If you want to be sure that the print (photo or painting) is around for more than a few years, it has to be printed So I print the images that are important --my daughter's wedding, some of the photos with my kids in them when we're on vacation, special places we've been, etc. I find that I'm printing more, not less.
Other things I post on my website, other websites, or give out on CDs or DVDs.
I sure that the prints will be viewable 20 or 50 years from now. Some of the other stuff may be viewable (websites go down, for example) but I suspect that most of it won't be. I'm sure all of us (at least those involved in digital things for more than a few years) have documents stored on zip disks, floppy disks, and other media that we can no longer view.
So at least for me, anything that is really important gets printed. Same holds for documents (letters, tax records, or whatever), if you want to be sure it's viewable in the future, you need to print it.