At Mill Springs in 2007 they did an Officer's Day on the Sunday of the event. Events included a three legged race, a tug of war, and "name that bugle call" (since we were doing all calls by the bugle that weekend). The company I fell in with also did a mail issue where the ladies of the group hand wrote letters to those participating and sent a few goods in a box from home. The cookies got eaten by ants but everything else was first rate.
Other things I have seen or participated in were courts martial and medical scenarios with (appropriate) researched cases and scripts, drill competition, speed firing, etc.