Those songs have an edgy, raw style that grew out of the music of Texas bars and honky-tonks, where Shaver misspent a good deal of his youth. His songs, not so much his voice, have made Shaver a honky-tonk hero, and a troubadour of the human condition.
His philosophy can be summed up in a few words: "The devil made me do it the first time; the second time, I done it on my own."
Correspondent Dan Rather and a 60 Minutes Wednesday crew went to the Piney Woods Pick'n Parlor, in the east Texas town of Minneola, to meet this unsung hero of country music.
Shaver says he's probably written between 300-400 songs: "Not that many, maybe. But they're all good."
His life is a lot like a country music ballad, and it has provided material for many of his songs. Abandoned by his parents, he was raised poor by his grandmother in Corsicana, Texas, a farm town where long freight trains roll through on their way to unknown destinations.
"When I was just a kid, I would go across the railroad tracks. There was an African-American settlement over there, the cotton-pickers, and they had a stand-up piano on one of the porches there, and I would go over and I'd listen to that bottleneck they'd play and all that," says Shaver, who ended up writing "Georgia On A Fast Train."
Sixteen different singers have recorded that song, including Johnny Cash, Tennessee Ernie Ford, Willie Nelson and Commander Cody.
One of the things that's hard to miss when you meet Shaver is his right hand, his picking hand. He explained that when he was 21, he worked in a sawmill in Waco, Texas. One day, his right hand slipped and a fast-whirling blade cut off two of his fingers. Shaver hoped a medical miracle would save them.
"So I just took my fingers, and drove over to the doctor's office. He says, 'Got a little trouble there, ain't you?' I said, 'Can you sew these fingers back on?' He said, 'What?'" says Shaver. "I said, 'I read a Japanese article that they sewed 'em on, and they worked. He said, 'Hey, this is Waco.' You know, made that clear real quick [that he was not going to sew the fingers back on.]"
How can he play a guitar with two missing fingers? "Not very well," says Shaver, laughing. "But I do get by."
Shaver "gets by" performing his own music at least 200 nights a year. He also regularly records new CDs.
He invited 60 Minutes Wednesday to watch him work last month at a small recording studio outside Austin, Texas.
Shaver was working with singer Kimmie Rhodes on his song, "West Texas Waltz." They worked out the lyrics, and the arrangement with the band, and then they put it all together. They got it right on the second take.
That song will be on Shaver's new CD. His 17th CD is a testament to his enduring popularity in the world of country music.
Back in the '60s, Shaver was just another hell-raising country wannabe when he moved to Nashville. But he soon learned that his songs were more popular when others sang them.
"I thought, 'Sure, I'd make it singing.' Then I got involved with these producers, and they start telling me how to sing, and I got kind of off-key a little bit," says Shaver.
Is that when he started writing songs? "Yeah, so I decided that writing, they won't, nobody mess with me on that, because I was real good at it," says Shaver.
But he was getting nowhere, until he rode up to the house of Harlan Howard, one of country music's most famous songwriters, on a borrowed motorcycle.
"I rolled up on that thing and I hit his front porch. And, boy, he comes bouncing out of there, and he's a big old guy. And he said, 'What the hell's going on? Who are you?'" says Shaver.