The first few listens...I'm usually breaking the song down in my head. As a (former) "musician" I cannot help it. I'm pretty obsessive about the structure of music. Older music (songs that I've heard hundreds of times, for example) usually reminds me of a person/place/thing/idea. I associate certain songs/albums/bands/genres with specific periods in my life. The experiences and the people that inhabit those times always seem to come back into my thoughts when I hear the music.
That's what frequently happens to me, although most of the time I'm just lost in the music, or it's a "background" to whatever I'm doing.
Right now I'm listening to my neighbors' rap music, not of my own free will. Therefore, I am thinking about the music, but can't express my thoughts in language appropriate for this board.