If the wood has a good finish (don't try on bare wood), mix equal parts of baking soda and regular white, nongel toothpaste. Lightly dampen corner of a clean, soft white cloth with water and dip into the paste. With circular motion gently buff the marks for a few minutes. Wipe area clean, and buff to a shine. Follow with furniture polish. (If rings remain after buffing five minutes or so, they may have penetrated the wood; you might have to refinish the piece).