Free- My favourite is PHPBB, just because I love the default skin of it , and I think the admin panel is snazzy. A close contender is MYBB, their most recent version is wicked.
Paid- Ive tried both VB and IPB, and have to say I think VB is absolutely amazing. Although both pack loads of features, I think the community behind VB is much larger, meaning there are a lot of mods available for you to use
I really like phpbb i don't understand why so many people would rather pay for vbulletin than get phpbb for free. I assume one of the reasons is that many people think they're getting something better if it costs a lot of money. I see vbulletin as nothing more than a status symbol.