taylor Swift is also great. That and the first hit she ever had (Our Song was it called?) were really good, don't give a crap about anything she did after tho.