Two options are available, depending on how you wish to use the data.
Backup all, or individual, forums within a course through the Backup in the Administration block within a Moodle course. The generated backup file can then be saved onto your computer and/or restored to another Moodle course.
Display discussions within a forum in nested form. Copy and paste these into software such as Microsoft Word. This would need to be done on a per-discussion basis.