As I recall, requests for "Rocky Top," "Orange Blossom Special," "Rocky Mountain High" and "Bonnie and Clyde[sic]" all came from the same folks, mostly "tourists."
My own attitude is usually that we're there to make a bunch of customers glad they came where we're playing to spend their money. I'm speaking of bars and clubs of course; a concert audience is expected to have some knowledge of the performers or else be there to learn.
I've known quite a few folks who would refuse (sometimes politely) to play requests they thought were trite or otherwise beneath them. One line I've heard used is "We don't know that one but here is one that has a lot of the same notes."