If the rungs are not too bad, the gouges can be filled with appropriate wood fillers and colored to match. I have done this work numerous times.
If the rungs are in bad shape, they should be replaced, as the rest of the chair will be weakened. Replacement rungs are usually not available for purchase, but a good furniture repair shop can get replacements made. Installing replacements usually involves taking the chair apart, or at least spreading the chair legs far enough to get the new piece in, and regluing everything once the new parts are in place. I make my own rungs on a wood lathe, and color them to match the rest of the chair. - Randy Buchter, Furniture Medic
Furniture Medic by Randy Buchter, January 2012
