Most parts of an old wood stove, including the door gaskets, door glass, fire bricks and the steel or cast iron panels, can be replaced as long as the parts are available. In some cases, some parts may have to be specially made.
Replacing the door gasket is one of the easiest fixes. The gasket creates a seal between the door edges and the stove. A worn gasket creates leaks that allow cooler air to get in from the outside. New gaskets are made of woven fiberglass rope, while the older ones use asbestos. The easiest way to get the proper fit is to take the door to a wood stove supply store and match it to the different gasket sizes.
Old stoves used tempered glass, but replacement glass is usually made of a clear ceramic material. The glass is held in by a flat, woven gasket that has adhesive on one side. Glass does tend to stain with heavy usage and can be cleaned using non-abrasive cleaners.
The fire brick that lines the firebox sometimes cracks. These specially sized bricks might be available at building supply stores, but if the stove is EPA certified, they must come from a wood stove supplier. Warping of the steel or cast iron can happen over time, but it doesn't usually affect the performance of the stove.
Warped parts usually have to be recast or even completely rebuilt in some cases. While replacing most parts may be considered a do-it-yourself project, a complete rebuild is something best left to professionals. An improper rebuild can lead to leaks and an inefficient stove.