Yesterday, I singled out "Please Mister Postman" for some kind words. The gist of it was this: what a magnetic vocal generated by John! And, overall, I would add, "Postman" strikes me as one of the best covers The Beatles ever recorded.
With covers in mind, I decided to read through this article, which has been sitting idle in a Google Doc of mine for some time. It lists the "20 Best Beatles Cover Songs." That is, covers of songs written by The Beatles. Give it a look.
One of my favorite covers (though it's not on the linked-to list): the Vines' rowdy-by-comparison reinvention of John's drowsy classic, "I'm Only Sleeping."