I'm a huge fan of XenForo. Pure vanilla XF works great, it has a lot of add-ons available as well as beautiful skins. It's also the forum suit that requires the least add-ons to be awesome, in my opinion. Second comes IPB, and for the free ones out there I prefer MyBB. phpBB is slowly replacing the latter though, as MyBB doesn't have that many good plugins or themes.
Certainly. My main issue was the apparent lack of a lightbox display for attached images. When I clicked on an attached image, it simply opened it on top of the forum, NOT a new window. So when I was done viewing, I naturally "closed" the window, which also closed the forum window. I found a plugin to correct this, but it was unfinished and even after I tinkered with it, I couldn't get it to work 100%.
Secondly, there seems to be more "official" add-ons and templates for XF, not just a bunch of users posting mods. But licensed programmers creating content (at least that's how it seemed).
Also, with my XF license I have full official tech support for a year and access to the very well written Picture/Video gallery.
Other things were just minor annoyances, but I've used XF for at least 4 years and was very happy with my first license so I opted for a second!
IPB is the best, of course! IPS has official apps (gallery, blogs, cms, etc, that are really useful and easy to add to your community), responsive theme, good ACP, social clubs, and a modern approach to forums. I've tried many different forums, but in my opinion IPB is the best, both as admin and as a user.