6-way Venn banana
That is until I saw Figure 3 from Compact genome of the Antarctic midge is likely an adaptation to an extreme environment.
5-way Venn roadkill
What’s odd is that Figure 2 in the latter paper is a nice, clear R/ggplot2 creation, using facet_grid(), so someone knew what they were doing.
That aside, the Antarctic midge paper is an interesting read; go check it out.
This led to some amusing Twitter discussion which pointed me to *A New Rose : The First Simple Symmetric 11-Venn Diagram.
[*] +1 for referencing The Damned, if indeed that was the intention.
What You're Doing Is Rather Desperate 
I’ve never particularly liked Venn diagrams of n>3, but there is a far nicer n=5 depiction than that lumpy mess in the midge paper: http://commons.wikimedia.org/wiki/File:Symmetrical_5-set_Venn_diagram.svg
The n=11 “New rose” is impressive, and rather pretty, but I’m not sure if it’s that interpretable.
I think beyond n = 3, it’s time for another kind of visualization. Agree, that example looks much nicer at least.
Shameless plug: we got kind of upset about seeing these in scientific publications over and over again and we did something about it. See for example our Nature Methods Points of View column (http://www.nature.com/nmeth/journal/v11/n8/full/nmeth.3033.html) and try UpSet (http://vcg.github.io/upset). The UpSet paper (http://vcg.github.io/upset/about/) has a case study demonstrating how UpSet can be applied to compare variant calls from multiple callers/configurations. See Figure 13 and Supplementary Figures 5, 6 & 7.