I'd say my vBulletin forum plays a big role on two my sites, particularly my Devil May Cry Forum and Fable 2 Forum. Most of the members of those sites immediately head to the forum and skip the homepage altogether simply because they much prefer the community that the forum provides. vBulletin rules!
I would like to think it's the content that make people come back to my site, vbulletin was a personal choice because it's easy to work with and the best of it's kind on the net, but I think my members would still come back no matter what I was using as long as they had something they find interesting to read when they get there.
About 50/50 for me. We also run a gaming league. However, the members wouldn't care that much if it was phpBB or IPB instead of vB. The admins would, though.
vBulletin does not play a big role on my website. Any forum scripts would have done the job. I just chose vBulletin because I heard it is more secure and can handle big loads.
For me, not as much because I run a content website with it. So not 100%. But a significant amount as the gallery and other features are built around the forum. Just not the main site, which I feel is most important.