Actually I heard of a story once where some guy that knows a little martial arts (not a movie star) saw Van Damme in a bar, and Van Damme said something smart to him, so they started arguing, and Van Damme challenged him to a fight. The guy punched Van Damme in the face one time and dropped him, and then left.
I thought that was pretty hilarious.
I've also heard when Van Damme is going to fly with his family, he'll buy one first class ticket for himself, and then buy regular tickets for his family, and then when it comes time to board the plane he'll say, "My family's going to sit first class with me." and if they argue he says, "Don't you know who I am?"
"90% of the game is half mental" - John Madden