Considering vBulletin debuted in 2000, I believe that phpBB (2001) and IPB (2002) wouldn't have existed if vB never did. That said, I'd probably be using something like WWWBoard of UBB.threads.
Probably MyBB; it's free, which is a big plus, and some aspects of it I actually like better than vBulletin, such as the much sleeker look and feel of the AJAX features. Same for Invision Power Board, although I can't help not feeling overly inclined to trust a company that has in just a few years raised its license prices from free to $150 for six months' support and upgrades. :/