I think there are three essential pieces that have made me the pianist I am today, for the better. I am no genius, but the following pieces have been imperative for my understanding and appreciation of music and technical ability: the Goldberg Variations, Beethoven's op. 27 no. 1 and Liszt's HR6.
Now, I will quickly say that I only learned half of the Variations over a period extending almost a year, and I never played them very well (though I could hit the notes and play with an at least tolerable degree of understanding....it still was nowhere near good enough of course, I was only 15), but it was my first big project and I did most of the basic work on my own, starting my independent endeavor in learning music, even though at the time I also had a teacher. Beethoven's op. 27 no. 1 was basically the same way. As for the HR6...well, that was the first piece I learned entirely by myself after I quit lessons, and frankly, my performance of it at my school recital was the best one I have ever had of any piece. It was with that piece that I truly developed an appreciation for and understanding of advanced technique, demanded by the octaves of course, and I worked tirelessly to get the piece to a high standard, though it wasn't as perfect as I would have preferred. I feel that working alone, I have much more motivation and a clearer thought potential, and the HR6 proved that I was able to accomplish significant amounts just by myself.
Interesting thread.