(Warning: Check with the manufacturer about instructions for your product!)  Most table rings are caused by moisture getting caught inside the finish.    First of all, always use a coaster, but in case of table rings, there are a variety of methods that work:

• A paste of olive oil and salt can be applied and then wiped off after two hours.
• You can also cover the water mark- with mayonnaise and then sprinkle with salt. Rub the mixture until the stain disappears and then buff until dry.
• The spot can be rubbed with non-gel toothpaste and baking soda. Buff the spot with a clean, soft cloth.
• After using any of these techniques, check to see if the spot needs re-waxing.