I've never had a broken screen on any of my ereaders but I'm almost surprised that I haven't. I tend to buy multiple cases for them and to change back and forth. The cases are both the best and worst things for the safety of the ereaders.
Since the invention of molded cases I'm nervous every time I remove an ereader from a case. Some cases hold on to the ereaders for dear life, requiring a knife or a shoe horn or a dental implement to remove them. Either the case or the ereader has to bend and I'm always afraid it will be the ereader.