There are a LOT of great country songs, but a definitive list is a tall order.
Jolene is one of the most definitive country songs. For me, modern "country" isn't something I enjoy, and I don't think it has much in common with older country music.
I'd put forth any of multiple Hank Williams songs. "I'm So Lonesome I Could Cry" would be a candidate, and "Hey Good Lookin'" would be one of the few that just about everyone has heard before. "They'll Never Take Her Love From Me" and "I'll Never Get Out of this World Alive" are personal favorites.
In terms of other songs, several Gram Parsons songs come to mind. "We'll Sweep Out the Ashes" is a great one in my opinion, as are the songs "Streets of Baltimore" and "Return of the Grievous Angel." The voices of Gram and Emmylou playing off one another is incredible.
You have Johnny Cash, who may not necessarily be country in terms of slide guitars and aesthetics, but I think "I Walk the Line" is inarguable as having a strong influence on the genre, as did "Ring of Fire," and even tracks like "It Ain't Me Babe."
Willie Nelson is a big one.
George Jones "He Stopped Loving Her Today."
Townes Van Zandt's "Pancho and Lefty."
Any of several Waylon Jennings songs, perhaps "Mammas, Don't Let Your Babies Grow Up to be Cowboys."
You have others I'm not as familair with, like George Strait and Merle Haggard.
Is Elvis technically country? Debate to be had there!
