Yeah, after that many years, it's time for a new one. The one thing that most people notice first (besides leakage) is a drop in the recovery capacity. That is the ability of the water heater to refresh the hot water back up to usable temperature. The reason it's hot at first is because the thermostat keeps the elements working until the water reaches the desired temp. However, once you begin drawing the water, it is unable to keep up with the use and you'll notice progressively less hot water.
Like Ramon said, one element is possibly bad which will make it take much longer to heat up. The other possibility is that calcium builds up on the elements and insulates it from the water making it less efficient. Still another possiblity is that the water heater has build up A LOT of crud on the bottom which takes up space making the effective size of the water heater much smaller. This can be cleared up somewhat by backflushing the water heater, which will flush the debris out of the water heater. It's simple: hook up a garden hose (good ones only) and drain all the crud out into the garden.
The last possibility is that the water heater was never hooked up correctly. There is an inlet and outlet for the water. Believe it or not, you CAN hook them up backwards and it will still work. Normally, the inlet drains into the bottom of the tank and the outlet draws from the top of the tank. As you know, the forces of convection causes cool water to settle on the bottom where it gets heated by the elements and the hottest water floats at the surface where it is drawn for use. That way, even as cool water enters to replenish the water consumed, only the hottest water exits. If it's hooked up incorrectly, you will draw hot water immediately but soon afterwards, you'll be drawing the cooler water from the bottom of the tank, even though the water heater still contains plenty of hot water.
Ok, capische?