robzilla - 11:01 pm on May 27, 2011 (gmt 0)
bbPress is not just a WordPress plugin, but standalone forum software developed by the creators of Wordpress. I like their philosophy, but I'm not sure they're living up to it with (what I've seen of) bbPress.
As for lightweight forum packages, I'd vote for phpBB. I'm not sure how lean the actual code is, but the software allows me to output lightweight pages without sacrificing functionality, using a simple but powerful templating system.
FluxBB is another promising package, but as of yet it does not have a proper templating system.