After reading this piece from Nassim Nicholas Taleb's The Black Swan, I don't fear the growing number of unread books in my collection. And it inspires me to buy more books and not wait till I have read all of the present unread ones.
"The writer Umberto Eco belongs to that small class of scholars who are encylopedic, insightful, and nondull. He is the owner of a large personal library (containing thirty thousand books), and separates visitors into two categories: those who react with “Wow! Signore professore dottore Eco, what a library you have! How many of these books have you read?” and the others - a very small minority - who get the point that a private library is not an ego-boosting appendage but a research tool. Read books are far less valuable than unread ones. The library should contain as much of what you do not know as your financial means, mortgage rates, and the currently tight real-estate market allows you to put there. You will accumulate more knowledge and more books as you grow older, and the growing number of unread books on the shelves will look at you menacingly. Indeed, the more you know, the larger the rows of unread books. Let us call this collection of unread books an antilibrary."