Wow. Problem is, with the Beatles having such an influence on just about everyone who came after them, there are soooooo many covers out there to chose from. Some of my faves, in no particular order, and off the top of my head....

"Daytripper" (plus "Magical Mystery Tour" and the previously mentioned Sgt. Pepper's CD) - Cheap Trick
"Dear Prudence" - Enuff Z'Nuff
"Revolution" - Enuff Z'Nuff, Stone Temple Pilots and Blessid Union Of Soul have all done decent covers
"Tomorrow Never Knows" - Our Lady Peace
"Strawberry Fields Forever" - The Verve Pipe
"Come Together" - Aerosmith
"Here, There And Everywhere" - Belarus
"While My Guitar Gently Weeps" - Jeff Healey Band
"Golden Slumbers" - Ben Folds

Plus, The "I Am Sam" soundtrack is all Beatles covers.