David McCandless of "Information is Beautiful" recently posted an image of the 7-set Venn diagram construction.
What rules generate Venn diagrams for an arbitrary number of sets $k$?
Since this is an interesting topic, I thought that it might be useful to collect interesting references on this topic. I made the post CW, feel free to edit it.
First of all the references given in Wikipedia article might be useful.
Here is an alphabetical list of some more interesting papers related to this topic.
Using ellipses, you can construct a symmetrical Venn diagram for all orders $k$: http://www.ams.org/notices/200611/fea-wagon.pdf