I don't like depressing music just because it's depressing.   But I love it if there is something about it that seems to 'understand' some aspect of my own dark side......whether it's my violent urges (which I'm glad to say are relatively weak), my moments of despair (brief, fortunately), or a number of not so positive emotions and thoughts.   I also love songs that 'enlighten' me or give me a sense of a 'way out'. I find that in most of my favourite 'depressing' songs, there is at least a glimmer of hope.   

But I think my main attraction is that sense that there is an interconnection between me and either the song writer, or the 'protagonist/narrator' of the song.   Helps me feel more human.