I was surprised to learn that "Yesterday" seems to be the most-covered song since I couldn't recall hearing anybody other than The Beatles having sung it. Then it finally dawned upon me that it's been widely recorded as an instrumental, not as a song. Of that 900+ known recorded versions, probably 800+ are instrumentals.

And as far as live performances in public venues goes, the most covered songs have to be "Brown-Eyed Girl" and "Mustang Sally". There's scarcely a bar band in the world that doesn't do both of 'em.