An other user (sorry, I forgot who) posted a link to this site a few days back. http://www.forummatrix.org It's a pretty cool site, letting you search for forums softwares, and compare them easly. A quick search returned these results:
Okay. You want a threaded Forum that is Free and Open Source and which stores data in MySQL.
The following 7 Forums match your criteria:
aterr, bttlxeForum, dnfBB, MyBB, NextBBS, Phorum and Yazd
I just used the "Choice wizard' to find that. Hopefully this will help your search.
art.googlies.net - personal website