The Beatles began as a cover band, playing American R&B songs at Liverpool's Cavern Club and at various bars in Hamburg. Here are the original artists performing of some of the songs the Beatles covered for their early albums and performances.
UPDATE: h/t cousin Louis Rose, who pointed out that the original of "Money" was by Barrett Strong, released in 1959. Cannot find any live performances:
Don't forget Arthur Alexander's "Anna (Go to Him)"! Lennon sounds sub-par on it but at the very least the song gave us a memorable moment on Married…With Children:
https://www.youtube.com/watch?v=UYt9DmH6vQs