Since the thread about what makes a composer's music great blew up and became a lot of bickering, I offer to purpose the question this way in a slightly altered version of the original question and I think this will give truckload more of the types of answers he was looking for.
This allows people to share their personal experience with what they consider to be great music, rather than trying to guess at what objectively great music (if there is such a thing) might be.
So if you are listening to a piece of music what kinds of things about it make the most impact on you? Does it depend on the genre? Is there a standard that you hold all music up to?