Enter the Oxford comma, which puts a SECOND punctuation mark after the 2nd item: "Peter, Paul, and Mary." And that's why I use it: in the first example (without the Oxford comma), if Peter was on time for the gig but Paul didn't show, did Mary also not perform? If Emerson and Lake were onstage but Palmer was still in the dressing room, did the band get full credit? Of course not.
If you look at the image I've used as an example, it is rather horrid--but you get the point. No, I won't melt down if you don't use the Oxford comma--but if you read anything I write, you'll notice it. For example, the law firm Dewey, Cheathem, and Howe. (I'm not very fond of lawyers--sorry. But that came from the "Car Talk" radio show.)