You do not have to use bbPress. But be aware that phpBB is a separate product. You cannot run it inside WordPress. You can only cross-link a WordPress installation and a separate phpBB installation in various ways. WordPress and phpBB can share a database (because they use different table prefixes). You can adjust the phpBB style and the WordPress theme so they look somewhat similar.
The last time I did this, I wrote a plugin to put a login form (a sidebar widget) on the WordPress home page, where a user can log in to phpBB. When they log in, they go immediately to the phpBB index page. On the phpBB index page I put a link back to WordPress. When a user is logged in to phpBB, the WordPress main menu contains a Forum item to link back to phpBB. I don’t plan to publish this plugin, because it is a specific solution for a specific purpose, but I could provide more details for anyone who wants to write a similar plugin.
