Voted for The Ship of Theseus.
I have always loved philosophical problems, and Theseus' Ship (or George Washington's axe) has always been my favorite. I still occasionally tell the GW axe story at parties to get a discussion going. It's also easy to explain in multiple languages :)
In case your not familiar with GW's axe, the version I tell is told in this format: 'George Washington was proud to be a man of tradition, and he was known to exclaim that he still had and used his Grandfather's same axe with regularity. So regular, in fact was his use, that he had changed the handle 5 times, and the head 3.'