I've always used PHPBB for my forums, it's always been good and there are no featured that I can think of that are missing from the latest version - and if there is anything that could be improved then there's most likely a mod to do it
All three are good. I like phpBB myself as it's free and easy to use. vBulletin has a charge and a yearly charge for maintenance. Both are good in their own right.
What's nice is that there are so many conversion scripts on the web that if you decide to change from one software to another, you can easily pick up a free conversion script and get it done within 30 minutes.
I've used phpBB in the past as well as IPB, subsiquently they are all good in their own rights as handson has said... many opt for VBulitin for larger forum sites such as HD or WHT though for most sites phpBB seems a good alternative though I still dislike the new admin panel personally. and IPB tends to be the better for certain customisations