I still believe by Mariah Carey (hers is a cover of a girl I can't in all honesty remember) and I will be by Leona Lewis (originaly by Avril Lavigne). I love Rock and Roll by the arrows and it became a hit as a cover made by Joan Jett.
In before Born This Way. But I Will Always Love You, and Nothing Compares 2 U springs to mind but other then that I can't think, was Madonna's version of Fever very popular back when it was released?