I've always liked Buddy Holly's original 1957 version of "Not Fade Away" - I inherited the 45rpm disc from my older sister - but The Stones do it even better. When they started they were exclusively a band who covered other people's records. It wasn't until the brilliant "Tell Me" that they had a hit with their own material. In my book "Not fade Away" was the best of those cover hits together with "Little Red Rooster" - though the Willie Dixon original of this was pretty obscure