No one mentions PHPBB? I must say it's between SMF and PHPBB for me
It's all about skinning it to be styled into your site. My best advice would be to find a skin that's close to what your site looks like and then just tweak the CSS. You can obviously insert your site header and footer and style it to fit better with your site, but it might become quite an excersize. Just make 100% sure you employ SPAM prevention tactics though as once your forum becomes popular it will most automatically become a target for spammers.
I have seen SPAMBOTs get right past image verification and even token based verification, a good one to use is the simple math question method (can't remember the plugin name), but it asks a stupid questions on registration eg What colour is the sky? or Is fire Hot? etc and users have to answer it to complete their registration. That seemed to work pretty well as bots don't have that logic.