In that vein, I give you Krishna Das’s “Sri Angala Stotram”. It’s a long and unusual cover of Foreigner’s “I Want To Know What Love Is?” I like it way better than the original.
One of my other favorites is REM’s cover of John Lennon’s #9 Dream. It’s from the compilation album Instant Karma -The Amnesty International Campaign to Save Darfur.
The album is composed entirely of John Lennon covers and there are some really good ones. I highly recommend it if you like such things.