Currently if you use the "view unanswered posts", "view unread posts", "view new posts" or "view active topics" searches phpBB will include all forums in the result and there is no way to limit these results. This is a problem as search results might become cluttered with forums you don't wan't/need in your result set. Examples being a "trash" forum or when looking at phpbb.com the "[3.0.x] Abandoned MODs" forum. Also if you visit a board just because you are interested in some forums it would be nice when those quick searches only display the results you are actually looking for.
I'd suggest adding a select box to the ucp (can be added to the "Edit display options" section) where a user can blacklist forums, these blacklisted forums will be taken in account when one of these default searches is used. Also if a blacklist is used the search results page will contain a link which can be used to display all results without having the need to reset your settings if you quickly want to see the result set for the complete board.
Each user has three choices for every forum on the board. Do I want to show or hide the forum (which will make the forum visible / not visible on places like the index and jumpbox), do I want to search / non search the forum (note that it is possible to search a forum that is hidden by the prior setting), and do I want to subscribe to a forum. Obviously phpBB3 already has the forum subscription option. I can tell you that my users very much like the show / hide option. Why have a different tag for search /no search and show / hide? Because as an example, I don't want to search the "off topic" forum but I do occasionally want to read it. So the "new topics since last visit" search results should not include anything from OT, but I can still see the forum on the index and go read it if / when I want to.