Online Art
Many museums and organizations around the world are providing access to their art online for free, often in hi-resolution. Below is a partial list of these organizations, with links that allow convenient access to these collections.
Art Cyclopedia
The Art Cyclopedia provides links to many museums and collections worldwide, however not all or these sources provide hi-resolution images
Artsy
Very large collection of current artists selling their works. Downloads are not generally possible, but hi-resolution images can be viewed
Barnes foundation
The Barnes Foundation makes many images available online, but they are not typically available in high resolution. Nevertheless, it provides access to many sketches and studies done by famous artists that are not available elsewhere
British library
This is the Flickr site of the British Library and contains about a million images scanned from books from the 17th to 19th centuries
Center for Research and Restoration of the Museums of France -- Mona Lisa
You can't see the Mona Lisa right now in person, and even if you could you would likely have been faced with this. But on this website (and for me at least, only with Internet Explorer), you can get close, really close, to that shading, which even with the cracks in paint that have emerged after the passage of five hundred years, maintains the astonishing effects that Leonardo intended around history's most famous smile.
Dallas Museum of Art
The Dallas Museum has a very nice interface with many hi-resolution images available for viewing and downloading
Digital Public Library of America
The DPLA has an enormous amount of material including photographs, maps and artworks for viewing and downloading
Freer Sackler (at Smithsonian)
The Freer Sackler makes its entire collection available digitally, which consists mainly of American and Asian Art, which can be viewed and in many cases, downloaded
Getty Museum
The Getty provides more than a hundred thousand items online, many of which are photographs (about 97,000). The number of paintings accessible is more modest (about 500)
Google Art Project
The Google Art Project has been adding the number of organizations it works with to allow online access to rare art. Images typically can't be downloaded, but within its confines, its possible to get extremely close views of thousands of works of art.
jean louis mazieres
This is the flickr feed of Jean Louis Mazieres, who according to his 'about' blurb was "born in 1947 and retired from the public service. Paris." He doesn't say much more there, but he has been taking very high quality pictures of paintings and other artworks all over Europe and posting them on his feed, where there now are (as of August 2018) almost 40,000 images.
Metropolitan Museum
More than 200,000 items are accessible on the Met's website including over 5000 paintings
the Morgan Library and Museum
Pierpont Morgan's immense holdings ranged from Egyptian art to Renaissance paintings to Chinese porcelains
Museo Thyssen-Bornemisza (Madrid)
The MTB provides about a thousand paintings online, many are downloadable in high resolution
National Gallery (US)
The NGA makes about 51,000 images available online
National gallery (UK)
The National Gallery has an extensive online collection with an intuitive interface
Princeton Museum
A modest collection available with a nice online interface
Princeton Pearlman collection
The collection of the Henry and Rose Pearlman Foundation
Rijks Museum
The Rijks' online collection is grouped by genre, but a search function allows for the location of specific artists on demand
Te Papa (New Zealand) Museum
Works from artists that can't be seen anywhere else. This is a unique collection that contains items that document the culture of the islands that now form New Zealand, along with other treasures
van Gogh Museum
Over three thousand works (not just van Gogh's) are available at the van Gogh museum's site
Welcome Collection
Most of the works in the Welcome collection acquired between 1890 and 1936 by Sir Henry Wellcome and his agents across the globe, and reflect the cultural and historical contexts of health and medicine
Yale Art Museum
Yale has one of the largest and best collections of great art of any university, and allows access to many of its items to be viewed and downloaded in high resolution
Professor Steven Zucker's feed
Another great, frequently updated, source on flickr; Professor Zucker also has consolidated lists of images here: click