I agree phpbb3 is free and open source plus has a lot of modifications. I think it ties for first palce with smf right now as the folks over that side have improved their code tremendously!
Vbulletin is definitely the thing to have, for those with money. Its great, the code is awesome plus the community is just amazing.
MyBB loses out to the others because it has a serious lack of modifications although it is growing bigger daily. With time, its going to become a heavyweight as well!
Free- MyBB (that's what my forum is using right now and I love it!)
Paid- I haven't used paid forums but I was an administrator on a Vbulletin forum before. I love the layout.