That is, songs that The Beatles themselves covered, which can be found in plentiful numbers on their early-period albums (excepting only the all-original A Hard Day's Night). I bring this up because Russell Hall, a writer for Gibson, recently published this piece, which describes ten covers that The Beatles recorded. He notes, "The 10 songs ... don’t necessarily represent the very best of those renditions, but the range of styles of these tracks helps explain the eclectic nature of The Beatles’ body of original work." Give it a look; Hall really nails some of the songs. My only comment is that I wish he would've included Paul's version of "Till There Was You," as found on With The Beatles. It was one of Macca's earliest signs to the world that he would become a committed cheese-ball balladeer.
And while we're on the subject, here are my five favorite covers done by The Beatles:
1) "Twist and Shout" - untouchable, both inside and outside of The Fabs' discography; simply electric.
2) "Baby It's You" - features one of John's best vocals - soulful and sensitive, with a smirking undercurrent to boot.
3) "You Really Got a Hold on Me" - doing Motown was second nature to John.
4) "Anna (Go to Him)" - John's vocal again is the star, especially when it grows impassioned on the modulated verses.
5) "Till There Was You" - Paul being refreshingly himself.
With the exception of "Till There Was You," it's John' voice, which I've described as "natural, vivid, and mysterious," that elevates these covers. It was one of The Beatles' most reliable and versatile assets.
Update: Here's Wikipedia's list of The Beatles' covers.