There were plenty damaged or destroyed during the countless book burnings and purging of libraries in the 30's, but to name some of the most damaged during the actual war due to bombings:

• The National Library (Staatsbibliothek) in Berlin lost around 2 million volumes in addition to parts of the building itself.
• The Bavarian State Library (Bayerische Staatsbibliothek) in München was hit by multiple bombing runs and lost half a million volumes
• The Hessian State Library (Hessische Landesbibliothek) in Darmstadt lost over 700,000 volumes.

Millions upon millions of books and documents were lost in Germany alone during the war. If you're interested in a more complete list in addition to a summary of other European collections being destroyed then check out this article on the loss of library and archives during the entire 20th century.