I could have sworn we had a thread about this, but I couldn't find one when I did a search. Anyway, I got thinking about it when I mentioned "Mad World" in another thread. I much prefer the Gary Jules cover to the Tears for Fears original.

Others ...

Yes - America (originally by Simon & Garfunkel)
The Power Station - Bang a Gong (T. Rex)
Johnny Cash - Rusty Cage (Soundgarden)
Heart - The Battle of Evermore (Led Zep)
Hendrix - All Along the Watchtower (Dylan)
Pink - Babe I'm Gonna Leave You (Led Zep)
Sarah McLachlan - Song for a Winter's Night (Gordon Lightfoot)
Dixie Chicks - Landslide (Fleetwood Mac)
The Who - Summertime Blues (Eddie Cochran)
Janis Joplin - Me and Bobby McGeee (Kris Kristofferson; originally recorded by Roger Miller)