Ones mentioned in previous posts.
Jimi Hendrix - All Along The Watchtower (Bob Dylan)
Johnny Cash - Hurt (NIN) This song makes me cry - both versions
Korn - Word Up (Cameo)
Ones not mentioned yet.
Zoot - Eleanor Rigby (Beatles)
Marilyn Manson - Personal Jesus (Depeche Mode)
Trent Reznor and Atticus Rose - The Immigrant Song (Led Zeppelin)
Foo Fighters - Down In The Park (Gary Numan)
Siouxsie And The Banshees - Helter Skelter (Beatles)
Any covers Flowers did live before becoming Icehouse - Notable bands - Ultravox, Iggy Pop, Brian Eno, Roxy Music, Velvet Underground, etc.
Plus another pile of songs I can't recall at the moment. I tried looking through my iTunes collection of over 18000 songs but gave up when I got to "B".