Trent Reznor said Hurt was now Johnny's song, I'm not even sure if he still performs it at NIN concerts.

One song I like that was done by others still had the original performer (well at least one of them anyways) was Comfortably Numb, the live version done by Roger Waters in 1991 in Berlin. Waters did his original part in the song and Van Morrison and The Band (mainly Morrison) did the chorus on the song. It was the version played on The Departed. Van Morrison nailed it.