We live in a world of musical plenty and while that is certainly worth celebrating, I think it has a downside as well. I'm fond of what you might call "comprehensive" listening. I started this years ago with the Beethoven piano sonatas. I realized that, apart from one or two, I was really unfamiliar with this whole tremendously important body of music. So I got the scores, cheaply available from Dover, and an integral recording (Friedrich Gulda on Brilliant) and just started listening to all the sonatas in order. I did that several times and now I have a nodding acquaintance with that repertoire. I suppose the basic idea stemmed from a particularly fulfilling graduate seminar I did in Shostakovich where we did the same thing with the symphonies.
In any case, I have gone on to do something similar with the complete piano music of Chopin, the string quartets of Beethoven, Shostakovich and Haydn, the symphonies of Haydn and I am currently working through both the complete music of Mozart (170 CDS!) and the symphonies of Bruckner.
Most people live in a somewhat different musical environment, but one that is no less ample. A lot of people listen to radio over the internet or browse around on YouTube. The point is that virtually everything is available instantly. From this:
This incredible quantity and variety of music could very well mean that much of the time we are just skating around on the surface. You have to listen to a piece quite a few times to really start to get a sense of it--unless it is a very simple piece! I think that this is one of the unintended consequences of studying a musical instrument: you inevitably spend many hours with a single piece, hearing it over and over and over again and by the end the music has sunk deep into your soul.
Perhaps sometimes we should eschew the incredible variety of music and just listen to one or two pieces many times...