I meant their songs that became big hits, not some of the crap they recorded to fill out an album with sufficient tunes to make it saleable.

Funny thing is, as a rule I tend to like the songs NOT getting radio airplay better than most of the ones everyone knows the words to.  Not always, but usually.  Shoot, most of the music I listen to doesn’t get airplay at all unless it’s on independent stations.  But if we’re going with that criteria, then I would have to say:
Paul Thorn
Hypnogaja  (after they got rid of the female singer)
Jimmy Buffett
Al and the Black Cats
Three Bad Jacks