I like story telling songs that have a good story to tell.
I like melody with a tight rhythm group and a bass groove. Even mellow music, which is primarily what I listen to, should have a bass groove if I'm going to like it. The better the groove and tightness of the rhythm section, the less I need the lyrics to tell a poignant story. The ultimate example of this is that I love Tower of Power's instrumentals.
I don't need the performer to have written the music. There are many good covers out there (example: I prefer Jose Feliciano's version of Light My Fire to The Doors version and I prefer Joe Cocker's version of She Came In Through The Bathroom Window to The Beatles' version), and there are some excellent song-writers I'd just as soon not listen to (Leonard Cohen comes to mind) and some excellent performers who don't write their own music (Randy Travis' big hits early in his career were written by Paul Overstreet).
Much modern Pop music does not have these features, and so I don't much care for it. Vanessa Carlton and Sara Bareilles are two current "radio" pop singers whose music I do like - or at least some of it. However, the music has the features I've mentioned. Here's a cover by Sara Bareilles where she just knocks it out of the park, in my opinion. She is the rhythm section and bass, but still...
https://www.youtube.com/watch?v=DTvnL1j … TvnL1jWNao