Antique furniture lover mkjarval writes in:
Any time you have doors or drawers that stick—whether from old age, paint or humidity etc—just rub an old (hopefully white or light coloured) candle over any of the spots that create friction. My mother got this tip from an old family friend who worked as a carpenter and it has helped make a few unusable pieces of furniture work like new again.
While we're talking about household fixes, see also how to silence squeaky floorboards with talcum powder. Thanks, mkjarval!