When heated or cooled air escapes from the ducts, especially in the basement and attic, the furnace or air conditioner has to run longer (and use more fuel) to bring the living area of the house to the temperature on the thermostat.
Our heating expert confessed that he never thought duct leakage was a big issue until he saw a thermographic image showing just how much heat is lost at the duct joints. Today he's a believer in duct sealing.
Sealing duct joints is a DIY project. It's not only easy—it's cheap! Simply buy aluminum-colored silicone caulk and caulk every joint in rectangular ductwork (clean the joints first with a household spray cleaner and a rag to remove dust). Use the caulk to seal around the take-off boots to each branch run. Buy high-temperature UL181 aluminum foil tape in the duct section of a home center and use that to seal the joints of round ductwork.
Never use ordinary duct tape. Despite its name, it isn't approved for duct sealing and it doesn't hold up well over the long term.