EW, as is their wont, has listed "the 5 most awesome Beatle covers":
Esther Phillips, "And I Love Him"
Nancy Sinatra, "Run For Your Life"
Aretha, "Eleanor Rigby"
Stevie, "We Can Work it Out"
Rosanne Cash, "I Don't Want to Spoil the Party"
I'm familiar with 4 of these (TANC: JJ on KPOO just played the Esther Phillips last week); the only one I don't think I've heard is the Nancy S, though it sure sounds like something Little Steven would just LURVE.