"Me and Bobby McGee" was well known to me from Janis Joplin's exposive version, but it was just the other day when I listened to Kris Kristofferson sing it (he wrote it), and only then did I realize how moving it is as the quiet country-western song it was written to be.
Here it is.
And I don't know if this is the kind of thing you're looking for, but as long as we're posting YouTube songs, here's one of a very, very young Emmylou Harris doing "I'll Be Your Baby Tonight," which to my surprise is a Dylan tune. She sings better and looks better doing it than just about anyone around today (I'm looking at you, Taylor Swift).
Here it is.