Wordpress Forum Intergration, please advise :)

I personally have always been a fan of Invision Board, they're systems are built on a solid framework. I've noticed vBulletin's code-base has improved over the years, but it still seems a bit rugged. IP.Boards administrative panel is a lot more intuitive than vBulletins dated iFrame setup...

As far as add-ons, extensions, plugins, ect go - vBulletin seems to have the largest selection. However, IP.Board's selection has really grown since they've created their marketplace.

Then you have the new-age attempt at forum software where things are sorted by popularity, a good example would be Vanilla Forums. I personally, am not a fan of this as it's a bit confusing to the average newcomer; it's not as intuitive.

Lastly, you're open-source solutions are enormous. The popular choices seem to be phpBB and Simple Machines forums. I've honestly not worked with many of the open-source solutions from a developers or administrative standpoint. As an end-user though, I prefer phpBB. Oh, Vanilla Forums is also open-source.

As far as basic features go and a comparison of the many forum systems available, http://www.forummatrix.org/ is a pretty decent tool to checkout.

Hope this helps and good luck with your business!

Edit:
To keep things fair, I just noticed vBulletin 5 Connect is in Beta and decided to give it a try. They seem to have redesigned a lot, their new Site Editing features are interesting, and the newly designed Admin CP have been significant improvements. However, they are still working with that iFrame layout and there are simply too many categories to look through. The administrative panel reminds me too much of WHM (Web Host Manager) in that you cannot find things in the first place you look. The only thing saving me from losing my sanity in those control panels are the search functionalities.

After playing with a vBulletin 5 Connect demo and the latest IP.Board Demo, I'd still have to say Invision Board is my favorite. Not only as an administrator and developer, but also from an end-users standpoint.

Edit 2:
Sorry, I totally skimmed over your message and missed the fact that you're looking for something to integrate with WordPress. I've never been too keen to the WordPress forum solutions. However, there are plugins and hooks (mostly free) to bridge a connection for the Users between WordPress and most of the popular forum systems. If you're insistent on using a fully integrated forum, then your best bet would probably be bbPress.