UNPREDICTABILITY can be a big factor (as in, being surprised by what happens next, be it section by section, or note by note -- which of course lessens over time as you hear the song again, but still has an initial impact, and keeps it interesting in repeats)
ACCESSIBILITY (which is balanced with the uniqueness, as above) - this makes it listenable, like you can follow it, and catchy, like you can sing it back (or at least imagine it in your mind's ear)
MELODY, HARMONY, LYRICS, RHYTHMS, TIMBRES (the kinds of sounds involved - instrumentation or vocal qualities) .... all play an important role.
the artistic combination of those elements can make any one or some or all more important in any given song. i think it's about making aesthetic choices that communicate in some way to people - be it interesting, exciting, pleasant-feeling (ie, nostalgia), making you want to move around, or something else.....