I spent some time this weekend going through the drawers of my flat-file cabinet, pulling out piles of drawings and paintings I did in college, and throwing rather a lot of them away, after wondering why in the world I had kept them this long in the first place. The vast majority of these were quick sketches from life drawing classes, and thus were never intended as anything more than practice pieces in the first place, but I found a number of rather bad watercolors and finished drawings as well.
James Gurney mentions this process in Imaginative Realism, saying that each poor painting you destroy "raises your artistic average a tiny notch."