Varnished wood should be left in its finished state, as paint will adhere improperly and could take on a knobby, slumped texture. In addition, finished wood is intended for finished display and should not be altered.
Antique furniture is a common victim of repainting. Finished work does not require painting and will often look sub-par if painted due to chemical interactions between paint and varnish. In addition, with no point of adhesion, the paint will dry and crack much more quickly than it might otherwise have done.
Repainting should only be done if wood is sanded down and all finish removed. Vintage pieces should never be sanded in the first place. New furniture is perfectly suitable for repainting.