No one has yet mentioned exhibition material, science fairs and the Womens' Institute. (I have also been involved with Masterclasses (see the reply by J. Collins) but that sort of thing has already been discussed.) Some of you may know Bangor's Maths and Knots website. That started off as a physical exhibition that toured the UK with the Pop Math Road Show. I seems to have been a great success (1990). We tried to show that Mathematics was a natural extension of logical curiosity by going into the problem of classifying knots and the use of Analogy in mathematics (Look at Ronnie Brown's website for links to a paper we wrote on how the exhibition was made.)
I adapted that material for a talk to the UK Womens' Institute at their residential college. The theme was Mathematics a human activity. (Again I can give more details if someone wants to follow it up.)
Thirdly I prepared material for use at the Wrexham Scientriffic Science event. Here I used some puzzles but not just the usual ones. I adapted material on optimisation from a course on OR and it was a great success. There were some people (adults) who spent over an hour discussing problems on scheduling, knapsack problems etc. I did not provide the algorithms (which would spoil the fun). The problems typically had a 'target' value, so if trying to maximise something anything over the target would be good. I tried to get them to explain why they thought their method was possibly going to give a good answer and was very pleased at some of the systematic and logical approaches that were used. The puzzles were printed out from a powerpoint presentation and then put on laminated cards. (EDIT: Combinatorial puzzles seem to be easy to attempt and go down well.)
I used the puzzle presentation as well in various MathclubMasterclass/Mathclub situations in Wales, Canada and ireland and always got a good response.