Here is a list of popular forum software. If you know of another script please reply to this and I will add it

phpBB - FREE
With a large and highly customisable set of key features coupled with a standards compliant interface, phpBB™ will grow with, and compliment your website. With millions of installations worldwide, it is no wonder phpBB™ is one of the most popular ways to create and support a community.

vBulletin - Paid $160 for Owned, $85 for Leased
vBulletin is a professional, affordable community forum solution. Thousands of clients, including many industry leading blue chip companies, have chosen vBulletin - It's the ideal choice for any size of community.

MyBB - FREE
MyBB is a powerful, efficient, multilingual, standards-compliant and free forum package. MyBB places full control over your discussion board at the tip of your fingers.

Invision Power Board - Paid + FREE DEMO $149.99 Standard, $299.99 Business
As the very core of our Community Suite package, we've made sure that IP.Board is an outstanding bulletin board system. The result of of over seven years experience in developing bulletin board software, IP.Board brings powerful and practical features while remaining intuitive and flexible - and it's now blazing fast too.

Simple Machines Forum (SMF) - FREE
A free, professional grade software package that allows you to set up your own online community within minutes. Its powerful custom made template engine puts you in full control of the lay-out of your message board and with our unique SSI - or Server Side Includes - function you can let your forum and your website interact with each other.

YaBB (Yet Another Bulletin Board) - FREE
YaBB is a leading FREE, Open Source community forum system (bulletin board, message board) written in Perl.

What about SMF? http://www.simplemachines.org/

Good point!! added that one now, thanks

A lot of people seem to be using YABBA. I personally haven't got any experience with it, but it seems rather large.

Good point! I just added that one now too Thanks!

IceBB is a very nice one. I was tossing up between it and MyBB as my choice.

http://icebb.net/

hey also blockstar.com is alos fine

I believe blockstar is more for building websites though...

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Of all the software that has been posted above, I have only try and use SMF, it is quite simple and easy to use. It also has lots of add-on for your forum using SMF.

I think vBulletin is without question a clear winner in terms of security, looks, features, and stability, and would therefore be the most effective forum software on the market in my opinion. It's definitely something you might want to check out, and there seems to be a lot of cheap licenses being sold on Digital Point. Just make sure the licenses are valid before purchasing them.