Limited screenshot sharing capabilities are now available in Japan for the 3DS. With it, you can share screenshots from certain games to Twitter and Tumblr.
Right now the only compatible games are Animal Crossing: New Leaf and Tomodachi Collection: New Life. The latter title is not currently planned for North America. Basically, according to Endgadget which has played with the software a bit, the interface lets you pick a screen from the game, and use the 3DS' built-in web browser to post your image online. It's picky about what screens you are able to use, however, preventing you from using screens taken with your camera, for example.
Nintendo has experimented with screenshot sharing in the Wii U's MiiVerse, and it's one of my favorite features. The Vita also allows you to take and share screens easily online, another feature I like a lot. I can't wait for North American 3DS systems to do the same, but I hope it is less restrictive than what is being outlined here.