While I, personally, prefer the RDBMS approach myself, and continouusly find new amazing ways of doing things when SQL is your only tool, a forum could be implemented as a flat file system, with top posts being directories and replies being files in that directory (and the top post content being a special file in the post directory). That way, the structure is immediately visible and can easily be manipulated through the standard OS tools, but searching becomes unwieldly.

It also has the advantage of being a low-tech approach, where you don't need a database server. Concurrency becomes a problem, but as long as you prohibit editing of posts, you can avoid that problem.