Read the title.
In my experience, free hosting is almost always a disappointment. Web hosting is ridiculously cheap most of the time. You can get plans for $5 a month and under, perfect for hosting a phpbb forum. Some even have cpanel configured to be able to automatically install phpbb for you, and to be able to be automatically updated when patches are released.
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So killerjackalope is saying 110mb.com. I might check that out. UziMonkey, maybe I'll look for those too.
I use 110mb.com, I'm reasonably sure they support all php, definitely most of it and give you FTP access.
They're free and support most coding stuff as far as I know, though some things need activated, not at any cost though.