Another use of quizzes is in inter-school maths competitions. The Exeter Maths Association branch runs a quiz for secondary schools and the event is always enthusiastically supported. Why not find out if such an event exists in your area? If not, why not start one?
At upper school level the analysis of quiz shows yields fascinating mathematics. What is the best strategy for Who Wants to be a Millionnaire? or The Weakest Link? How could these games be modelled? Rob Eastaway and Jeremy Wyndham's excellent new popular maths book How Long is a Piece of String? devotes a whole chapter to such questions.