I used to administer a couple of phpBB forums for my employer. One of them drew 40-50 spam messages a day, about 10x as many spam messages as customer messages! Eventually the company shut the spammy board down, because the spam was relentless.

The other issue with phpBB is its susceptibility to hacking. It's long been one of the most vulnerable scripts out there and the hackers can use its vulnerability to get root access on your server! Supposedly it has gotten better, but I've seen hackers get root through phpBB at two former employers, and it isn't pretty.

If you're serious about running a message board, spring for serious message board software, like vBulletin or Invision Power Board. You'll get much better tools to deal with the spam.