I see the two main audiences for this feature having rather different needs for it:
Teachers: the ability to export the whole forum/all discussions as a record of the activity in the forum. E.g. As a record of student postings where ratings are part of the students' course marks. Also possibly, although of lesser usefulness, as a resource for future courses, e.g. topics or questions which spawned lively discussion.
Students: ability to export only discussions in which the student participated, for inclusion in eportfolios or as part of the student's course notes for future reference.
Formats: either PDF or DOCX or HTML would work for most of our users.
I have a small concern re: privacy. If Jane Student and Joe Student both participate in a forum discussion, when Jane exports the discussion, are Joe's postings included? If they are, should Jane have the ability to copy Joe's postings, which were made privately, within a course accessible to only Participants?