phpBB is still very relevant, even after all these years
Teg I have always been a fan of ProBoards hosted forums.
ZandraJoi I've only had Proboards but I think they are quite user-friendly.
The problem is, however good a free platform is, people won't take it seriously. Some people think that it is not a reliable option for any professional projects.
But having visited a few Proboards forums recently, I think it is a very interesting platform.
XF and InvisionPower were the top players in the last 2 years. I will give credit to the fact that their competition crumbled than anything else for paid platforms doing very good.
Now that Flarum is stable and MyBB working full time on v1.9, there is a really hope for forum software industry.