Depending on the depth of the scratch or dent, you can sometimes raise the wood by swelling it with steam heat. Place a terrycloth towel over the area and apply heat with a regular steam iron. Take it slow and check often.
If you succeed in raising the area of the scratch, you will probably still have to sand or steel wool the surface, stain, and reapply a finishing coat of some type in the area of the scratches so that it all blends together.
This works pretty well on oak floors, so don't know why it wouldn't work on furniture as well. Good luck, and let me know how it turns out.