I did some research on this a couple of years back and came to the conclusion that phpBB and vBulletin were the best in terms of features and they had the largest installed base.

However, I never went forward with the project.

phpBB is an open source solution
http://www.phpbb.com/

vBulletin is paid and expensive and was bought by Internet brands which runs a lot of forums. It's supposed to be a very good piece of software.
http://www.vbulletin.com/
http://www.vbulletin.com/forum/showthread.php?p=1383883
http://en.wikipedia.org/wiki/VBulletin
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Best Forum Web Hosting (2008)

SOURCES:
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http://en.wikipedia.org/wiki/Beehive_Forum


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phpbb3 - Best Forum Software

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Just based on personal use, I did like the overall popularity and availability of resources for phpBB however I generally chose PHP Fusion instead. Even though it's more of a CMS, I preferred the forum settings/configuration to phpBB.

It seemed more customizable and had a decent enough following that there were a ton of "infusions" (plugins/addons) that fit my needs entirely. It still uses MySQL as the backend, and seemed to load a bit quicker for me than any of the phpBB sites I had used.

Also, the themes are pretty neat and they do fairly routine updates to the software that's easily upgraded through the admin console.

I suppose if I were to list 3 they would be:

1) PHP Fusion
2) phpBB
3) PunBB

PunBB is a very lightweight BB system that's not quite as complex as the other two, however it offers speed and security over anything else. I think it's likely aimed more at personal use, but it seems scalable to larger audiences so who knows. Worth a shot!
Source(s):
http://php-fusion.co.uk/
http://www.phpfusion-mods.com/
http://www.phpfusion-mods.net/
http://beta.phpfusion-mods.com/
http://www.phpbb.com/
http://punbb.informer.com/

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PHPBB
beacouse it has very good community and lot of themes and plugins

BBpress
good integration with wordpress and the great spam protection

SMF
this is also one of the very good free BB software
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phpBB was the choice of many "big" sites back in the days, it's well known, has nice themes and many plugins

SMF on the other hand is the choice of those who are afraid of phpBB's security, it doesn't get so much attention so the security risks are minimal, it's very simple and the themes for it are as ugly as hell

As for punBB - Unfortunately no one can be told what PunBB is - you have to see it for yourself.
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I had a very positive experience using phpBB for a forum. It had very good traffic. I don't operate it now since I sold it 1 year ago but it was running perfect for quite a long time. However the new owner switched to vBulletin.

I can't comment on other solutions from personal experience but I have heard that SMF and Vanilla are also good.
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honestly,
stick with the new mybb 1.4
Very Professional
All plugins available
Very Fast
Very Elegant
Has almost everything paid software has.
I use it and vB, if you dont want to pay then mybb is the best
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It sounds like you already know which software to pick. I think it now becomes a question of whether you want to manage it yourself vs. having it hosted.

If you manage it yourself, you have to apply upgrades, patches, add-on modules for anti-spam as an example. This means you either have to spend the time or hire someone to manage it for you. This also comes down to the level of customization you require. Do you want to modify the software in such a way that it wouldn't be possible at a hosted provider? Not only do you have to worry about the Bulletin Board software, but you also have to worry about patching the Operating System and most likely the Web Server (probably Apache) as well. You also have to worry about securing that system as well, ensuring it doesn't get hacked. You also have to make sure you protect yourself so you don't get attacked by SQL injections. Do you have that expertise or do you know someone who has that expertise? If you run into a problem, and you've decided to go with hosting the BB yourself, do you have access to the right expertise? Or is it something you have knowledge of and can fix it immediately?

I'd say it comes down to how you want to spend your time.

With a hosting provider, my guess is you won't have the level of control in terms of modifying code to customize things the way you want to do things.
Find out what kind of access is given to you if any and what the level of control is. With a hosting provider, you don't have to worry about patching the system, though I would inquire as to how the maintenance is performed on the BB and when and how long it takes. I'd inquire about an SLA as well and how they give you advance notice so you can warn your users. If you are going with a hosting provider, make sure they have well communicated plans, if there are issues and when maintenance happens. Find out how its communicated, what happens during emergency maintenance situations?

Does the BB have some sort of API you can hook into for customizations from the hosting provider?

Hopefully I've given you something to think about, while I've posed many questions rather than answers, I'm hoping it might help you figure out what it is you really want.

Flexibility, what kind of control of the software do you want?

Administration, Do you want control, what kind of control, how deep do you want access (i.e. do you want to have access to the actual code to modify it?)

Another thing to think about is cost
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As a web developer for about 5 years I have had my best and easiest experience with PHPBB, although it’s very simple to use and has many features one of its disadvantages is that it's impossible to purge users and so spammers usually have a fun time messing around.

After PHPBB I moved onto Invision Power Boards, once again really simple, actually extremely simple with lots of template possibilities.

Then throughout the course of a few years I moved over to SMF, really impressive except for the lack of customization. I found it to be extremely difficult to find good free templates, but the modules where usually very well made and were put to good use.

Now I’m using vBulletin, it's amazing in every way, great customization ability, but for a novice user it will seem very intimidating.

My top 3 free boards:
1. SMF
2. PHPBB
3. Invision Free (invisionfree.com)
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I'm surprised no one has mentioned Geeklog yet. I've been using Geeklog for the last couple years and its great. It's a bit more than a bulletin board, but you can use it that way if you'd like. However it has great support for graphic files and html tags (within your post), so you can make your posts look like blog articles.

Since Geeklog offers "fat" posts the threading of the discussion is maintained (and viewable) only within the main post. But there is a great search engine that comes with it, so you can find related posts with ease.

http://www.geeklog.net/
Source(s):
http://www.geeklog.net/

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