www.phpbb.com for phpbb
www.xmbforum.com for Xmb
www.woltlab.db for Burning Board
IkonBoard ( who have recently released a php version. search for it, dunno the address)
yapbb (once again search)
phorum --search
openbb -- openbb.com I think
Most have a mysql backend.
My favourate one would be Burning Board which you can get from www.woltlab.db, although phpbb2 has some nice new features.
There are loads more of them, but you'll have to do a search(I recommend google, or lycos). You can also ask at the community forums for each of these, although you might have to be sneaky(ie don't ask for other alternatives, ask why their board is better than various other boards, and ask for examples),