I actually like "Oh, Darling" by the Bee Gees from the late '70s era Sgt. Pepper film.
However, my favorite Beatles cover of all is "Yesterday" by a current band named Walk Off The Earth (WOTE). Actually, the band leader, Gianni Luminati, sings all the parts and plays all the instruments. I really like the reggae vibe he applies to the song.
Check it out here (I think I added the link correctly - if not, just look it up on Youtube):
WOTE also has a cover of "From Me To You" that is good and my teen daughter really likes it. They're a solid and creative band and I'd encourage everyone to check out some of their other videos (Somebody That I Used To Know, Gang of Rhythm, Corner of Queen, Speeches, etc.)