One "screening" test I've read is to periodically fill one glass with cold water from your tap, and then a glass with hot water. If the hot water has a rusty tinge to it, you might have worn throught spots on the inner lining of the tank, and the water is in contact with the liquid plumr actual tank wall, and making rust. This will lead to tank failure.
My own hot water heater has been out of its 7 plumb supply year warranty for 6 years. I've kept it because it is on the first floor, with a drain, and not such a risk if it failed.
It is not unreasonable to worry about the age of the water heater, especially given the hassle and expense if it fails.
Tankless water heaters have been gaining market share in the US. These type of heaters have a larger burner, and a lot of tubing, but no tank. They are a staple of apartment life in Europe, and many people even turn the pilot light off overnight so there is no waste.
Several of my neighbors have installed this type of hot water heater, and they all report high satisfaction. No more running out of hot water. If properly sized (easy enough for a place with one shower, one dishwasher, and a few sinks) you won't get a cold shower when someone turns on the dishwasher. The units are very energy efficient, and take up much less space.
I've found a link to show you a picture, but pipe repair strongly advise asking around to find out what is being installed in your area. Be sure the plumber you select has done an install of one of these before, or you might wind up paying for him to learn.
It sounds as if you are thinking of resale value. If so, ask a few realtors to determine if buyers have particuarly strong positive or negative reactions to tankless water heaters.