Is it about time to replace the water heater?
Newer water heaters do not last as nearly as long as they used to. Nowadays, you are lucky to get 10 years out of one. This is due to the way they are manufactured.

There are still some water heaters around that are from the 1960s that work perfectly fine. The tanks on some of those heaters are made out of copper, and won't corrode like modern steel tanks.

Your tank most likely has replaceable sacrificial anodes in the tank. These anodes will corrode instead of the walls of the tank. The life of your heater will be much longer if the anodes are maintained. These are fairly universal, so you should be able to find ones that are compatible. The anodes should be inspected or replaced at least every 5 years.

The newer heaters do offer an energy savings, and some of them have a programmable timer on them which can turn down the temperature at night, and when you are away. They are also better insulated, so there is less heat loss. You can purchase a water heater blanket which will add an additional layer of insulation to the tank.

As long as there aren't any signs of failure on the tank such as rust spots, etc, then you should be good to go. Just as a warning, tanks can fail suddenly, and without warning. A leaking water heater could potentially flood your entire basement. There are water leak detection alarms on the market that are inexpensive which set off an alarm similar to a smoke detector if a leak is detected. It would be a good idea to install one just in case. Even newer water heaters can fail, so it is actually a good practice to have one of these alarms for any water tank installation.