Any of the following are pretty good. Just depends on what you are looking for: http://getvanilla.com/ http://www.phpbb.com/ http://simplemachines.org/ http://punbb.informer.com/
Thank you mwasif. I am concerned about the server getting overloaded and is a shared server enough to run a forum ?
It depends on how large it is. For small - medium sized forums, it is more than enough. Forums like the size of DP, you would need a dedicated server.
I use smf for a forum that gets about 1400-2000 UVs a day...holds up awesome... Easy to customize the look of too.
If you are starting a new forum then shared hosting should be enough. You might need a dedicated server after a year...
I used phpBB2 on a shared server and it had around 50,000 posts. We had around 400-700 posts per day which isn't really that much but it still ran fine. Integrate into what? Which type of site, or more specifically, a CMS site, static website, custom dynamic website?
PunBB is easy to integrate into an existent layout. When including (requiring) /[pun_root]/includes/common.php you can access the whole punBB api, interact with forums, get user statistics.
I'm a big vbulletin fan myself, however if I were to use a opensource solution i would use simplemachines. It seems to have a very large following, so chances of wanting something for the forum might already be done.
SMF is probably your best bet. I have been a member at many forums that use it, and I find it extremely good.
I'm use cakePHP framework to create my website, and I'm looking for forum script that simple and easy to integrate to the framework.
MyBB seems to be the best bet as far as stability and usability goes, however PhpBB is the only one of an entire list that uses tableless CSS for design, allowing for your pages to get indexed properly. Ever wandered why so many links in sigs don't get spidered on DP? Because this board uses table based forum script. Despite high page rank, spiders are having troubles properly penetrating the content that's behind countless tables crossed over each other. Table less is the only way to go. PhpBB seems to be the only one that fulfills this requirement.