I was going to say invision community as that's what I have been using for seven years and used to be active mod that run it back in 2010 however I got to take notes that Discourse Software as come up in life lately and seeing more of that and it's getting active used among use
I have seen a number of communities using Discourse lately. I'm not a fan of the layout though, or really any "modern" forum software design. Xenforo is the most popular software for sure, numerous forums use Xenforo. As for free software, I've been seeing a few people going with phpBB as of late.
In my personal opinion I would give XenForo the best Premium Software. It's price point, community size, and customization options are its biggest winners.
As far as free software I'd give the win to SMF. 2.1 has being actively worked on,. the customization options are growing quickly, multi language support is top notch, and the community is awesome.