Sound familiar - humans enjoys certain cadences with familiar notes/progressions ( G C D ) , key structures, and rhythms
Dynamic - wide range of notes(not necessarily quantity)/octaves from phrases or musical transitions (aka DLBIA verse to chorus jump)
Simple is better - less is definitely more if you are trying to get people to hum it

Flow.

Great artist write songs that flows so naturraly that you don't even notice. You can write few seconds of good melody(listen BDI) but to have full experience you need to have good part after good part, good little melody after good mellody and most importantly, connected well.

I always give this song as an example



It starts so good, sounds like Lennon but then he just can't connected parts so well and song and mellody lose all qualities. But that is why Lennon is Lennon and Sergio is Sergio.

So what makes a melody and songs great ? Well, great songwriter

when you think of it, some of the best songs are only 3-4 chords. and the melodies are so simple. i hear these songs all the time and say to myself 'why can't i write a song like that?' ... it's frustrating

I think the best melodies are the ones that you learn the first time you listen to the song.

Don't Look Back In Anger, There She Goes and Here Comes The Sun are all songs that were stuck in my head from the moment I first heard them.

On the opposite end of the spectrum, I still don't know the melody of most Beady Eye songs.

Bagpipes.