What Products Will Clean Mold Off Of Wood Furniture And How Can I Prevent This In A Closed Up Home?

If the wood has varnish/shellac/polyurethane coating on it, you can try a mild solution of soap and water in a damp sponge first. If that doesn't work, try a cleaner like Pinesol or Lysol. Try a small spot first in an inconspicuous spot to make sure it doesn't damage wood. I doubt your house is so closed up that humidity would cause mold on furniture or wood in general. But if it is, and you know that is the cause, buy a dehumidifier to remove the moisture from the air.