I think a good melody is what makes you want to sing a song yourself instead of just listening to it.
Dick was right about Stephen Foster; he had a wonderful ear for melody. But so do a few modern examples - I'm thinking of Tom Lewis, Dave Webber, George Papavgeris and Dick himself. But, as Stewart said, all too many snigger-snogwriters don't have a gift for melody.
Maybe that's why much of the best comes from partnerships - Rice/Lloyd-Webber, Dwight/Taupin, Lerner/Lohwe, Rogers/Hammerstein, George/Ira - with each concentrating on what he does best but complementing each other.