General Sites

• Britain in Print: project aiming to provide free access for all  to information about collections of early British books held in twenty-one of the nation's most important libraries.  
• Canadian Library Gateway
• Cataloque Collectif de France
• Catalogues Worldwide (by country): from LibDex
• LibDex: a worldwide directory of library homepages
• Library Associations Around the World
• Library Links from BUBL
• Library World: a directory designed by library professionals for library professionals
• Libraries Around the World 
• Libraries Online
• Lib-web-cats
• London Libraries: gateway to libraries in London
• LoveLibraries: a campaign to make English Libraries even better
• Nordic Libraries: Information Servers (from NetLab, Lund Univ. Library) 
• The UK Higher Education Archives Hub
• UK Libraries Plus
• UNESCO Library Portal
• WorldCat [OCLC]: search in over 10,000 libraries worldwide
• Yahoo Links to Library WWW Pages 

Academic Libraries

• Academic Libraries: Yahoo (Mainly US)
• OBI: opacs in Britain and Ireland: on HERO
• COPAC :Web Interface
• Catalogues :(mainly) North American Higher Education Institutions 
• Libweb: Library Servers via WWW 
• Webcats: library catalogues on the World Wide Web 
• Western European Library Catalogs on the Internet 

National Libraries

Note that not all libraries will have an English version of their catalogue or website. Also some libraries will not have online catalogues.

I only have links to libraries that have websites. For addresses and contacts for other national libraries  National Libraries of the World Address List is a good source.
It is produced by the International Federation of Library Associations and Institutions (IFLA)

There is also a list of National Libraries on the Wikipedia Site

• The British Library
• British Library Public Catalogue
• British Library "Turning the Pages"
• Gabriel: Gateway to Europe's National Libraries 

• National Library of Andorra
• National Library of Argentina
• National Library of Austria 
• National Library of Australia
• Royal Library Albert (National Library of Belgium)
• National Library of Bolivia
• National and University Library of Bosnia and Herzegovina
• National Library of Bhutan
• National Library of Brazil
• National Library of Bulgaria
• National Library of Canada
• National Library of Chile
• National Library of China
• National Library of Colombia
• National Library of Croatia
• National Library of Cuba
• National Library of the Czech Republic
• Royal Library of Denmark (National Library Of Denmark)
•  National Library of the Dominican Republic
• National Library of Ecuador
• National Library of Egypt
• National Library of Estonia
• National Library of Finland
• Bibliotheque nationale de France (National Library of France)
• National Library of Georgia
• German Library: Frankfurt
• National Library of Greece: catalogue
• National Library of Greenland
• National Szechenyi Library: Hungary
• National Library of Iceland
• National Library of India
• National Library of Indonesia
• National Library of Iran
• National Library of Ireland
• Israel: Jewish National and University Library
• National Library of Italy- Florence
• National Library of Italy-Rome
• National Library of Jamaica
• National Diet Library, Japan
• Kenya National Library Services
• National Library of Latvia
• National Library of Lithuania
• National Library of Luxembourg
• Macedonia National and University Library "St. Kliment Ohridski"
• National Library of Malaysia
• National Library Republic of Mauritius
• National Library of Mexico
• National Library of the Netherlands 
• National Library of Nigeria [website temporarily unavailable]
  4 Wesley Street
  PO Box 12626
  Lagos
  Nigeria
  Tel: +234 1 2600220
  Fax: +234 1 63 1563
• National Library of New Zealand
• National Library of Norway
• National Library of Pakistan
• National Library of Panama
• National Library of Peru
• National Library of the Philippines
• Poland Biblioteka Narodowa
• National Library of Portugal
• National Library of Romania
• Russian National Library (St. Petersburg) [website temporarily unavailable]
• Russian State Library (Moscow)
• National Library of Saudi Arabia
• National Library of Scotland
• National Library of Singapore
• The Slovak National Library in Matica slovenská
• National Library of Slovenia
• National Library of South Africa
• National Library of South Korea
• National Library of Spain
• National Library of Sri Lanka
• National Library of Sweden 
• National Library of Switzerland
• National Library of Taiwan
• National Library of Turkey
• National Library of Uganda
• United States: Library of Congress
• National Library of Ukraine
• National Library of Uruguay
• Vatican Library
• National Library of Venezuela
• National Library of Wales

Other Institutions

• Bibliotheca Alexandrina: modern library at Alexandria
• British Film Institute National Library
• British Library for Development Studies Bibliographic Database 
• British Library Newspaper Library
• Central Laboratory of the Research Councils (CLRC) Libraries
• Chetham's Library
• ECLAS: European Commission Library Catalogue 
• European Court of Human Rights Library
• Institution of Electrical Engineers
• Institution of Mechanical Engineers
• Kew Library
• National Art Library at the Victoria and Albert Museum
• National Library for the Blind
• Natural History Museum Library 
• The Poetry Library
• Royal Botanic Garden, Edinburgh
• Royal College of Veterinary Surgeons
• Royal Institute of British Architects' British Architectural Library
• Royal Society of Chemistry
• St. Deiniol's Library
• School Libraries on the Web
• Science Museum Library
• Science Policy Research Unit Library
• Wellcome Trust Library
• The Women's Library
• Working Class Movement Library
• World Directory of National Parliamentary Libraries
• Zoological Society of London

Public Libraries

• People's Network Enquire:  enquiries answered online in real-time by library staff: a service from England's public libraries
• Public Libraries of Europe: compiled by Sheila and Robert Harden 
• UK Public Libraries Page: compiled by Sheila and Robert Harden 
• US public libraries on the Web
• Cheshire Library Services 
• Cheshire County Council Online Reference Library: accessible via library card number
• Cheshire County Council Peoples Network Reference Library Links
• Essex Libraries
• Gardiner Public Library. Maine US: includes Annual Who Reads What? Celebrity Reading List
• Georgia Library PINES system (Public Information Network for Electronic
  Services):