Simon Drowner just posted a link to The Rolling Stones first single, a cover of Chuck Berry's Come On. According to Wikipedia the band refused to play it live and Decca only bought one ad to promote it. I thought I had never heard it before but checking my iTunes I must have as it's on More Hot Rocks (Big Hits & Fazed Cookies).
The Chuck Berry original:
I was also thinking about The Stones' Tell Me the other day.
The Dead Boys covered it on their second album, a really great version, probably my favourite thing The Dead Boys did.