However, if I have 4 sets, then it gets more complicated (and isn't yet handled by matplotlib-venn). A Venn diagram must show all possible intersections. Venn used overlapping ellipses to show how this could be achieved.
|Diagram by RupertMillard from Wikimedia Commons|
This is where Venn diagrams differ from Euler diagrams. Euler diagrams don't show empty intersections, so they can look much simpler than Venn diagrams, and can contain fully-nested circles. There are Venn diagrams that can represent all the overlaps of 5 and 6 sets, but we'd end up with some extremely complex diagrams that don't really aid the visualisation of our data.
Update (20th March 2014): Here are a couple of completely over the top diagrams: a pine tree and a banana. Venn or Euler?