Faucets, showerheads and glass. White crust on fixtures, film on shower doors, clogged aerators. WHO notes that above about 200 mg/L, hard water can leave scale in pipes and tanks, especially when it's heated.
Water heaters. In an accelerated lab study funded by the Water Quality Research Foundation (WQRF), gas tankless heaters running on very hard water (26 grains per gallon) dropped from 80% to 72% efficiency before they were descaled. Electric tank heaters collected far more scale on hard water than on soft. It was a lab test, so it shows the direction, not a dollar figure for your home.
Dishwashers and washing machines. In the same study, machines run 240 cycles on unsoftened hard water had deposits throughout; the soft-water machines were nearly scale-free.
Soap and detergent. Hardness reacts with soap, so you get scum and need more of it. WHO notes higher soap use above about 200 mg/L, and separate WQRF lab studies of laundry and dishwashers found softened water cleaned as well or better with less detergent.
Skin and hair. Many people prefer how softened water feels. But a randomized trial of 336 children with eczema found that adding a water softener gave no additional benefit over usual care. We don't claim soft water treats any skin or hair condition.
WHO · Acceptability aspects (hardness) · Battelle / WQRF study summary · WQRF · detergent studies (findings) · Softened Water Eczema Trial