Here is a list of forum software that brings something new into the world, as of year 2013.
To list a new piece of forum software, please reply to this topic with a forum name and link — only. Then reply again to your own reply, and clarify what novelties the software brings along. (In this way, [other people's descriptions of why the forum software is innovative] can be upvoted above yours.)
I'll start with Discourse and Project Ivory :-)
Update 2013-03-11: Not terrible many people visit this page. I started another conversation at Reddit instead, here: http://www.reddit.com/r/subofrome/comments/19u88d/best_modern_forum_software_and_features_bulletin/