According to the U.S. Dept. Of Energy, a tankless water heater is more efficient and uses less energy than a conventional water heater, providing a $25 to $107 in annual savings. If your hot water use is low (less than 41 gallons per day), a tankless water heater will be 24% to 34% more efficient.
I have a solar water heater in my house, so not in my case. I do have a tankless water heater in my RV. Definitely worth it there.