vBulletin: Seems to be the worst (keyword is seems), since I tried to get an account on both Caverns of Blood Forums and Dreamviews Forums, and both have the same problem. When I enter my account info, it says the usual stuff, (no need for account verification though, which is good because… since it’s offtopic, see below), but then when I try to customize my profile and save changes, it says Permission denied, even when I log back out and log in again! But in the case of Dreamviews, it actually said Time-out when I tried to customize my profile after I clicked on Edit Profile (since the account name was there even though it said Permission denied), and logging out and logging back in worked! And, in Dreamviews, when I try to change my profile picture to something that is lower than the maximum amount, it says “Unable to save picture”. Don’t use vBulletin if you know what’s good for you.
ProBoards: Seems to be the best one so far (keyword is seems 😉 ), since you can create your own avatar using Flash, or choose your own, and there aren’t any problems that I experienced with it! The only problem is that it requires account verification. Proboards is used by the RKC Petz Forums. Even the search works somewhat well. The only problem I had was user error 😉
Invisionfree: See ProBoards (‘cept the user error part 😉 ). Some of the forums that use this are Re-Volt Live and Our Re-Volt Pub.
Forumotion: Also good. See ProBoards (again, other than the user error part 😉 ). Its advantage is that you can view forum profiles while being a guest. I forgot whether ProBoards allows you to do that, but the other two certainly don’t 😉 Junior Adventures Network and the Slums of Elwood Forums use this.
Custom Forums: Of course, the real winner is Custom Forums (if possible). If you make your own forums, you have full control over how to make something work, and when people complain about bugs, they can complain to you and you can fix it, unlike the others which are third-party.
Simple Chat: There are many chat services, but one has closed down and it was the one that hosted the Furb-o-Vision chat, so… 😉 Not the best option unless you maintain your site regularly and do backups of the chat. I know about Cbox, but I’m sure there are others that you might want to check out. I think simple chat is the best one if it works well, since you don’t have to sign up and you can talk about anything you like. It also is easy to implement. The only problem is you can’t search for a topic you talked about previously without going through pages and pages of archives.
So, simple chat and custom forums seem to win! Second is Forumotion, third is Proboards, third is Invisionfree, and fourth is vBulletin.
Don’t know about WordPress, though. Maybe custom WordPress allows chat? 😮 (Or you can just comment 😉 )
Oh BTW, since some of these forums don’t allow you to search without logging in (or don’t allow you to type less than 3 letters in you search query, or their search is generally bad), type this into Google: search query you want to type site:site you want to search in (no space; you can type dedoimedo.com, http://www.dedoimedo.com, http://dedoimedo.com, or even x.com/rubberducky/pink/! 😉 ). Example: windows xp site:dedoimedo.com.
(Offtopic Edit on Aug 4, 2017: Here’s why no account verification is good: At the time of writing this post, my Yahoo e-mail account wasn’t accessible since when I clicked Sign in, it said Server Error, try again later. A few days later, it somehow worked again and I could sign in, but my point still stands; but I do understand why account verification is there; it’s to prevent spam along with CAPTCHA.)