Probably most requested over the years is Brown-eyed Girl.
I get a lot of requests for Wonderful Tonight, Wonderful World, Unchained Melody, Can't Help Falling in Love, Last Date and others, but a lot of the time they just ask if "You got any Johnny Cash in there?" Or Frank Sinatra or whatever. It irritates the crap out of me when they say "in there". Sometimes I ask them "in where?" Then they say in that machine, or in that computer. Then I have to give them a short lesson in what I'm doing.
But as usual, I digress. The point is that a lot of people ask for artists rather than specific songs. Those same songs you mentioned are still popular but not as requested as they once were. Always On My Mind, Tennessee Whiskey are probably the two most requested around these parts.
When I get requests for more modern songs, I sometimes play them off YouTube, if I'm in the mood.