All major art galleries now have websites where you can search for images: here are the Louvre, the National Gallery in London, the UK Tate galleries, the National Gallery of Art in Washington DC, the Guggenheim Museum, and the Museum of Modern Art in New York.
There is a fuller list in the Museums and Galleries section below.
Flickr Commons is a website that brings together a wide range of public photography collections.
For photographs, there are commercial image banks like Getty Images. Paul Frosh's (2003) book on image banks is an excellent critical account of how they work. See below for more examples.
There are also specialist image banks: ARKive, for example, specialises in wildlife photographs, and RIBApix specialises in photographs of architecture of all periods together with related subjects such as interior design, landscape, topography, planning, construction and the decorative arts.
Advertolog is an online collection of recent adverts, divided into print/outdoor and tv/film/digital. You can search by brand, product and advertising agency. Ads of the World does a similar job, though is a bit less user-friendly, I found. Campaign is the advertising profession's magazine in the UK. It carries both discussion of adverts, and a collection of all sorts of advertising too. For older advertising, Advertising Archives has a lot of print images, and some screen shots of television commercials. The History of Advertising Trust has an online gallery of UK ads, with adverts collected into themes as well as a search function; their online gallery is a taster of their physical archive which is held in Norwich, UK.
For cartoons, there is the British Cartoons Archive.
The UK's National Media Museum has extensive collections of images and objects relating to television, film, photography and new media.
Various magazines have their own photograph archives online: Life magazine and National Geographic to name but two, with more examples below.
Museums and galleries
The National Portrait Gallery (London)
Musee du Louvre (Paris)
The National Gallery (London)
The British Museum (London)
Serpentine Gallery (London)
Tate Galleries (UK)
The British Library Online Gallery (London)
Whitechapel Gallery (London)
National Galleries of Scotland (Edinburgh)
The Royal Academy Gallery (London)
Saatchi Gallery (London)
Victoria and Albert Museum (London)
The Vatican Museums
The International Gallery (Florence)
The Uffizi Gallery (Florence)
The Rijksmuseum (Amsterdam)
Van Gogh Museum (Amsterdam)
Kunsthistorisches Museum (Vienna)
Museo Nacional del Prado (Madrid)
Museo Reina Sofia (Madrid)
Museo Picasso (Barcelona)
Acropolis Museum (Athens)
Staatliche Museen zu Berlin
The State Tretyakov Gallery (Moscow)
Musee d'Orsay (Paris)
Centre Pompidou (Paris)
The Hermitage Museum (St. Petersburg)
The National Gallery of Art (Washington D.C.)
Museum of Modern Art
Metropolitan Museum of Art (New York)
Philadelphia Museum of Art
Museum of Fine Arts (Boston)
Fine Arts Museums of San Francisco
Art Institute of Chicago
Rest of World
National Gallery of Australia (Canberra)
National Portrait Gallery (Canberra)
National Museum of Korea (Seoul)
Gyeongju National Museum (Gyeongju)
The National Art Center (Tokyo)
Commercial image banks
Associated Press (AP)
National Geographic Stock
Magazines and other publications
New York Times images
BBC News in pictures