We put 16" wheels on our bikes primarily for the obvious reason - they allow for a compact folded bike.
However, smaller wheels bring other advantages: they offer superior acceleration and lose less speed to wind resistance. Bromptons high-pressure tyres, offer similar rolling resistance to that of large wheels; the unpaced (i.e. unassisted) cycling world speed record was set using a small-wheeled Moulton AM7 (51.29 mph over 200m in 1986).
Smaller wheels are also lighter and stronger than larger, longer-spoked wheels, but many people worry about their capacity to handle potholes and other unforgiving terrains. Despite appearances, our wheels fare well on pitted streets, their greater maneuverability makes it easier to avoid the obstacles.
Our bikes really can do amazing things!