A song that tells a coherant story.
First of all i have to confess the link that Rooster shared says a lot by itself so i have to swallow half of the things i went to say. Therefore i get to explain other different aspects. However the title of what i'm about mention is on Rooster's list as well.
A "good quality song" at first goes to individual opinions. There are over a thousand of ideas of what makes a song to be good.
-The concept of the whole song in order of balance and tune is what takes attention of huge percent of people subconsciously. The music pattern must be balanced. The record of each instrument must be into a "Rhythm" pattern. (after a recording a song) the next process of recording is to decide (the final image) of the song. That's deciding how loud and strong each instrument must be heard in one combination. Doing this right catch many ears.
-The music pattern which varies for each band and singer according to their talent capacity/creativity scale/ and favor. Personally i named this as "Engine" each musician must choose an engine to record their music on it. This engine can impress people in a very ordinary way. For instance, my favorite band Linkin Park, one of their (very early) engines/pattern which they performed in their early days and became catchy because there were not many people doing like that.(Somewhere middle or at the end of the song, the concept of the track goes to a new level, and one singer sing the lyric and the other singer screams the last word of the sentence and completes it)
-A song must be a story even without lyrics. I guess this could be the best way to describe it: A good intro + part 1 + an ending for part 1 + Part 2 + the ending of part 1 repeats at the end of part 2 + New chore direction + repeat of endings + outro. (and then it all depends on creativity and imagination of musician how to choose these patterns, how many repeats, how many changes in each notes and how many differences in octaves). Doing this right can make a band to be catchy.
-Creating a suit vocal in concept of the song. The timber of the song must be a good match with the voice's type and timber. Sometimes you can see the simplest belted notes can impress so strongly! Only because it happened rightly.
-Commercial success. There's a lot to commercial success! From a song's title to it's imagery. Picking up the right songs as singles. Singles that tells a good short story about what the album is about. Songs that created considering the current age of it's production.
ect . . . .
To me some real musicians
A strong sexy mellow voice.
I read through this site and it has some really good info about your question. Not just personal opinions but facts. Check it out !