How does the shape of an espresso cup affect the flavor?
As I see it, the typical espresso cup shape and material (Thanks JAIL!) does three things for espresso:


the thick ceramic insulates the coffee, helping it retain heat as
well as protecting your fingers from being burnt;
the shape is compact rather than wide or tall, minimizing the ratio of surface area to volume, to further retain heat;
the tapered cup and round bottom allow you to easily mix sugar and/or chocolate into your espresso, getting an even distribution in the liquid.


The round bottom of the typical espresso cup also makes it easy to clean.  I have some very decorative square-bottomed espresso cups, and the inner corners are pretty much permanently stained.