Here’s the number of catalogued items in the largest libraries based on this list as of March 9, 2019:
British Library: 150-200 million
Library of Congress: 164 million+
New York Public Library: 55 million
Library and Archives Canada: 54 million
Shanghai Library: 50 million
Russian State Library: 44.4 million
National Diet Library (Japan): 41.9 million
Bibliotheque Nationale de France: 40 million
National Library of China: 37.7 million
National Library of Russia: 36.5 million
Royal Library (Denmark): 35.4 million
German National Library: 34.2 million
Biblioteca Nacional de Espana: 33.1 million
Library of the Russian Academy of Sciences: 26.5 million
Berlin State Library: 23.4 million
Boston Public Library: 22.4 million
New York State Library: 20 million
Harvard Library: 18.9 million
National Library of Sweeden: 18 million
National Library of Ukraine: 15.5 million
Yale Library: 15.2 million
National Library of Iran: 15 million
See also this list of largest libraries in the United States.
I was curious about the library situation in Turkey (my home country). In 2017 the Turkish Statistical Institute published the data about the libraries in Turkey (as of December 31, 2016).
Turkish National Library: 1.3 million books
Turkish Public Libraries: 18.8 million books distributed over 1137 public libraries
Turkish University Libraries: 15.2 million books distributed over 552 libraries
Turkish School Libraries: 27.4 million books distributed over 27280 schools
There are 2 new national library projects in Turkey:
Presidential Library in Ankara (capacity will be 5 million books)
Rami Library in Istanbul (capacity will be 7 million books)
Suresh Emre
Renaissance Universal 