I'm glad that someone has done this, though I wish they had used names rather than flags; I would never be able to identify three of the entities on the outer part of the orange circle as Andorra, San Marino and Monaco. Fortunately some of the names and additional explanation is available at the Strange Maps blog at Big Think.*
This diagram is a particularly instructive map, too: it neatly visualises the gaps and overlaps between all kinds of supranational institutions in Europe – differences which for the most part are too subtle for any but the most attentive observer. All will be aware of the ‘Europe’ that is a less than homogenous conglomerate of nation states, with an unwieldy Brussels bureaucracy at its centre. This European Union, which consists of 27 member states, is merely the most visible of several European unions, all committed to different versions of the same goal: European integration.
The diagram also includes one statelet whose euros are much sought after by collectors.
Previously on Neatorama: The Great British Venn Diagram.
*Addendum: A hat tip to Feodor for noting that Strange Maps got the diagram from Wikipedia's "Supranational European Bodies," where the flags are clickable to the corresponding country entries. (It is also described there as a Euler diagram, not a Venn diagram).