The shape and material of your cups will affect the overall taste and experience you get from your coffee as this can concentrate the aromas.
A cup that can retain heat longer will ensure that all the complex compounds in your coffee remain “alive”.
When the rim of your cup covers your nose as you sip you can appreciate the aroma more intensely.
A bigger surfaced cup, although easier for latte art, will result in a quicker loss of viscosity and temperature.
For espresso the bottom of the cup is also important as a more rounded bottom surface will give a stronger and thicker crema. This due to the fact that the espresso rolls over itself in a wave like fashion as it falls into the cup, resulting in a better built crema.