I used phpBB years ago, (version 1), but I'm a mod on some other forums that use version 2, don't like it still. I tried quite a few others a few years back. Used IPB for a while, then they went to a pay service (and dwindled from there sadly, I remember when the dev's stated it would never be a pay-for software, they lost quite a bit of community, many of which went to...), then went to
SMF. SMF is essentially the latest version of YaBBse. Features are wonderful (IPB level when I started using it, now above it), the modification systems is the most simple of any I've seen anywhere (phpBB's is about the worst I've seen). Has a converter to convert a phpBB(2) database to SMF (always make backups of course) so you would not lose anything. Been using it for years, know it inside and out if you need any help with trying it. I'd say install it on your server in a different directory, have it create a new DB from the DB of this phpBB board (the converter does not touch the phpBB db beyond reading it, but as always, make backups, can never have too many, I make a nightly snapshot of my site), and give it a whirl before you try to convert the main forums.
So, yes, I recommend
SMF. Well, I recommend about 10 others above phpBB, just SMF is at the top of my list.
(Also, if phpBB has a mod log like SMF, you've seen that I've already deleted some spam-posts...)