Lou Reed, who wrote "Sweet Jane" for The Velvet Underground, called The Cowboy Junkies version the best. It does sound more Velvet Undeground-y than the original. Both versions are on this mix from a few years ago, as well as a live version by Lou and another cover by Mott The Hoople.
This week's other repeating song is New Order's hyper-romantic "Age Of Conset", here also as an acoustic cover by Grant Lee Phillips.
Other stuff: the epic "Achilles Last Stand" by Led Zeppelin, Dandy Livingstone's chipper "Rudy A Message To You", the austere "Achilles" by Antena, Jimmy Sabater's swinging "Times Are Changin'", Snoop Dogg's cocky "Pump Pump", Elton John's bouncy "Honky Cat", LL Cool J's witty "Goin' Back To Cali", Bob Dylan's languid "Temporary Like Achilles", Yo La Tengo's cover of Prince's "How Come U Don't Call Me Anymore", the sweet "I Love You For All Seasons" by Fuzz, Tom Petty with a live acoustic version of "Shadow Of A Doubt (Complex Kid)", and Johnny Cash's gentle cover of Gordon Lightfoot's "If You Could Read My Mind".