This plugin is another simple one. It allows you to set an inactivity limit on threads shown on the forum main page. The default is set to 7 days, and if you like that setting, then all you have to do is put the file in your my-plugins directory. If you want to change it, it's easy enough (desciption in the readme).
You can download the file and read the instructions at http://faq.rayd.org/bbpress_limit_recent_activity/
You can see it being used at http://www.rayd.org/forums/ (notice how there are no threads in the "Latest Discussion" section whose last post is older than a week).
Enjoy!