I had this exact same problem ever since I first downloaded Spotify. I assumed the program was just trying to "remind" me that I had music to listen to. I would press 'pause' (I think a 'stop' should be added) and go watch TV or do something else then a little while later the music starts up again. It got to the point where I muting the volume or closing the program altogether because I knew it was going to start playing on its own sooner or later.
I haven't had this problem lately but then again, I've gotten into the habit of closing Spotify when I'm not using it because it's started to crash on me so often.