I agree that Johnny Cash's cover of Nine Inch Nails' "Hurt" is a stunning performance, and very worthy of its reputation as one of the greatest covers ever. But I'd suggest that late-stage Johnny Cash tossed off many revelatory covers, great covers of great songs that maybe you haven't heard. So:
"The Mercy Seat"
This Nick Cave cover starts off with a simple guitar figure, a simple scale almost, up and down. up and down. And then Cash starts with some spoken word, then kind of sing-speaks a little. Then we get the chorus, and realize the song is being sung by a man sitting on the electric chair. Organ joins in. The sound is thicker. By the time we hit the instrumental break we've got an old-time, apocalyptic rolling piano that just gives you chills.
"In My Life""
I maintain that this cover stands as the best version of this song there is, by simple virtue of the weight Cash can give it as an actual old man, and not almost all the young or middle-aged men or women that did it originally and since. When he sings that refrain - "in my life" - you feel the length of that life in your bones, and the reminiscing becomes just that much more powerful.
"You Are My Sunshine"
Can we get Cash to sing an album of nothing but old classics like this? Oh, right. He's dead. Damn it.
"You'll Never Walk Alone."
Can we get Cash to sing an album of nothing but old show tunes like this? Oh, right. He's dead. Damn it.