There's no easy way to integrate WordPress and phpBB without causing issues. You can't put phpBB forum inside WordPress because they share some function names and variables, unless you hack A LOT of files. The best we could achieve is to style both softwares the same, and use one's API functions to get user data from another's database and combine them, with proper cookie authorization (for WordPress). The challenge is phpBB requires more user information than WordPress, so it's best to let users register using phpBB, and then let them comment on the WordPress blog using those registered accounts (you will need to register those accounts on WordPress, too.)
Another thing's worth mentioning is the two softwares use different password hashing mechanism, which might also cause a lot of headache.
I did successfully integrate phpBB and WordPress, but the only reason I did that was because the forum is already active and there are already thousands of members. If you're planning to start a new forum that has support for WordPress, using BuddyPress or bbPress would be more ideal (they're developed by some WordPress guys). They're not that feature-rich, but is enough for a simple forum.
There are other new WordPress forum projects, such as Simple Press. Here's the link
in case you guys want to take a look