It's called biopredation in the furniture restoration business -- attacks on your furniture by animals and micro-organisms. Termites, ants and some types of beetles can bore holes in wood and cause serious damage. Mice like to make their nests in old upholstery or may turn up in other furniture depending on what's stored there (avoid storing food in heirloom furniture, or at least make sure it's tightly sealed). Tell-tale signs of these kinds of infestations include holes, wood dust and droppings. You can try various products to get rid of the creepy-crawlies, but be careful -- sprays might damage the finish on your furniture. Depending on the extent of the damage and the infestation, you might need to get professional help.
Micro-organisms that attack furniture include mold and mildew. These usually result from keeping the furniture in damp, dark and warm environments. If the problem isn't too severe, you can probably get rid of mold or mildew spots on wooden furniture. Work outside when it's sunny, warm and dry, and use gloves and a mask. Start by cleaning it with a mild detergent solution and allowing the furniture to dry. Then follow up with a bleach solution (1/4 cup of bleach to 1 gallon of water). Note that the bleach solution may change the finish slightly, so test it out in a small area first if you're worried. After the furniture dries again, clean it a third time using a detergent containing borax, which will help keep growth from happening again.
If upholstered furniture gets moldy or mildewed, you can dry it out and attempt to clean it using a mild
detergent and the borax solution (bleach will ruin your upholstery). It's much more difficult to keep mold and mildew from returning in upholstery, however. You'll need to be on watch for signs of regrowth and may have to throw the furniture away. In the case of both wooden and upholstered furniture, consult with an expert if the damage is severe.
Heirloom furniture needs a little extra TLC so it will be in good condition for you to pass down, but caring for it is easy when you know what to do.