Basics

Methods

Various sensors such as Ultrasonic Distance Sensors and VERY basic LIDAR/TOF sensors can detect hand/object prescence
Some models also utilize a bump sensor (perhaps a load cell?) to allow bump muting and unmuting of flow

Some RV and Boat Sinks use a foot pump
This keeps hands free
This could be adapted to a physical valve, or button in a logic circut (Only unmutes flow, faucet must be on, and used to select flow)
Thus it allows for the user to stop and start flow without using hands (due to dirt, soap, or holding of object such as cooking pot ect)
A Shower "Pause" button may be of use for stopping water when "standing out of the way" ocassionally
A Seperate temperature and flow control for sinks and showers may also reduce the waste from "testing" the water temperature (Making a notch/paint mark at the preffered spot of the knob is a very low tech way to do this as well)
A Press lever below the spout for water (more contact points so more possibility for disease spread in high traffic areas perhaps?)

MUCH more gimicky and complex
SOME uses make sense such as dispensing a certain amount of water for filling applications, thus removing waste from dumping water after overshooting a volume, this also has a convienence factor
This may be more useful for devices such as water dispensers (either standalone, or in a culinary refrigerator)
A lab water dispenser/faucet may also be such a use case