An overwhelming majority of photographs are now viewed on small screens. I don't know if anyone has the numbers, but I'm guessing that less than 1% end up as a print. Being a person that loves the Fine Print, this saddens me. Smartphones and computers are great, but the experience of viewing a photo on a small screen is nothing at all like looking at a large, detailed print, up close and in person.
Some photos are best viewed as large prints. Others work best in smaller sizes. Highly detailed images tend to work best as large prints, whereas high contrast images with stark compositions work best on small screens and in smaller print sizes. This may at least partially explain the popularity of simple, graphically punchy images on photo sharing sites such as Instagram, Tumblr, and 500px.
Michael Kenna is a highly regarded landscape photographer known for his high contrast, compositionally strong images. For over 25 years he has printed most of his images at 8" square. The images on his website are presented small as well. His work emphasizes abstract shapes, with little regard for surface detail or textures - perfect for displaying in smaller formats.
My image Ferrari Ranch Wetlands, Study 2 (below) works best as a large print. Viewed at what is now the typical screen size (under 12") it doesn't have a lot to offer. The composition is static and the detail gets lost on a small screen. But, printed in gelatin silver at 20” square, the rich detail and subtle tones make for a totally different (and satisfying) viewing experience, particularly up close at “pixel peeping” distances. It clearly demonstrates the idea that images do best when displayed in their ideal medium and proper scale.