In my opinion the primary tables are:
(and the _acl_* tables ofc, but you dont wanna them now
The rest is up to you. For example, if you have custom bbcodes then it's good to backup de _bbcodes table, otherwise it's useless. If you have custom groups, then you probably want to backup the _groups table as well. And so forth.
Have a quick look at http://wiki.phpbb.com/display/DEV/Tables
In your case I think you should backup all tables but the _acl_* ones.