Yes, programmable thermostats can reduce the energy used for air conditioning or heating by 5 to 30% IF they are properly programmed. Just installing the thermostat isn't enough; you need to enter a schedule designed to be sure the heating and cooling systems do not run when not needed, and are set back when the comfort needs are more flexible.
Programmable thermostats, while not always digital, save money by turning the air conditioner to a higher setting (or heater to a lower setting) when no one is present in the house, or in the evenings when it is cooler. You can achieve the same savings without the programmable thermostat, but you would have to remember to change your thermostat every day when you leave the house, and turn it down every night when you go to bed. In addition, if you are using the thermostat to regulate your heater, you would wake to a cold house.